Fit Confirmatory Factor Analysis Models
Description
Fit a Confirmatory Factor Analysis (CFA) model.
Usage
cfa(model = NULL, data = NULL, ordered = NULL, aux = NULL, sampling_weights = NULL, sample_cov = NULL, sample_mean = NULL, sample_th = NULL, sample_nobs = NULL, group = NULL, cluster = NULL, constraints = "", wls_v = NULL, nacov = NULL, ov_order = "model", ...)cfa(model = NULL, data = NULL, ordered = NULL, aux = NULL, sampling_weights = NULL, sample_cov = NULL, sample_mean = NULL, sample_th = NULL, sample_nobs = NULL, group = NULL, cluster = NULL, constraints = "", wls_v = NULL, nacov = NULL, ov_order = "model", ...)
Arguments
model |
A description of the user-specified model. Typically, the model
is described using the lavaan model syntax. See
|
data |
An optional data frame containing the observed variables used in the model. If some variables are declared as ordered factors, lavaan will treat them as ordinal variables. |
ordered |
Character vector. Only used if the data is in a data.frame. Treat these variables as ordered (ordinal) variables, if they are endogenous in the model. Importantly, all other variables will be treated as numeric (unless they are declared as ordered in the data.frame.) Since 0.6-4, ordered can also be logical. If TRUE, all observed endogenous variables are treated as ordered (ordinal). If FALSE, all observed endogenous variables are considered to be numeric (again, unless they are declared as ordered in the data.frame.) |
aux |
Character vector. Names of auxiliary observed variables, used to
make the missing-at-random (MAR) assumption more plausible under missing
data (continuous data only). With |
sampling_weights |
A variable name in the data frame containing
sampling weight information. Currently only available for non-clustered
data. Depending on the |
sample_cov |
Numeric matrix. A sample variance-covariance matrix. The rownames and/or colnames must contain the observed variable names. For a multiple group analysis, a list with a variance-covariance matrix for each group. |
sample_mean |
A sample mean vector. For a multiple group analysis, a list with a mean vector for each group. |
sample_th |
Vector of sample-based thresholds. For a multiple group analysis, a list with a vector of thresholds for each group. |
sample_nobs |
Number of observations if the full data frame is missing and only sample moments are given. For a multiple group analysis, a list or a vector with the number of observations for each group. |
group |
Character. A variable name in the data frame defining the groups in a multiple group analysis. |
cluster |
Character. A (single) variable name in the data frame defining the clusters in a two-level dataset. |
constraints |
Additional (in)equality constraints not yet included in the
model syntax. See |
wls_v |
A user provided weight matrix to be used by estimator |
nacov |
A user provided matrix containing the elements of (N times)
the asymptotic variance-covariance matrix of the sample statistics.
For a multiple group analysis, a list with an asymptotic
variance-covariance matrix for each group. See the |
ov_order |
Character. If |
... |
Many more options can be specified, using 'name = value'.
See |
Details
The cfa function is a wrapper for the more general
lavaan function, using the following default arguments:
int.ov.free = TRUE, int.lv.free = FALSE,
auto.fix.first = TRUE (unless std.lv = TRUE),
auto.fix.single = TRUE, auto.var = TRUE,
auto.cov.lv.x = TRUE, auto.efa = TRUE,
auto.th = TRUE, auto.delta = TRUE,
and auto.cov.y = TRUE.
Value
An object of class lavaan, for which several methods
are available, including a summary method.
References
Yves Rosseel (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. doi:10.18637/jss.v048.i02
See Also
Examples
## The famous Holzinger and Swineford (1939) example HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) summary(fit, fit.measures = TRUE)## The famous Holzinger and Swineford (1939) example HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) summary(fit, fit.measures = TRUE)
Demo dataset for illustrating a linear growth model
Description
A toy dataset containing measures on 4 time points (t1,t2, t3 and t4), two predictors (x1 and x2) influencing the random intercept and slope, and a time-varying covariate (c1, c2, c3 and c4).
Usage
data(Demo.growth)data(Demo.growth)
Format
A data frame of 400 observations of 10 variables.
t1-
Measured value at time point 1
t2-
Measured value at time point 2
t3-
Measured value at time point 3
t4-
Measured value at time point 4
x1-
Predictor 1 influencing intercept and slope
x2-
Predictor 2 influencing intercept and slope
c1-
Time-varying covariate time point 1
c2-
Time-varying covariate time point 2
c3-
Time-varying covariate time point 3
c4-
Time-varying covariate time point 4
See Also
Examples
head(Demo.growth)head(Demo.growth)
Demo dataset for illustrating a multilevel CFA
Description
A toy dataset containing measures on 6 items (y1-y6), 3 within-level covariates (x1-x3) and 2 between-level covariates (w1-w2). The data is clustered (200 clusters of size 5, 10, 15 and 20), and the cluster variable is “cluster”.
Usage
data(Demo.twolevel)data(Demo.twolevel)
Format
A data frame of 2500 observations of 12 variables.
y1-
item 1
y2-
item 2
y3-
item 3
y4-
item 4
y5-
item 5
y6-
item 6
x1-
within-level covariate 1
x2-
within-level covariate 2
x3-
within-level covariate 3
w1-
between-level covariate 1
w2-
between-level covariate 2
cluster-
cluster variable
Examples
head(Demo.twolevel) model <- ' level: 1 fw =~ y1 + y2 + y3 fw ~ x1 + x2 + x3 level: 2 fb =~ y1 + y2 + y3 fb ~ w1 + w2 ' fit <- sem(model, data = Demo.twolevel, cluster = "cluster") summary(fit)head(Demo.twolevel) model <- ' level: 1 fw =~ y1 + y2 + y3 fw ~ x1 + x2 + x3 level: 2 fb =~ y1 + y2 + y3 fb ~ w1 + w2 ' fit <- sem(model, data = Demo.twolevel, cluster = "cluster") summary(fit)
Exploratory Factor Analysis
Description
Fit one or more Exploratory Factor Analysis (EFA) model(s).
Usage
efa(data = NULL, nfactors = 1L, sample_cov = NULL, sample_nobs = NULL, rotation = "geomin", rotation_args = list(), ov_names = NULL, bounds = "pos.var", ..., output = "efa")efa(data = NULL, nfactors = 1L, sample_cov = NULL, sample_nobs = NULL, rotation = "geomin", rotation_args = list(), ov_names = NULL, bounds = "pos.var", ..., output = "efa")
Arguments
data |
A data frame containing the observed variables we need for the
EFA. If only a subset of the observed variables is needed, use the
|
nfactors |
Integer, integer vector, or a list. The desired number of
factors to extract. Can be a single number, or a vector of numbers
(e.g., |
sample_cov |
Numeric matrix. A sample variance-covariance matrix. The rownames and/or colnames must contain the observed variable names. Unlike sem and CFA, the matrix may be a correlation matrix. |
sample_nobs |
Number of observations if the full data frame is missing and only the sample variance-covariance matrix is given. |
rotation |
Character or a list with first element a character variable.
The character variable is the rotation method to be used. Possible options
are varimax, quartimax, orthomax, oblimin, quartimin, geomin, promax,
entropy, mccammon, infomax, tandem1, tandem2, oblimax, bentler, simplimax,
target.strict, target (alias for pst), pst (=partially specified target),
cf, crawford-ferguson,
cf-quartimax, cf-varimax, cf-equamax,
cf-parsimax, cf-facparsim, biquartimin, bigeomin. The latter two are
for bifactor rotation only. The rotation algorithms (except promax
and target) are similar to those from the GPArotation package, but have
been reimplemented for better control. The promax method is taken from the
stats package. The target.strict method is equal to the target method in
the GPArotation package. The target method is in fact the pst method where
all non-zero elements (in the target matrix) are ignored.
Options for the rotation algorithm can be provided in the list after the method.
The default options (and their alternatives) are |
rotation_args |
List. Options related to the rotation algorithm. DEPRECATED.
The options should now be given in the |
ov_names |
Character vector. The variables names that are needed for the EFA. Should be a subset of the variables names in the data.frame. By default (if NULL), all the variables in the data are used. |
bounds |
Per default, |
... |
Additional options to be passed to lavaan, using 'name = value'.
See |
output |
Character. If |
Details
The efa function is essentially a wrapper around the
lavaan function. It generates the model syntax (for a given number
of factors) and then calls lavaan() treating the factors (in each
block) as a set that should be rotated. Each block is rotated
independently. Categorical data is handled as usual by first computing
an appropriate (e.g., tetrachoric or polychoric) correlation matrix,
which is then used as input for the EFA.
Multiple groups (via the group= argument) and twolevel data
(via the cluster= argument) are supported, and these may be
combined. By default, the same number of factors is extracted in every
block, but a different number of factors per block can be requested by
supplying nfactors as a list (see the nfactors argument).
The promax rotation method (taken from the stats package) is only
provided for convenience. Because promax is a two-step algorithm (first
varimax, then oblique rotation to get simple structure), it does not
use the gpa or pairwise rotation algorithms, and as a result, no
standard errors are provided.
Value
If output = "lavaan", an object of class
lavaan. If output = "efa",
a list of class efaList for which a print(),
summary() and fitMeasures() method are available. Because
we added the (standardized) loadings as an extra element, the loadings
function (which is not a generic function) from the stats package will
also work on efaList objects.
See Also
lav_efalist_summary for a summary method if the output is
of class efaList.
Examples
## The famous Holzinger and Swineford (1939) example fit <- efa(data = HolzingerSwineford1939, ov.names = paste("x", 1:9, sep = ""), nfactors = 1:3, rotation = list("geomin", geomin_epsilon = 0.01, rstarts = 1)) summary(fit, nd = 3L, cutoff = 0.2, dot.cutoff = 0.05) fitMeasures(fit, fit.measures = "all") # target rotation target <- matrix(0, 9, 3) target[1:3, 1] <- 1 target[4:6, 2] <- 1 target[7:9, 3] <- 1 fit2 <- efa(data = HolzingerSwineford1939, ov.names = paste("x", 1:9, sep = ""), nfactors = 3, rotation = list("target", target = target)) summary(fit2) ## Not run: # twolevel EFA with a different number of factors per level: # one factor at the within level, two factors at the between level fit3 <- efa(data = Demo.twolevel, ov.names = paste0("y", 1:6), cluster = "cluster", nfactors = list(c(1, 2))) summary(fit3) ## End(Not run)## The famous Holzinger and Swineford (1939) example fit <- efa(data = HolzingerSwineford1939, ov.names = paste("x", 1:9, sep = ""), nfactors = 1:3, rotation = list("geomin", geomin_epsilon = 0.01, rstarts = 1)) summary(fit, nd = 3L, cutoff = 0.2, dot.cutoff = 0.05) fitMeasures(fit, fit.measures = "all") # target rotation target <- matrix(0, 9, 3) target[1:3, 1] <- 1 target[4:6, 2] <- 1 target[7:9, 3] <- 1 fit2 <- efa(data = HolzingerSwineford1939, ov.names = paste("x", 1:9, sep = ""), nfactors = 3, rotation = list("target", target = target)) summary(fit2) ## Not run: # twolevel EFA with a different number of factors per level: # one factor at the within level, two factors at the between level fit3 <- efa(data = Demo.twolevel, ov.names = paste0("y", 1:6), cluster = "cluster", nfactors = list(c(1, 2))) summary(fit3) ## End(Not run)
Instrumental Variable (MIIV-2SLS) Estimation
Description
Estimate a structural equation model using model-implied instrumental
variables and two-stage least squares (MIIV-2SLS), a non-iterative,
equation-by-equation alternative to maximum likelihood (Bollen, 1996).
This page documents how to invoke the estimator, the options that can be
passed via the estimator = list() argument, how to specify
instruments manually with the |~ operator, and the lavInspect()
fields that are relevant for IV estimation.
Details
Instead of minimizing a single discrepancy function for the whole model, MIIV-2SLS estimates each measurement and structural equation separately by two-stage least squares (2SLS). For each equation, the instruments are other observed variables in the model that are (under the hypothesized model) uncorrelated with the equation's composite error term: the model-implied instrumental variables (MIIVs). Because the equations are estimated separately, a misspecification in one equation does not necessarily propagate to the others, the method is non-iterative, and no starting values are required.
The estimator is selected by setting estimator = "IV" (the alias
"MIIV" is also accepted; names are case-insensitive), for example
fit <- sem(model, data = Data, estimator = "IV")
Estimation proceeds in two stages. In the first stage, the directed effects (factor loadings and regression coefficients) are estimated equation-by-equation by 2SLS. In the second stage, the undirected effects (residual variances and covariances) are estimated by a weighted least-squares step applied to the residual moments. Standard errors are available for both stages (see the options below).
Both continuous and ordered-categorical data are supported (for ordered data,
the polychoric-based PIV estimator of Bollen & Maydeu-Olivares, 2007 is used).
Simple equality constraints (e.g. equal factor loadings) and general linear
equality constraints (e.g. a == 2*b) are honored. Multiple groups are
supported, with standard errors (for continuous, two-stage-missing and
categorical data), including the mean structure and cross-group equality
constraints for measurement invariance testing (configural, metric and scalar,
e.g. via group.equal = c("loadings", "intercepts")). For scalar
invariance the latent-mean (and intercept) estimates are obtained by a joint
GLS solve over the mean structure (see iv_mean_structure), which matches
the maximum likelihood mean estimates given the model-implied covariance
matrix. The IV estimator is restricted to single-level models.
Estimator options
Options specific to the IV estimator are passed as named elements of a list
to the estimator argument, alongside the estimator name:
fit <- sem(model, data = Data,
estimator = list(estimator = "IV",
iv_varcov_method = "2RLS",
iv_sargan_adjust = "BH"))
The option names use snake_case. For backward compatibility, dot.case names
(e.g. iv.varcov.method) are also accepted and silently converted.
-
iv_method: -
Character. The instrumental-variable method. Currently only
"2SLS"(two-stage least squares) is available. Default is"2SLS". -
iv_samplestats: -
Logical. If
TRUE(the default), the equations are estimated from the sample moments (covariances and means) rather than from the raw data. This is required for categorical data and when only sample moments are provided as input. -
iv_varcov_method: -
Character. The second-stage method used to estimate the residual variances and covariances. One of
"ULS","GLS","2RLS","RLS"or"NONE". Default is"RLS"(reweighted least squares). For categorical data,"ULS"is used. If"NONE", the variance/covariance parameters are not estimated. -
iv_sargan: -
Logical. If
TRUE(the default), overidentification tests are computed for each overidentified equation. Two tests are reported side by side: the classical Sargan test (Sargan, 1958), which assumes normality (continuous data) and is not valid for polychoric correlations; and a robust, residual-based test that is valid more generally. The robust test is Browne's (1984) residual statistic applied to the single equation, computed with the asymptotic covariance matrix (ACOV) of the sample statistics: the distribution-free (ADF) ACOV of the sample covariances for continuous data (so it is robust to non-normality, and is then equivalent to Hansen's overidentification test), or the polychoric ACOV for categorical data. Both tests share the same degrees of freedom (number of instruments minus number of regressors). For continuous data with missing values the robust test is not available. The results can be retrieved withlavInspect(fit, "sargan")(or, equivalently,lavInspect(fit, "hansen")). -
iv_sargan_adjust: -
Character. A multiple-comparison adjustment applied to the per-equation overidentification p-values, using any method accepted by
p.adjust("holm","hochberg","hommel","bonferroni","BH","BY","fdr", or"none"). Default is"none". When a method other than"none"is requested, extrasargan.pval.adjandbrowne.pval.adjcolumns are added to the table returned bylavInspect(fit, "sargan"). -
iv_weak: -
Character. How to respond to weak instruments, diagnosed per equation by the first-stage F-statistic (Staiger & Stock, 1997). One of:
-
"warn": -
(the default) report the affected equations and their first-stage F, and suggest supplying stronger instruments manually; the estimates are not changed.
-
"prune": -
greedily drop the weakest excess instruments from weak, overidentified equations (never below just-identified) and report what was dropped.
-
"none": -
skip the weak-instrument check.
-
-
iv_weak_threshold: -
Numeric. The first-stage F-statistic below which instruments are deemed weak. Default is
10. -
iv_vcov_stage1: -
Character. The standard-error method for the first-stage (directed) coefficients. One of
"lm.vcov","lm.vcov.dfres","gamma"or"none". Default is"lm.vcov.dfres"for continuous data and"gamma"for categorical data. The"gamma"method requiresiv_samplestats = TRUE. When the model contains simple equality constraints among the directed coefficients (e.g. equal factor loadings), the"lm.vcov"/"lm.vcov.dfres"methods use a variance-weighted restricted-2SLS covariance for the constrained coefficients (as in the MIIVsem package); setiv_vcov_stage1 = "gamma"to obtain the delta-method (moment-Jacobian) standard errors instead. -
iv_vcov_stage2: -
Character. The standard-error method for the second-stage (undirected) parameters. One of
"h2","delta"or"none". Default is"h2". The"h2"method requiresiv_samplestats = TRUE. -
iv_vcov_gamma_modelbased: -
Logical. If
TRUE(the default), the normal-theory weight matrix (gamma) used for the standard errors is based on the model-implied covariance matrix; ifFALSE, it is based on the unrestricted (H1) sample covariance matrix. -
iv_mean_structure: -
Character. How the free mean-structure parameters (observed intercepts and latent means) are estimated. With
"wls"(the default) they are obtained by a joint GLS solve that fits the model-implied means to the sample means across all groups, pooling parameters that are constrained equal across groups (e.g. intercepts for scalar invariance); this matches the maximum likelihood mean estimates (given the model-implied covariance matrix). With"moments"the intercepts are recomputed per equation and shared intercepts are pooled by a (simpler) nobs-weighted average. The two agree unless intercepts are constrained across groups (scalar invariance). -
iv_vcov_jack_numerical,iv_vcov_jaca_numerical,iv_vcov_jacb_numerical: -
Logical. If
TRUE, the corresponding Jacobians used in the standard-error computation are obtained numerically rather than from analytic expressions. The default isFALSE; these are mainly intended for checking the analytic derivatives. -
iv_mimic_ml: -
Logical. If
FALSE(the default), the IV estimator uses unbiased divisors: the sample covariance matrix is divided by(sample.cov.rescale = FALSE) and the per-equation residual variances (the RSS terms entering the standard errors and the Sargan test) use thedivisor. IfTRUE, the maximum likelihood divisoris used throughout: the sample covariance is rescaled to the ML divisorand the residual variances use thedivisor as well. As a result, for just-identified models the IV point estimates and standard errors match the ML solution exactly.
Specifying instruments manually (the |~ operator)
By default lavaan determines the model-implied instruments for each equation
automatically. The |~ operator overrides this choice for a specific
equation: the left-hand side is the dependent variable of the equation (for a
latent variable, its scaling indicator), and the right-hand side lists the
instruments to use.
model <- '
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + y2 + y3 + y4
dem60 ~ ind60
# use only x2 and x3 as instruments for the
# dem60 ~ ind60 equation
y1 |~ x2 + x3
'
fit <- sem(model, data = PoliticalDemocracy, estimator = "IV")
This is useful when the automatically selected instruments are weak (see
iv_weak above) or when subject-matter knowledge suggests a different
set of instruments.
External instruments. The instruments listed on the right-hand side of
|~ need not be part of the model. If an instrument is an observed
variable that does not otherwise appear in the model (it is not an indicator,
a predictor, an outcome, or otherwise mentioned), it is treated as an
external instrument: it is read from the data so that its covariances
with the model variables are available to the 2SLS estimator, but it never
enters the model-implied summary statistics. The model degrees of freedom, the
fit measures, and the model-implied moments are therefore exactly the same as
if the instrument had not been mentioned; only the equations for which it is
used are affected. External instruments require raw data (a data=
argument); they are not available when only sample moments are supplied. For
categorical data the external instruments must themselves be ordered
(categorical); the augmented polychoric correlations and the asymptotic
covariance of the sample statistics are then used for the estimates and the
standard errors. Single-group and multiple-group categorical models are
supported, but (for now) not equality constraints among the directed
coefficients (e.g. measurement invariance) together with external instruments.
## z is not part of the model; it is used only as an
## instrument for the (endogenous) regression y ~ x
model <- '
y ~ x
y |~ z
'
fit <- sem(model, data = Data, estimator = "IV")
For external instruments the point estimates and the directed-coefficient (loading and regression) standard errors are the usual 2SLS quantities. The second-stage (residual variance and covariance) standard errors also account for the sampling variability of the instrument moments: the directed coefficients depend on the instrument-model covariances, and this uncertainty is propagated into the variance/covariance parameters through the full (augmented) moment Jacobian.
Missing data
For continuous data with missing values, the IV estimator defaults to a
two-stage (FIML) approach: the saturated mean vector and covariance matrix are
estimated by the EM algorithm, the model is then estimated from these moments,
and the standard errors are corrected for the additional uncertainty stemming
from the EM estimates (Savalei & Bentler, 2009). This default is used when the
data contain missing values and the user does not set the missing
argument. Set missing = "robust.two.stage" for sandwich-corrected
standard errors (Savalei & Falk, 2014), or missing = "listwise" to
delete incomplete cases instead. Two-stage missing-data estimation is also
available for multiple-group models.
Multiple groups and measurement invariance
Multiple-group models are supported, with point estimates and standard errors
for continuous, two-stage-missing and categorical data. Cross-group equality
constraints are imposed in the usual way, either through shared parameter
labels in the model syntax or through the group.equal argument, so the
standard measurement-invariance sequence is available: configural
(group.equal = NULL), metric (group.equal = "loadings") and
scalar (group.equal = c("loadings", "intercepts")).
A parameter that is constrained equal across groups is estimated by pooling the
information from all groups; for a configural model the per-group estimates (and
their standard errors) reproduce the separate single-group fits. The mean
structure (observed intercepts and latent means) is estimated by a joint GLS
solve over all groups (see iv_mean_structure), which reproduces the
maximum likelihood mean estimates given the model-implied covariance matrix.
Inspecting the instruments and the Sargan test
Several lavInspect fields are specific to IV estimation:
-
lavInspect(fit, "iv"): -
(aliases
"miiv","instruments") a per-equation table with the dependent variable (lhs), the regressors (rhs), the observed variables actually used (lhs_new,rhs_new), the equation type (type:"miiv","ols"or"user"), and the instruments (iv) for that equation. -
lavInspect(fit, "sargan"): -
a per-equation table with the overidentification tests: the degrees of freedom (
df), the classical Sargan statistic (sargan.stat) and its p-value (sargan.pval), and the robust Browne residual-based statistic (browne.stat) and its p-value (browne.pval); seeiv_sarganabove. For categorical data the classical Sargan p-value isNA(not valid), so use thebrowne.*columns. Adjusted p-values (sargan.pval.adjandbrowne.pval.adj) are added wheniv_sargan_adjustis set.lavInspect(fit, "hansen")is an alias. -
lavInspect(fit, "eqs"): -
the underlying per-equation information.
References
Bollen, K. A. (1996). An alternative two stage least squares (2SLS) estimator for latent variable equations. Psychometrika, 61(1), 109-121.
Bollen, K. A., & Maydeu-Olivares, A. (2007). A polychoric instrumental variable (PIV) estimator for structural equation models with categorical variables. Psychometrika, 72(3), 309-326.
Browne, M. W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37(1), 62-83.
Sargan, J. D. (1958). The estimation of economic relationships using instrumental variables. Econometrica, 26(3), 393-415.
Savalei, V., & Bentler, P. M. (2009). A two-stage approach to missing data: Theory and application to auxiliary variables. Structural Equation Modeling, 16(3), 477-497.
Savalei, V., & Falk, C. F. (2014). Robust two-stage approach outperforms robust full information maximum likelihood with incomplete nonnormal data. Structural Equation Modeling, 21(2), 280-302.
Staiger, D., & Stock, J. H. (1997). Instrumental variables regression with weak instruments. Econometrica, 65(3), 557-586.
See Also
lavaan, sem, lavOptions,
lavInspect.
Examples
## The classic Bollen (1989) Political Democracy example model <- ' # measurement model ind60 =~ x1 + x2 + x3 dem60 =~ y1 + y2 + y3 + y4 dem65 =~ y5 + y6 + y7 + y8 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 ' ## fit using MIIV-2SLS instead of maximum likelihood fit <- sem(model, data = PoliticalDemocracy, estimator = "IV") summary(fit) ## the model-implied instruments used for each equation lavInspect(fit, "iv") ## the per-equation Sargan overidentification tests lavInspect(fit, "sargan") ## pass estimator options via estimator = list(...) fit2 <- sem(model, data = PoliticalDemocracy, estimator = list(estimator = "IV", iv_varcov_method = "2RLS", iv_sargan_adjust = "BH", iv_weak = "warn")) lavInspect(fit2, "sargan") ## specify instruments manually with the |~ operator: ## use only x2, x3 as instruments for the dem60 ~ ind60 equation model.iv <- ' ind60 =~ x1 + x2 + x3 dem60 =~ y1 + y2 + y3 + y4 dem60 ~ ind60 y1 |~ x2 + x3 ' fit3 <- sem(model.iv, data = PoliticalDemocracy, estimator = "IV") lavInspect(fit3, "iv") ## equality constraints are honored (here: equal loadings across factors) model.eq <- ' ind60 =~ x1 + x2 + x3 dem60 =~ y1 + a*y2 + b*y3 + c*y4 dem65 =~ y5 + a*y6 + b*y7 + c*y8 dem60 ~ ind60 dem65 ~ ind60 + dem60 ' fit4 <- sem(model.eq, data = PoliticalDemocracy, estimator = "IV") coef(fit4) ## multiple groups: metric measurement invariance (equal loadings) HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit.metric <- sem(HS.model, data = HolzingerSwineford1939, estimator = "IV", group = "school", group.equal = "loadings") summary(fit.metric)## The classic Bollen (1989) Political Democracy example model <- ' # measurement model ind60 =~ x1 + x2 + x3 dem60 =~ y1 + y2 + y3 + y4 dem65 =~ y5 + y6 + y7 + y8 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 ' ## fit using MIIV-2SLS instead of maximum likelihood fit <- sem(model, data = PoliticalDemocracy, estimator = "IV") summary(fit) ## the model-implied instruments used for each equation lavInspect(fit, "iv") ## the per-equation Sargan overidentification tests lavInspect(fit, "sargan") ## pass estimator options via estimator = list(...) fit2 <- sem(model, data = PoliticalDemocracy, estimator = list(estimator = "IV", iv_varcov_method = "2RLS", iv_sargan_adjust = "BH", iv_weak = "warn")) lavInspect(fit2, "sargan") ## specify instruments manually with the |~ operator: ## use only x2, x3 as instruments for the dem60 ~ ind60 equation model.iv <- ' ind60 =~ x1 + x2 + x3 dem60 =~ y1 + y2 + y3 + y4 dem60 ~ ind60 y1 |~ x2 + x3 ' fit3 <- sem(model.iv, data = PoliticalDemocracy, estimator = "IV") lavInspect(fit3, "iv") ## equality constraints are honored (here: equal loadings across factors) model.eq <- ' ind60 =~ x1 + x2 + x3 dem60 =~ y1 + a*y2 + b*y3 + c*y4 dem65 =~ y5 + a*y6 + b*y7 + c*y8 dem60 ~ ind60 dem65 ~ ind60 + dem60 ' fit4 <- sem(model.eq, data = PoliticalDemocracy, estimator = "IV") coef(fit4) ## multiple groups: metric measurement invariance (equal loadings) HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit.metric <- sem(HS.model, data = HolzingerSwineford1939, estimator = "IV", group = "school", group.equal = "loadings") summary(fit.metric)
Fit Measures for a Latent Variable Model
Description
This function computes a variety of fit measures to assess the global fit of a latent variable model.
Usage
fitMeasures(object, fit_measures = "all", baseline_model = NULL, h1_model = NULL, fm_args = list(standard.test = "default", scaled.test = "default", rmsea.ci.level = 0.90, rmsea.close.h0 = 0.05, rmsea.notclose.h0 = 0.08, robust = TRUE, cat.check.pd = TRUE), output = "vector", ...) fitmeasures(object, fit_measures = "all", baseline_model = NULL, h1_model = NULL, fm_args = list(standard.test = "default", scaled.test = "default", rmsea.ci.level = 0.90, rmsea.close.h0 = 0.05, rmsea.notclose.h0 = 0.08, robust = TRUE, cat.check.pd = TRUE), output = "vector", ...)fitMeasures(object, fit_measures = "all", baseline_model = NULL, h1_model = NULL, fm_args = list(standard.test = "default", scaled.test = "default", rmsea.ci.level = 0.90, rmsea.close.h0 = 0.05, rmsea.notclose.h0 = 0.08, robust = TRUE, cat.check.pd = TRUE), output = "vector", ...) fitmeasures(object, fit_measures = "all", baseline_model = NULL, h1_model = NULL, fm_args = list(standard.test = "default", scaled.test = "default", rmsea.ci.level = 0.90, rmsea.close.h0 = 0.05, rmsea.notclose.h0 = 0.08, robust = TRUE, cat.check.pd = TRUE), output = "vector", ...)
Arguments
object |
An object of class |
fit_measures |
If |
baseline_model |
If not NULL, an object of class
|
h1_model |
If not NULL, an object of class |
fm_args |
List. Additional options for certain fit measures. DEPRECATED.
The options should now be specified in the |
output |
Character. If |
... |
Further arguments passed to or from other methods. Not currently
used for |
Details
When a scaled (or robust) test statistic is requested (for example, by using
test = "satorra.bentler"), the function will also return fit indices
based on the scaled chi-square statistic, rather than the standard version.
These scaled versions of fit measures, such as CFI and RMSEA, are calculated in
the same way as their standard counterparts, with the key difference being that
the scaled chi-square statistic is used in place of the regular one. In the
output of fitMeasures(), these appear with the .scaled suffix,
or in the Scaled column of the summary() output.
However, this substitution-based approach—used in SEM software for many
years—has since been shown to be incorrect. Improved versions of robust fit
indices have been proposed, offering better theoretical properties. Although
still under development and not yet implemented for all estimation settings,
these improved robust fit measures are provided when available. They appear
with a .robust suffix in the output of fitMeasures(), or in the
Scaled column of the summary() output on a row labeled
Robust. As a general recommendation, these newer robust versions should
be used whenever available, in preference to the older scaled ones. See the
references below for more details.
It is also worth noting that, for models involving ordered categorical data,
robust fit indices are only computed if the underlying matrix of tetrachoric or
polychoric correlations is positive definite. If this condition is not
met—which is not uncommon in small samples—the robust measures are reported
as NA.
Finally, in some situations (especially when the data contains missing values),
computing these robust fit indices may be computationally intensive. To avoid
long runtimes, the calculation of robust fit measures can be disabled by
setting the robust argument to FALSE in the fit_measures list.
FMG p-values can be selected through the existing standard.test
mechanism, for example
fitMeasures(fit, "pvalue", fm_args = list(standard.test = "peba4")).
No separate FMG-specific fit-measure names are needed.
Value
A named numeric vector of fit measures.
References
Brosseau-Liard, P. E., Savalei, V., & Li, L. (2012). An investigation of the sample performance of two nonnormality corrections for RMSEA. Multivariate behavioral research, 47(6), 904-930. doi:10.1080/00273171.2012.715252
Brosseau-Liard, P. E., & Savalei, V. (2014). Adjusting incremental fit indices for nonnormality. Multivariate behavioral research, 49(5), 460-470. doi:10.1080/00273171.2014.933697
Savalei, V. (2018). On the computation of the RMSEA and CFI from the mean-and-variance corrected test statistic with nonnormal data in SEM. Multivariate behavioral research, 53(3), 419-429. doi:10.1080/00273171.2018.1455142
Savalei, V. (2021). Improving fit indices in structural equation modeling with categorical data. Multivariate Behavioral Research, 56(3), 390-407. doi:10.1080/00273171.2020.1717922
Savalei, V., Brace, J. C., & Fouladi, R. T. (2023). We need to change how we compute RMSEA for nested model comparisons in structural equation modeling. Psychological Methods. doi:10.1037/met0000537
Zhang, X., & Savalei, V. (2023). New computations for RMSEA and CFI following FIML and TS estimation with missing data. Psychological Methods, 28(2), 263-283. doi:10.1037/met0000445
Foldnes, N., Moss, J., & Gronneberg, S. (2024). Improved goodness of fit procedures for structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 1-13. doi:10.1080/10705511.2024.2372028
Foldnes, N., Gronneberg, S., & Moss, J. (2026). Penalized eigenvalue block averaging: Extension to nested model comparison and Monte Carlo evaluations. Behavior Research Methods, 58(4). doi:10.3758/s13428-026-02968-4
Examples
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) fitMeasures(fit) fitMeasures(fit, "cfi") fitMeasures(fit, c("chisq", "df", "pvalue", "cfi", "rmsea")) fitMeasures(fit, c("chisq", "df", "pvalue", "cfi", "rmsea"), output = "matrix") fitMeasures(fit, c("chisq", "df", "pvalue", "cfi", "rmsea"), output = "text") fitMeasures(fit, "pvalue", fm_args = list(standard.test = "peba4")) ## specify another threshold for RMSEA confidence interval fitMeasures(fit, list( fit.measures = c("cfi", "rmsea"), rmsea.ci.level = 0.95)) ## fit a more restricted model fit0 <- cfa(HS.model, data = HolzingerSwineford1939, orthogonal = TRUE) ## Calculate RMSEA_D (Savalei et al., 2023) ## See https://psycnet.apa.org/doi/10.1037/met0000537 fitMeasures(fit0, "rmsea", h1_model = fit)HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) fitMeasures(fit) fitMeasures(fit, "cfi") fitMeasures(fit, c("chisq", "df", "pvalue", "cfi", "rmsea")) fitMeasures(fit, c("chisq", "df", "pvalue", "cfi", "rmsea"), output = "matrix") fitMeasures(fit, c("chisq", "df", "pvalue", "cfi", "rmsea"), output = "text") fitMeasures(fit, "pvalue", fm_args = list(standard.test = "peba4")) ## specify another threshold for RMSEA confidence interval fitMeasures(fit, list( fit.measures = c("cfi", "rmsea"), rmsea.ci.level = 0.95)) ## fit a more restricted model fit0 <- cfa(HS.model, data = HolzingerSwineford1939, orthogonal = TRUE) ## Calculate RMSEA_D (Savalei et al., 2023) ## See https://psycnet.apa.org/doi/10.1037/met0000537 fitMeasures(fit0, "rmsea", h1_model = fit)
Fit Growth Curve Models
Description
Fit a Growth Curve model. Only useful if all the latent variables in the model
are growth factors. For more complex models, it may be better to use the
lavaan function.
Usage
growth(model = NULL, data = NULL, ordered = NULL, aux = NULL, sampling_weights = NULL, sample_cov = NULL, sample_mean = NULL, sample_th = NULL, sample_nobs = NULL, group = NULL, cluster = NULL, constraints = "", wls_v = NULL, nacov = NULL, ov_order = "model", ...)growth(model = NULL, data = NULL, ordered = NULL, aux = NULL, sampling_weights = NULL, sample_cov = NULL, sample_mean = NULL, sample_th = NULL, sample_nobs = NULL, group = NULL, cluster = NULL, constraints = "", wls_v = NULL, nacov = NULL, ov_order = "model", ...)
Arguments
model |
A description of the user-specified model. Typically, the model
is described using the lavaan model syntax. See
|
data |
An optional data frame containing the observed variables used in the model. If some variables are declared as ordered factors, lavaan will treat them as ordinal variables. |
ordered |
Character vector. Only used if the data is in a data.frame. Treat these variables as ordered (ordinal) variables, if they are endogenous in the model. Importantly, all other variables will be treated as numeric (unless they are declared as ordered in the data.frame.) Since 0.6-4, ordered can also be logical. If TRUE, all observed endogenous variables are treated as ordered (ordinal). If FALSE, all observed endogenous variables are considered to be numeric (again, unless they are declared as ordered in the data.frame.) |
aux |
Character vector. Names of auxiliary observed variables, used to
make the missing-at-random (MAR) assumption more plausible under missing
data (continuous data only). With |
sampling_weights |
A variable name in the data frame containing
sampling weight information. Currently only available for non-clustered
data. Depending on the |
sample_cov |
Numeric matrix. A sample variance-covariance matrix. The rownames and/or colnames must contain the observed variable names. For a multiple group analysis, a list with a variance-covariance matrix for each group. |
sample_mean |
A sample mean vector. For a multiple group analysis, a list with a mean vector for each group. |
sample_th |
Vector of sample-based thresholds. For a multiple group analysis, a list with a vector of thresholds for each group. |
sample_nobs |
Number of observations if the full data frame is missing and only sample moments are given. For a multiple group analysis, a list or a vector with the number of observations for each group. |
group |
Character. A variable name in the data frame defining the groups in a multiple group analysis. |
cluster |
Character. A (single) variable name in the data frame defining the clusters in a two-level dataset. |
constraints |
Additional (in)equality constraints not yet included in the
model syntax. See |
wls_v |
A user provided weight matrix to be used by estimator |
nacov |
A user provided matrix containing the elements of (N times)
the asymptotic variance-covariance matrix of the sample statistics.
For a multiple group analysis, a list with an asymptotic
variance-covariance matrix for each group. See the |
ov_order |
Character. If |
... |
Many more options can be specified, using 'name = value'.
See |
Details
The growth function is a wrapper for the more general
lavaan function, using the following default arguments:
meanstructure = TRUE,
int.ov.free = FALSE, int.lv.free = TRUE,
auto.fix.first = TRUE (unless std.lv = TRUE),
auto.fix.single = TRUE, auto.var = TRUE,
auto.cov.lv.x = TRUE, auto.efa = TRUE,
auto.th = TRUE, auto.delta = TRUE,
and auto.cov.y = TRUE.
Value
An object of class lavaan, for which several methods
are available, including a summary method.
References
Yves Rosseel (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. doi:10.18637/jss.v048.i02
See Also
Examples
## linear growth model with a time-varying covariate model.syntax <- ' # intercept and slope with fixed coefficients i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4 s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4 # regressions i ~ x1 + x2 s ~ x1 + x2 # time-varying covariates t1 ~ c1 t2 ~ c2 t3 ~ c3 t4 ~ c4 ' fit <- growth(model.syntax, data = Demo.growth) summary(fit)## linear growth model with a time-varying covariate model.syntax <- ' # intercept and slope with fixed coefficients i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4 s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4 # regressions i ~ x1 + x2 s ~ x1 + x2 # time-varying covariates t1 ~ c1 t2 ~ c2 t3 ~ c3 t4 ~ c4 ' fit <- growth(model.syntax, data = Demo.growth) summary(fit)
Holzinger and Swineford Dataset (9 Variables)
Description
The classic Holzinger and Swineford (1939) dataset consists of mental
ability test scores of seventh- and eighth-grade children from two
different schools (Pasteur and Grant-White). In the original dataset
(available in the MBESS package), there are scores for 26 tests.
However, a smaller subset with 9 variables is more widely used in the
literature (for example in Joreskog's 1969 paper, which also uses the 145
subjects from the Grant-White school only).
Usage
data(HolzingerSwineford1939)data(HolzingerSwineford1939)
Format
A data frame with 301 observations of 15 variables.
id-
Identifier
sex-
Gender
ageyr-
Age, year part
agemo-
Age, month part
school-
School (Pasteur or Grant-White)
grade-
Grade
x1-
Visual perception
x2-
Cubes
x3-
Lozenges
x4-
Paragraph comprehension
x5-
Sentence completion
x6-
Word meaning
x7-
Speeded addition
x8-
Speeded counting of dots
x9-
Speeded discrimination straight and curved capitals
Source
This dataset was originally retrieved from http://web.missouri.edu/~kolenikovs/stata/hs-cfa.dta (link no longer active) and converted to an R dataset.
References
Holzinger, K., and Swineford, F. (1939). A study in factor analysis: The stability of a bifactor solution. Supplementary Educational Monograph, no. 48. Chicago: University of Chicago Press.
Joreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 183-202.
See Also
Examples
head(HolzingerSwineford1939)head(HolzingerSwineford1939)
Utility Functions: Constraints
Description
Utility functions for equality and inequality constraints.
Usage
lav_con_parse(partable = NULL, constraints = NULL, theta = NULL, debug = FALSE) lav_pt_con_ceq(partable, con = NULL, debug = FALSE, txt_only = FALSE) lav_pt_con_ciq(partable, con = NULL, debug = FALSE, txt_only = FALSE) lav_pt_con_def(partable, con = NULL, debug = FALSE, txt_only = FALSE, warn = TRUE)lav_con_parse(partable = NULL, constraints = NULL, theta = NULL, debug = FALSE) lav_pt_con_ceq(partable, con = NULL, debug = FALSE, txt_only = FALSE) lav_pt_con_ciq(partable, con = NULL, debug = FALSE, txt_only = FALSE) lav_pt_con_def(partable, con = NULL, debug = FALSE, txt_only = FALSE, warn = TRUE)
Arguments
partable |
A lavaan parameter table. |
constraints |
A character string containing the constraints. |
theta |
A numeric vector. Optional vector with values for the model parameters in the parameter table. |
debug |
Logical. If TRUE, show debugging information. |
con |
An optional partable where the operator is one of ‘==’, ‘>’, ‘<’ or ‘:=’ |
txt_only |
Logical. If TRUE, only the body of the function is returned as a character string. If FALSE, a function is returned. |
warn |
Logical. If FALSE, warnings are suppressed. |
Details
This is a collection of lower-level constraint-related functions that are used in the lavaan code. They are made public at the request of package developers. Below is a brief description of what they do:
The lav_con_parse function parses the constraints
specification (provided as a string, see example), and generates
a list with useful information about the constraints.
The lav_pt_con_ceq function creates a function
which takes the (unconstrained) parameter vector as input, and
returns the slack values for each equality constraint. If the equality
constraints hold perfectly, this function returns zeroes.
The lav_pt_con_ciq function creates a function
which takes the (unconstrained) parameter vector as input, and
returns the slack values for each inequality constraint.
The lav_pt_con_def function creates a function
which takes the (unconstrained) parameter vector as input, and
returns the computed values of the defined parameters.
Examples
myModel <- 'x1 ~ a*x2 + b*x3 + c*x4' myParTable <- lavParTable(myModel, as_data_frame = FALSE) con <- ' a == 2*b b - c == 5 ' conInfo <- lav_con_parse(myParTable, constraints = con) myModel2 <- 'x1 ~ a*x2 + b*x3 + c*x4 a == 2*b b - c == 5 ' ceq <- lav_pt_con_ceq(partable = lavParTable(myModel2)) ceq( c(2,3,4) )myModel <- 'x1 ~ a*x2 + b*x3 + c*x4' myParTable <- lavParTable(myModel, as_data_frame = FALSE) con <- ' a == 2*b b - c == 5 ' conInfo <- lav_con_parse(myParTable, constraints = con) myModel2 <- 'x1 ~ a*x2 + b*x3 + c*x4 a == 2*b b - c == 5 ' ceq <- lav_pt_con_ceq(partable = lavParTable(myModel2)) ceq( c(2,3,4) )
lavaan data functions
Description
Utility functions related to the Data slot
Usage
# update data slot with new data (of the same size) lav_data_update(lavdata = NULL, new_x = NULL, boot_idx = NULL, boot_clus = NULL, lavoptions = NULL, ...)# update data slot with new data (of the same size) lav_data_update(lavdata = NULL, new_x = NULL, boot_idx = NULL, boot_clus = NULL, lavoptions = NULL, ...)
Arguments
lavdata |
A lavdata object. |
new_x |
A list of (new) data matrices (per group) of the same size. They replace the data stored in the internal data slot. |
boot_idx |
A list of integers. If bootstrapping was used to produce the data in newX, use these indices to adapt the remaining slots. |
boot_clus |
A list of integer matrices (per group), or NULL. For a cluster bootstrap of two-level data, the (relabeled) cluster ids of the resampled rows, used to adapt the multilevel (Lp) slots. |
lavoptions |
A named list. The Options slot from a lavaan object. |
... |
To accept old argument names with dots or capitals. No other arguments are accepted. |
Examples
# generate syntax for an independence model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) # extract data slot and options lavdata <- fit@Data lavoptions <- lavInspect(fit, "options") # create bootstrap sample boot.idx <- sample(x = nobs(fit), size = nobs(fit), replace = TRUE) newX <- list(lavdata@X[[1]][boot.idx,]) # generate update lavdata object newdata <- lav_data_update(lavdata = lavdata, new_x = newX, lavoptions = lavoptions)# generate syntax for an independence model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) # extract data slot and options lavdata <- fit@Data lavoptions <- lavInspect(fit, "options") # create bootstrap sample boot.idx <- sample(x = nobs(fit), size = nobs(fit), replace = TRUE) newX <- list(lavdata@X[[1]][boot.idx,]) # generate update lavdata object newdata <- lav_data_update(lavdata = lavdata, new_x = newX, lavoptions = lavoptions)
Summarizing EFA Fits
Description
S3 summary and print methods for class efaList.
Usage
lav_efalist_summary(object, nd = 3L, cutoff = 0.3, dot.cutoff = 0.1, alpha.level = 0.01, lambda = TRUE, theta = TRUE, psi = TRUE, fit.table = TRUE, fs.determinacy = FALSE, eigenvalues = TRUE, sumsq.table = TRUE, lambda.structure = FALSE, se = FALSE, zstat = FALSE, pvalue = FALSE, ...) lav_efalist_summary_print(x, nd = 3L, cutoff = 0.3, dot.cutoff = 0.1, alpha.level = 0.01, ...)lav_efalist_summary(object, nd = 3L, cutoff = 0.3, dot.cutoff = 0.1, alpha.level = 0.01, lambda = TRUE, theta = TRUE, psi = TRUE, fit.table = TRUE, fs.determinacy = FALSE, eigenvalues = TRUE, sumsq.table = TRUE, lambda.structure = FALSE, se = FALSE, zstat = FALSE, pvalue = FALSE, ...) lav_efalist_summary_print(x, nd = 3L, cutoff = 0.3, dot.cutoff = 0.1, alpha.level = 0.01, ...)
Arguments
object |
An object of class |
x |
An object of class |
nd |
Integer. The number of digits that are printed after the decimal point in the output. |
cutoff |
Numeric. Factor loadings smaller than this value (in absolute value) are not printed (even if they are significantly different from zero). The idea is that only medium to large factor loadings are printed, to better see the overall structure. |
dot.cutoff |
Numeric. Factor loadings larger (in absolute value) than this value, but smaller (in absolute value) than the cutoff value are shown as a dot. They represent small loadings that may still need your attention. |
alpha.level |
Numeric. If the p-value of a factor loading is smaller
than this value, a significance star is printed to the right of the
factor loading. To switch this off, use |
lambda |
Logical. If |
theta |
Logical. If |
psi |
Logical. If |
fit.table |
Logical. If |
fs.determinacy |
Logical. If |
eigenvalues |
Logical. If |
sumsq.table |
Logical. If |
lambda.structure |
Logical. If |
se |
Logical. If |
zstat |
Logical. If |
pvalue |
Logical. If |
... |
Further arguments passed to or from other methods. |
Value
The function lav_efalist_summary computes and returns a list of
summary statistics for the list of EFA models in object.
Examples
## The famous Holzinger and Swineford (1939) example fit <- efa(data = HolzingerSwineford1939, ov.names = paste("x", 1:9, sep = ""), nfactors = 1:3, rotation = list("geomin", geomin_epsilon = 0.01, rstarts = 1)) summary(fit, nd = 3L, cutoff = 0.2, dot.cutoff = 0.05, lambda.structure = TRUE, pvalue = TRUE)## The famous Holzinger and Swineford (1939) example fit <- efa(data = HolzingerSwineford1939, ov.names = paste("x", 1:9, sep = ""), nfactors = 1:3, rotation = list("geomin", geomin_epsilon = 0.01, rstarts = 1)) summary(fit, nd = 3L, cutoff = 0.2, dot.cutoff = 0.05, lambda.structure = TRUE, pvalue = TRUE)
lav_export_estimation
Description
lavaan provides a range of optimization methods with the optim.method argument (nlminb, BFGS, L-BFGS-B, GN, and nlminb_constr). 'lav_export_estimation' allows exporting objects and functions necessary to pass a lavaan model into any optimizer that takes a combination of (1) starting values, (2) fit-function, (3) gradient-function, and (4) upper and lower bounds. This allows testing new optimization frameworks.
Usage
lav_export_estimation(lavaan_model)lav_export_estimation(lavaan_model)
Arguments
lavaan_model |
a fitted lavaan model |
Value
List with:
-
get_coef - When equality constraints are present, lavaan applies internal transformations. get_coef is a function that reconstructs the output of the coef function for the parameters.
-
starting_values - starting_values to be used in the optimization
-
objective_function - objective function, expecting the current parameter values and the lavaan model
-
gradient_function - gradient function, expecting the current parameter values and the lavaan model
-
lower - lower bounds for parameters
-
upper - upper bound for parameters
Examples
library(lavaan) model <- ' # latent variable definitions ind60 =~ x1 + x2 + x3 dem60 =~ y1 + y2 + y3 + y4 dem65 =~ y5 + a*y6 + y7 + y8 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 ' fit <- sem(model, data = PoliticalDemocracy, do.fit = FALSE) est <- lav_export_estimation(lavaan_model = fit) # The starting values are: est$starting_values # Note that these do not have labels (and may also differ from coef(fit) # in case of equality constraints): coef(fit) # To get the same parameters, use: est$get_coef(parameter_values = est$starting_values, lavaan_model = fit) # The objective function can be used to compute the fit at the current estimates: est$objective_function(parameter_values = est$starting_values, lavaan_model = fit) # The gradient function can be used to compute the gradients at the current estimates: est$gradient_function(parameter_values = est$starting_values, lavaan_model = fit) # Together, these elements provide the means to estimate the parameters with a large # range of optimizers. For simplicity, here is an example using optim: est_fit <- optim(par = est$starting_values, fn = est$objective_function, gr = est$gradient_function, lavaan_model = fit, method = "BFGS") est$get_coef(parameter_values = est_fit$par, lavaan_model = fit) # This is identical to coef(sem(model, data = PoliticalDemocracy)) # Example using ridge regularization for parameter a fn_ridge <- function(parameter_values, lavaan_model, est, lambda){ return(est$objective_function(parameter_values = parameter_values, lavaan_model = lavaan_model) + lambda * parameter_values[6]^2) } ridge_fit <- optim(par = est$get_coef(est$starting_values, lavaan_model = fit), fn = fn_ridge, lavaan_model = fit, est = est, lambda = 10) est$get_coef(parameter_values = ridge_fit$par, lavaan_model = fit)library(lavaan) model <- ' # latent variable definitions ind60 =~ x1 + x2 + x3 dem60 =~ y1 + y2 + y3 + y4 dem65 =~ y5 + a*y6 + y7 + y8 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 ' fit <- sem(model, data = PoliticalDemocracy, do.fit = FALSE) est <- lav_export_estimation(lavaan_model = fit) # The starting values are: est$starting_values # Note that these do not have labels (and may also differ from coef(fit) # in case of equality constraints): coef(fit) # To get the same parameters, use: est$get_coef(parameter_values = est$starting_values, lavaan_model = fit) # The objective function can be used to compute the fit at the current estimates: est$objective_function(parameter_values = est$starting_values, lavaan_model = fit) # The gradient function can be used to compute the gradients at the current estimates: est$gradient_function(parameter_values = est$starting_values, lavaan_model = fit) # Together, these elements provide the means to estimate the parameters with a large # range of optimizers. For simplicity, here is an example using optim: est_fit <- optim(par = est$starting_values, fn = est$objective_function, gr = est$gradient_function, lavaan_model = fit, method = "BFGS") est$get_coef(parameter_values = est_fit$par, lavaan_model = fit) # This is identical to coef(sem(model, data = PoliticalDemocracy)) # Example using ridge regularization for parameter a fn_ridge <- function(parameter_values, lavaan_model, est, lambda){ return(est$objective_function(parameter_values = parameter_values, lavaan_model = lavaan_model) + lambda * parameter_values[6]^2) } ridge_fit <- optim(par = est$get_coef(est$starting_values, lavaan_model = fit), fn = fn_ridge, lavaan_model = fit, est = est, lambda = 10) est$get_coef(parameter_values = ridge_fit$par, lavaan_model = fit)
Utility Functions: Gradient and Jacobian
Description
Utility functions for computing the gradient of a scalar-valued function or the Jacobian of a vector-valued function by numerical approximation.
Usage
lav_func_grad_complex(func, x, h = .Machine$double.eps, ..., fallback_simple = TRUE) lav_func_jacobian_complex(func, x, h = .Machine$double.eps, ..., fallback_simple = TRUE) lav_func_grad_simple(func, x, h = sqrt(.Machine$double.eps), ...) lav_func_jacobian_simple(func, x, h = sqrt(.Machine$double.eps), ...)lav_func_grad_complex(func, x, h = .Machine$double.eps, ..., fallback_simple = TRUE) lav_func_jacobian_complex(func, x, h = .Machine$double.eps, ..., fallback_simple = TRUE) lav_func_grad_simple(func, x, h = sqrt(.Machine$double.eps), ...) lav_func_jacobian_simple(func, x, h = sqrt(.Machine$double.eps), ...)
Arguments
func |
A real-valued function returning a numeric scalar or a numeric vector. |
x |
A numeric vector: the point(s) at which the gradient/Jacobian of the function should be computed. |
h |
Numeric value representing a small change in ‘x’ when computing the gradient/Jacobian. |
... |
Additional arguments to be passed to the function ‘func’. |
fallback_simple |
Logical. If TRUE, and the function evaluation fails, we call the corresponding simple (non-complex) method instead. |
Details
The complex versions use complex numbers to gain more precision, while retaining the simplicity (and speed) of the simple forward method (see references). These functions were added to lavaan (around 2012), when the complex functionality was not yet part of the numDeriv package. They were used internally, and made public in 0.5-17 at the request of other package developers.
References
Squire, W. and Trapp, G. (1998). Using Complex Variables to Estimate Derivatives of Real Functions. SIAM Review, 40(1), 110-112.
Examples
# very accurate complex method lav_func_grad_complex(func = exp, x = 1) - exp(1) # less accurate forward method lav_func_grad_simple(func = exp, x = 1) - exp(1) # very accurate complex method diag(lav_func_jacobian_complex(func = exp, x = c(1,2,3))) - exp(c(1,2,3)) # less accurate forward method diag(lav_func_jacobian_simple(func = exp, x = c(1,2,3))) - exp(c(1,2,3))# very accurate complex method lav_func_grad_complex(func = exp, x = 1) - exp(1) # less accurate forward method lav_func_grad_simple(func = exp, x = 1) - exp(1) # very accurate complex method diag(lav_func_jacobian_complex(func = exp, x = c(1,2,3))) - exp(c(1,2,3)) # less accurate forward method diag(lav_func_jacobian_simple(func = exp, x = c(1,2,3))) - exp(c(1,2,3))
Utility Functions For Covariance Matrices
Description
Convenience functions to deal with covariance and correlation matrices.
Usage
lav_getcov(x, lower = TRUE, diagonal = TRUE, sds = NULL, names = paste("V", 1:nvar, sep="")) getCov(x, lower = TRUE, diagonal = TRUE, sds = NULL, names = paste("V", 1:nvar, sep="")) lav_char2num(s) char2num(s) lav_cor2cov(r, sds, names = NULL, ...) cor2cov(r, sds, names = NULL, ...)lav_getcov(x, lower = TRUE, diagonal = TRUE, sds = NULL, names = paste("V", 1:nvar, sep="")) getCov(x, lower = TRUE, diagonal = TRUE, sds = NULL, names = paste("V", 1:nvar, sep="")) lav_char2num(s) char2num(s) lav_cor2cov(r, sds, names = NULL, ...) cor2cov(r, sds, names = NULL, ...)
Arguments
x |
The elements of the covariance matrix. Either inside a character
string or as a numeric vector. In the former case, the function
|
lower |
Logical. If |
diagonal |
Logical. If |
sds |
A numeric vector containing the standard deviations to be
used to scale the elements in |
names |
The variable names of the observed variables. |
s |
Character string containing numeric values; commas and semi-colons are ignored. |
r |
A correlation matrix, to be scaled into a covariance matrix. |
... |
To accept old argument name |
Details
The lav_getcov function is typically used to input the lower
(or upper) triangular elements of a (symmetric) covariance matrix. In many
examples found in handbooks, only those elements are shown. However, lavaan
needs a full matrix to proceed.
The lav_cor2cov function is the inverse of the cov2cor
function, and scales a correlation matrix into a covariance matrix given
the standard deviations of the variables. Optionally, variable names can
be given.
Examples
# The classic Wheaton et. al. (1977) model # panel data on the stability of alienation lower <- ' 11.834, 6.947, 9.364, 6.819, 5.091, 12.532, 4.783, 5.028, 7.495, 9.986, -3.839, -3.889, -3.841, -3.625, 9.610, -21.899, -18.831, -21.748, -18.775, 35.522, 450.288 ' # convert to a full symmetric covariance matrix with names wheaton.cov <- lav_getcov(lower, names=c("anomia67","powerless67", "anomia71", "powerless71","education","sei")) # the model wheaton.model <- ' # measurement model ses =~ education + sei alien67 =~ anomia67 + powerless67 alien71 =~ anomia71 + powerless71 # equations alien71 ~ alien67 + ses alien67 ~ ses # correlated residuals anomia67 ~~ anomia71 powerless67 ~~ powerless71 ' # fitting the model fit <- sem(wheaton.model, sample_cov=wheaton.cov, sample_nobs=932) # showing the results summary(fit, standardized=TRUE)# The classic Wheaton et. al. (1977) model # panel data on the stability of alienation lower <- ' 11.834, 6.947, 9.364, 6.819, 5.091, 12.532, 4.783, 5.028, 7.495, 9.986, -3.839, -3.889, -3.841, -3.625, 9.610, -21.899, -18.831, -21.748, -18.775, 35.522, 450.288 ' # convert to a full symmetric covariance matrix with names wheaton.cov <- lav_getcov(lower, names=c("anomia67","powerless67", "anomia71", "powerless71","education","sei")) # the model wheaton.model <- ' # measurement model ses =~ education + sei alien67 =~ anomia67 + powerless67 alien71 =~ anomia71 + powerless71 # equations alien71 ~ alien67 + ses alien67 ~ ses # correlated residuals anomia67 ~~ anomia71 powerless67 ~~ powerless71 ' # fitting the model fit <- sem(wheaton.model, sample_cov=wheaton.cov, sample_nobs=932) # showing the results summary(fit, standardized=TRUE)
Provides a formatted label for use in tikz, svg or Rplot
Description
Creates the code used to show the label in tikz, svg or R. The label is plotted in an xy-plot if show = TRUE.
Usage
lav_label_code(label = "", value = "", show =FALSE, idx_font_size = 20L, dy = 7L, italic = TRUE, auto_subscript = TRUE)lav_label_code(label = "", value = "", show =FALSE, idx_font_size = 20L, dy = 7L, italic = TRUE, auto_subscript = TRUE)
Arguments
label |
A character string in one of the formats
If value is specified in parameter |
value |
A character string specifying a value or empty. |
show |
A logical indicating that the result should be plotted in an Rplot. |
idx_font_size |
An integer specifying font size to use for the subscript in svg. |
dy |
An integer specifying the distance to move the baseline of the subscript in svg. |
italic |
A logical indicating whether the label's font should be italic. Only used for tikz output and in the displayed Rplot when the result is not an expression. |
auto_subscript |
Logical, if TRUE and |
Details
If both label and value are empty, the resulting codes are
also empty and nothing will be shown.
If label is empty and value is not, processing is done as if
label was specified and value was empty.
If label contains the string "1van", the label value is set to "1".
This allows distinct names for regression intercepts while still labeling
them as "1".
If name in label is a Greek character or varepsilon,
the function attempts to generate code that shows the Greek symbol. If
label contains an index part, the function attempts to generate
code that displays this value as a subscript. In the svg code, the values
idx_font_size and dy are used for the subscript. If a
value is present, the function attempts to show this value after the
label, with an equal sign between the two.
Value
a list with members svg, tikz and r, giving the result.
Examples
lav_label_code("x3") lav_label_code("beta10", 0.65, show = TRUE) lav_label_code("A_i,j=0.45", show = TRUE) lav_label_code("Gamma") lav_label_code(value="1.2345")lav_label_code("x3") lav_label_code("beta10", 0.65, show = TRUE) lav_label_code("A_i,j=0.45", show = TRUE) lav_label_code("Gamma") lav_label_code(value="1.2345")
Deprecated functions with long names
Description
Functions that are deprecated following the adoption of shorter names in May 2026.
Usage
lav_matrix_duplication_ginv_pre_post(A = matrix(0, 0, 0)) lav_matrix_orthogonal_complement(A = matrix(0, 0, 0)) lav_func_gradient_complex( func, x, h = .Machine$double.eps, ..., fallback.simple = TRUE) lav_matrix_duplication_ginv_post(A = matrix(0, 0, 0)) lav_func_gradient_simple( func, x, h = sqrt(.Machine$double.eps), ...) lav_matrix_vech_row_idx(n = 1L, diagonal = TRUE) lav_matrix_vech_col_idx(n = 1L, diagonal = TRUE) lav_matrix_antidiag_idx(n = 1L) lav_matrix_duplication_pre_post(A = matrix(0, 0, 0)) lav_matrix_duplication_ginv_pre(A = matrix(0, 0, 0)) lav_matrix_commutation_pre_post(A = matrix(0, 0, 0)) lav_partable_unrestricted( lavobject = NULL, lavdata = NULL, lavpta = NULL, lavoptions = NULL, lavsamplestats = NULL, lavh1 = NULL, sample.cov = NULL, sample.mean = NULL, sample.slopes = NULL, sample.th = NULL, sample.th.idx = NULL, sample.cov.x = NULL, sample.mean.x = NULL) lav_partable_independence( lavobject = NULL, lavdata = NULL, lavpta = NULL, lavoptions = NULL, lavsamplestats = NULL, lavh1 = NULL, sample.cov = NULL, sample.mean = NULL, sample.slopes = NULL, sample.th = NULL, sample.th.idx = NULL, sample.cov.x = NULL, sample.mean.x = NULL) lav_matrix_vechru_idx(n = 1L, diagonal = TRUE) lav_matrix_upper2full(x, diagonal = TRUE) lav_matrix_lower2full(x, diagonal = TRUE) lav_matrix_commutation_mn_pre( A, m = 1L, n = 1L) lav_samplestats_from_data( lavdata = NULL, lavoptions = NULL, WLS.V = NULL, NACOV = NULL) lav_matrix_vechru_reverse(x, diagonal = TRUE) lav_matrix_vechr_idx(n = 1L, diagonal = TRUE) lav_matrix_vechu_idx(n = 1L, diagonal = TRUE) lav_matrix_diagh_idx(n = 1L) lav_partable_attributes(partable, pta = NULL) lav_matrix_vechr_reverse(x, diagonal = TRUE) lav_matrix_vechu_reverse(x, diagonal = TRUE) lav_matrix_vech_idx(n = 1L, diagonal = TRUE) lav_matrix_diag_idx(n = 1L) lav_matrix_duplication_post(A = matrix(0, 0, 0)) lav_matrix_duplication_ginv(n = 1L) lav_matrix_commutation_post(A = matrix(0, 0, 0)) lav_matrix_symmetric_sqrt(S = matrix(0, 0, 0)) lav_matrix_vech_reverse(x, diagonal = TRUE) lav_matrix_duplication_pre(A = matrix(0, 0, 0)) lav_matrix_commutation_pre(A = matrix(0, 0, 0)) lav_partable_complete(partable = NULL, start = TRUE) lav_matrix_vechru(S, diagonal = TRUE) lav_partable_constraints_def( partable, con = NULL, debug = FALSE, txtOnly = FALSE, warn = TRUE) lav_partable_constraints_ceq( partable, con = NULL, debug = FALSE, txtOnly = FALSE) lav_partable_constraints_ciq( partable, con = NULL, debug = FALSE, txtOnly = FALSE) lav_partable_from_lm( object, est = FALSE, label = FALSE, as.data.frame. = FALSE) lav_constraints_parse( partable = NULL, constraints = NULL, theta = NULL, debug = FALSE) lav_matrix_vechr(S, diagonal = TRUE) lav_matrix_vechu(S, diagonal = TRUE) lav_matrix_bdiag(...) lav_matrix_trace(..., check = TRUE) lav_partable_labels( partable, blocks = c("group", "level"), group.equal = "", group.partial = "", type = "user") lav_matrix_vecr(A) lav_matrix_vech(S, diagonal = TRUE) lav_partable_merge( pt1 = NULL, pt2 = NULL, remove.duplicated = FALSE, fromLast = FALSE, warn = TRUE) lav_matrix_vec(A) lav_matrix_duplication(n = 1L) lav_matrix_commutation(m = 1L, n = 1L) lav_matrix_cov(Y, Mu = NULL) lav_partable_ndat(partable) lav_partable_npar(partable) lav_partable_add(partable = NULL, add = list()) lav_partable_df(partable)lav_matrix_duplication_ginv_pre_post(A = matrix(0, 0, 0)) lav_matrix_orthogonal_complement(A = matrix(0, 0, 0)) lav_func_gradient_complex( func, x, h = .Machine$double.eps, ..., fallback.simple = TRUE) lav_matrix_duplication_ginv_post(A = matrix(0, 0, 0)) lav_func_gradient_simple( func, x, h = sqrt(.Machine$double.eps), ...) lav_matrix_vech_row_idx(n = 1L, diagonal = TRUE) lav_matrix_vech_col_idx(n = 1L, diagonal = TRUE) lav_matrix_antidiag_idx(n = 1L) lav_matrix_duplication_pre_post(A = matrix(0, 0, 0)) lav_matrix_duplication_ginv_pre(A = matrix(0, 0, 0)) lav_matrix_commutation_pre_post(A = matrix(0, 0, 0)) lav_partable_unrestricted( lavobject = NULL, lavdata = NULL, lavpta = NULL, lavoptions = NULL, lavsamplestats = NULL, lavh1 = NULL, sample.cov = NULL, sample.mean = NULL, sample.slopes = NULL, sample.th = NULL, sample.th.idx = NULL, sample.cov.x = NULL, sample.mean.x = NULL) lav_partable_independence( lavobject = NULL, lavdata = NULL, lavpta = NULL, lavoptions = NULL, lavsamplestats = NULL, lavh1 = NULL, sample.cov = NULL, sample.mean = NULL, sample.slopes = NULL, sample.th = NULL, sample.th.idx = NULL, sample.cov.x = NULL, sample.mean.x = NULL) lav_matrix_vechru_idx(n = 1L, diagonal = TRUE) lav_matrix_upper2full(x, diagonal = TRUE) lav_matrix_lower2full(x, diagonal = TRUE) lav_matrix_commutation_mn_pre( A, m = 1L, n = 1L) lav_samplestats_from_data( lavdata = NULL, lavoptions = NULL, WLS.V = NULL, NACOV = NULL) lav_matrix_vechru_reverse(x, diagonal = TRUE) lav_matrix_vechr_idx(n = 1L, diagonal = TRUE) lav_matrix_vechu_idx(n = 1L, diagonal = TRUE) lav_matrix_diagh_idx(n = 1L) lav_partable_attributes(partable, pta = NULL) lav_matrix_vechr_reverse(x, diagonal = TRUE) lav_matrix_vechu_reverse(x, diagonal = TRUE) lav_matrix_vech_idx(n = 1L, diagonal = TRUE) lav_matrix_diag_idx(n = 1L) lav_matrix_duplication_post(A = matrix(0, 0, 0)) lav_matrix_duplication_ginv(n = 1L) lav_matrix_commutation_post(A = matrix(0, 0, 0)) lav_matrix_symmetric_sqrt(S = matrix(0, 0, 0)) lav_matrix_vech_reverse(x, diagonal = TRUE) lav_matrix_duplication_pre(A = matrix(0, 0, 0)) lav_matrix_commutation_pre(A = matrix(0, 0, 0)) lav_partable_complete(partable = NULL, start = TRUE) lav_matrix_vechru(S, diagonal = TRUE) lav_partable_constraints_def( partable, con = NULL, debug = FALSE, txtOnly = FALSE, warn = TRUE) lav_partable_constraints_ceq( partable, con = NULL, debug = FALSE, txtOnly = FALSE) lav_partable_constraints_ciq( partable, con = NULL, debug = FALSE, txtOnly = FALSE) lav_partable_from_lm( object, est = FALSE, label = FALSE, as.data.frame. = FALSE) lav_constraints_parse( partable = NULL, constraints = NULL, theta = NULL, debug = FALSE) lav_matrix_vechr(S, diagonal = TRUE) lav_matrix_vechu(S, diagonal = TRUE) lav_matrix_bdiag(...) lav_matrix_trace(..., check = TRUE) lav_partable_labels( partable, blocks = c("group", "level"), group.equal = "", group.partial = "", type = "user") lav_matrix_vecr(A) lav_matrix_vech(S, diagonal = TRUE) lav_partable_merge( pt1 = NULL, pt2 = NULL, remove.duplicated = FALSE, fromLast = FALSE, warn = TRUE) lav_matrix_vec(A) lav_matrix_duplication(n = 1L) lav_matrix_commutation(m = 1L, n = 1L) lav_matrix_cov(Y, Mu = NULL) lav_partable_ndat(partable) lav_partable_npar(partable) lav_partable_add(partable = NULL, add = list()) lav_partable_df(partable)
Arguments
... |
See argument |
A |
See argument |
add |
See argument |
as.data.frame. |
See argument |
blocks |
See argument |
check |
See argument |
con |
See argument |
constraints |
See argument |
debug |
See argument |
diagonal |
See argument |
est |
See argument |
fallback.simple |
See argument |
fromLast |
See argument |
func |
See argument |
group.equal |
See argument |
group.partial |
See argument |
h |
See argument |
label |
See argument |
lavdata |
See argument |
lavh1 |
See argument |
lavobject |
See argument |
lavoptions |
See argument |
lavpta |
See argument |
lavsamplestats |
See argument |
m |
See argument |
Mu |
See argument |
n |
See argument |
NACOV |
See argument |
object |
See argument |
partable |
See argument |
pt1 |
See argument |
pt2 |
See argument |
pta |
See argument |
remove.duplicated |
See argument |
S |
See argument |
sample.cov |
See argument |
sample.cov.x |
See argument |
sample.mean |
See argument |
sample.mean.x |
See argument |
sample.slopes |
See argument |
sample.th |
See argument |
sample.th.idx |
See argument |
start |
See argument |
theta |
See argument |
txtOnly |
See argument |
type |
See argument |
warn |
See argument |
WLS.V |
See argument |
x |
See argument |
Y |
See argument |
Details
Function names are shortened by the following replacements:
- _mvnorm
-
_mvn
- _cluster
-
_cl
- _missing
-
_mi
- _matrix
-
_mat
- _duplication
-
_dup
- _commutation
-
_com
- _information
-
_info
- _samplestats
-
_samp
- _satorra_bentler
-
_sb
- _SatorraBentler
-
_sb
- _yuan_bentler
-
_yb
- _inverted
-
_inv
- _estimate
-
_est
- _symmetric
-
_sym
- _lavaan_step
-
_step
- _univariate
-
_uni
- _fit_measures
-
_fit
- _constraints
-
_con
- _scores
-
_sc
- _reverse
-
_rev
- _vech_sigma
-
_sigma
- _vechsigma
-
_sigma
- _object_inspect
-
_inspect
- _orthogonal
-
_ortho
- _gradient
-
_grad
- _partable
-
_pt
Utility Functions: Matrices and Vectors
Description
Utility functions for Matrix and Vector operations.
Usage
# matrix to vector lav_mat_vec(a) lav_mat_vecr(a) lav_mat_vech(s, diagonal = TRUE) lav_mat_vechr(s, diagonal = TRUE) # matrix/vector indices lav_mat_vech_idx(n = 1L, diagonal = TRUE) lav_mat_vech_row_idx(n = 1L, diagonal = TRUE) lav_mat_vech_col_idx(n = 1L, diagonal = TRUE) lav_mat_vechr_idx(n = 1L, diagonal = TRUE) lav_mat_vechru_idx(n = 1L, diagonal = TRUE) lav_mat_diag_idx(n = 1L) lav_mat_diagh_idx(n = 1L) lav_mat_antidiag_idx(n = 1L) # vector to matrix lav_mat_vech_rev(x, diagonal = TRUE) lav_mat_vechru_rev(x, diagonal = TRUE) lav_mat_upper2full(x, diagonal = TRUE) lav_mat_vechr_rev(x, diagonal = TRUE) lav_mat_vechu_rev(x, diagonal = TRUE) lav_mat_lower2full(x, diagonal = TRUE) # the duplication matrix lav_mat_dup(n = 1L) lav_mat_dup_pre(a = matrix(0,0,0)) lav_mat_dup_post(a = matrix(0,0,0)) lav_mat_dup_pre_post(a = matrix(0,0,0)) lav_mat_dup_ginv(n = 1L) lav_mat_dup_ginv_pre(a = matrix(0,0,0)) lav_mat_dup_ginv_post(a = matrix(0,0,0)) lav_mat_dup_ginv_pre_post(a = matrix(0,0,0)) # the commutation matrix lav_mat_com(m = 1L, n = 1L) lav_mat_com_pre(a = matrix(0,0,0)) lav_mat_com_post(a = matrix(0,0,0)) lav_mat_com_pre_post(a = matrix(0,0,0)) lav_mat_com_mn_pre(a, m = 1L, n = 1L) # sample statistics lav_mat_cov(y, mu = NULL) # other matrix operations lav_mat_sym_sqrt(s = matrix(0,0,0)) lav_mat_ortho_complement(a = matrix(0,0,0)) lav_mat_bdiag(...) lav_mat_trace(..., check = TRUE)# matrix to vector lav_mat_vec(a) lav_mat_vecr(a) lav_mat_vech(s, diagonal = TRUE) lav_mat_vechr(s, diagonal = TRUE) # matrix/vector indices lav_mat_vech_idx(n = 1L, diagonal = TRUE) lav_mat_vech_row_idx(n = 1L, diagonal = TRUE) lav_mat_vech_col_idx(n = 1L, diagonal = TRUE) lav_mat_vechr_idx(n = 1L, diagonal = TRUE) lav_mat_vechru_idx(n = 1L, diagonal = TRUE) lav_mat_diag_idx(n = 1L) lav_mat_diagh_idx(n = 1L) lav_mat_antidiag_idx(n = 1L) # vector to matrix lav_mat_vech_rev(x, diagonal = TRUE) lav_mat_vechru_rev(x, diagonal = TRUE) lav_mat_upper2full(x, diagonal = TRUE) lav_mat_vechr_rev(x, diagonal = TRUE) lav_mat_vechu_rev(x, diagonal = TRUE) lav_mat_lower2full(x, diagonal = TRUE) # the duplication matrix lav_mat_dup(n = 1L) lav_mat_dup_pre(a = matrix(0,0,0)) lav_mat_dup_post(a = matrix(0,0,0)) lav_mat_dup_pre_post(a = matrix(0,0,0)) lav_mat_dup_ginv(n = 1L) lav_mat_dup_ginv_pre(a = matrix(0,0,0)) lav_mat_dup_ginv_post(a = matrix(0,0,0)) lav_mat_dup_ginv_pre_post(a = matrix(0,0,0)) # the commutation matrix lav_mat_com(m = 1L, n = 1L) lav_mat_com_pre(a = matrix(0,0,0)) lav_mat_com_post(a = matrix(0,0,0)) lav_mat_com_pre_post(a = matrix(0,0,0)) lav_mat_com_mn_pre(a, m = 1L, n = 1L) # sample statistics lav_mat_cov(y, mu = NULL) # other matrix operations lav_mat_sym_sqrt(s = matrix(0,0,0)) lav_mat_ortho_complement(a = matrix(0,0,0)) lav_mat_bdiag(...) lav_mat_trace(..., check = TRUE)
Arguments
a |
A general matrix. |
s |
A symmetric matrix. |
y |
A matrix representing a (numeric) dataset. |
diagonal |
Logical. If TRUE, include the diagonal. |
n |
Integer. When it is the only argument, the dimension of a square matrix. If m is also provided, the number of columns of the matrix. |
m |
Integer. The number of rows of a matrix. |
x |
Numeric. A vector. |
mu |
Numeric. If given, use mu (instead of sample mean) to center, before taking the crossproduct. |
... |
One or more matrices, or a list of matrices. |
check |
Logical. If |
Details
These are a collection of lower-level matrix and vector functions that are used throughout the lavaan code. They are made public at the request of package developers. Below is a brief description of what they do:
The lav_mat_vec function implements the vec operator (for
'vectorization') and transforms a matrix into a vector by stacking the
columns of the matrix one underneath the other.
The lav_mat_vecr function is similar to the lav_mat_vec
function but transforms a matrix into a vector by stacking the
rows of the matrix one underneath the other.
The lav_mat_vech function implements the vech operator
(for 'half vectorization') and transforms a symmetric matrix
into a vector by stacking the columns of the matrix one underneath the
other, but eliminating all supradiagonal elements. If diagonal = FALSE,
the diagonal elements are also eliminated.
The lav_mat_vechr function is similar to the lav_mat_vech
function but transforms a matrix into a vector by stacking the
rows of the matrix one underneath the other, eliminating all
supradiagonal elements.
The lav_mat_vech_idx function returns the vector indices of the lower
triangular elements of a symmetric matrix of size n, column by column.
The lav_mat_vech_row_idx function returns the row indices of the
lower triangular elements of a symmetric matrix of size n.
The lav_mat_vech_col_idx function returns the column indices of the
lower triangular elements of a symmetric matrix of size n.
The lav_mat_vechr_idx function returns the vector indices of the
lower triangular elements of a symmetric matrix of size n, row by row.
The lav_mat_vechu_idx function returns the vector indices of the
upper triangular elements of a symmetric matrix of size n, column by column.
The lav_mat_vechru_idx function returns the vector indices
of the upper triangular elements of a symmetric matrix of size n, row by row.
The lav_mat_diag_idx function returns the vector indices of the
diagonal elements of a symmetric matrix of size n.
The lav_mat_diagh_idx function returns the vector indices of
the lower part of a symmetric matrix of size n.
The lav_mat_antidiag_idx function returns the vector indices of
the anti diagonal elements of a symmetric matrix of size n.
The lav_mat_vech_rev function (alias:
lav_mat_vechru_rev and lav_mat_upper2full) creates a
symmetric matrix, given only upper triangular elements, row by row. If
diagonal = FALSE, a diagonal with zero elements is added.
The lav_mat_vechr_rev (alias: lav_mat_vechu_rev and
lav_mat_lower2full) creates a symmetric matrix, given only the lower
triangular elements, row by row. If diagonal = FALSE, a diagonal with zero
elements is added.
The lav_mat_dup function generates the duplication matrix
for a symmetric matrix of size n. This matrix duplicates the elements in
vech(S) to create vec(S) (where S is symmetric). This matrix is very
sparse, and should probably never be explicitly created. Use one of
the functions below.
The lav_mat_dup_pre function computes the product of the
transpose of the duplication matrix and a matrix A. The A matrix should have
n*n rows, where n is an integer. The duplication matrix is not explicitly
created.
The lav_mat_dup_post function computes the product of a
matrix A with the duplication matrix. The A matrix should have n*n columns,
where n is an integer. The duplication matrix is not explicitly created.
The lav_mat_dup_pre_post function first pre-multiplies a
matrix A with the transpose of the duplication matrix, and then post multiplies
the result again with the duplication matrix. A must be square matrix with n*n
rows and columns, where n is an integer. The duplication matrix is not
explicitly created.
The lav_mat_dup_ginv function computes the generalized
inverse of the duplication matrix. The matrix removes the duplicated elements
in vec(S) to create vech(S). This matrix is very sparse, and should probably
never be explicitly created. Use one of the functions below.
The lav_mat_dup_ginv_pre function computes the product of the
generalized inverse of the duplication matrix and a matrix A with n*n rows,
where n is an integer. The generalized inverse of the duplication matrix
is not explicitly created.
The lav_mat_dup_ginv_post function computes the product of a
matrix A (with n*n columns, where n is an integer) and the transpose of the
generalized inverse of the duplication matrix. The generalized inverse of the
duplication matrix is not explicitly created.
The lav_mat_dup_ginv_pre_post function first pre-multiplies
a matrix A with the transpose of the generalized inverse of the duplication
matrix, and then post multiplies the result again with the transpose of the
generalized inverse matrix. The matrix A must be square with n*n rows and
columns, where n is an integer. The generalized inverse of the duplication
matrix is not explicitly created.
The lav_mat_com function computes the commutation matrix, a
permutation matrix that transforms vec(A) (with m rows and n columns)
into vec(t(A)).
The lav_mat_com_pre function computes the product of the
commutation matrix with a matrix A, without explicitly creating the commutation
matrix. The matrix A must have n*n rows, where n is an integer.
The lav_mat_com_post function computes the product of a
matrix A with the commutation matrix, without explicitly creating the
commutation matrix. The matrix A must have n*n rows, where n is an integer.
The lav_mat_com_pre_post function first pre-multiplies
a matrix A with the commutation matrix, and then post multiplies the result again with the commutation matrix, without explicitly creating the
commutation matrix. The matrix A must have n*n rows, where n is an integer.
The lav_mat_com_mn_pre function computes the product of the
commutation matrix with a matrix A, without explicitly creating the commutation
matrix. The matrix A must have m*n rows, where m and n are integers.
The lav_mat_cov function computes the sample covariance matrix of
its input matrix, where the elements are divided by N (the number of rows).
The lav_mat_sym_sqrt function computes the square root of a
positive definite symmetric matrix (using an eigen decomposition). If some of
the eigenvalues are negative, they are silently fixed to zero.
The lav_mat_ortho_complement function computes an orthogonal
complement of the matrix A, using a qr decomposition.
The lav_mat_bdiag function constructs a block diagonal matrix from
its arguments.
The lav_mat_trace function computes the trace (the sum of the
diagonal elements) of a single (square) matrix, or if multiple matrices are
provided (either as a list, or as multiple arguments), we first compute their
product (which must result in a square matrix), and then we compute the trace;
if check = TRUE, we check if the (final) matrix is square.
References
Magnus, J. R. and H. Neudecker (1999). Matrix Differential Calculus with Applications in Statistics and Econometrics, Second Edition, John Wiley.
Examples
# upper elements of a 3 by 3 symmetric matrix (row by row) x <- c(30, 16, 5, 10, 3, 1) # construct full symmetric matrix S <- lav_mat_upper2full(x) # compute the normal theory `Gamma' matrix given a covariance # matrix (S), using the formula: Gamma = 2 * D^{+} (S %x% S) t(D^{+}) Gamma.NT <- 2 * lav_mat_dup_ginv_pre_post(S %x% S) Gamma.NT# upper elements of a 3 by 3 symmetric matrix (row by row) x <- c(30, 16, 5, 10, 3, 1) # construct full symmetric matrix S <- lav_mat_upper2full(x) # compute the normal theory `Gamma' matrix given a covariance # matrix (S), using the formula: Gamma = 2 * D^{+} (S %x% S) t(D^{+}) Gamma.NT <- 2 * lav_mat_dup_ginv_pre_post(S %x% S) Gamma.NT
lavaan model functions
Description
Utility functions related to internal model representation (lavmodel)
Usage
# set/get free parameters lav_model_set_parameters(lavmodel, x = NULL) lav_model_get_parameters(lavmodel, glist = NULL, type = "free", extra = TRUE, ...) # compute model-implied statistics lav_model_implied(lavmodel, glist = NULL, delta = TRUE, ...) # compute standard errors lav_model_vcov_se(lavmodel, lavpartable, vcov = NULL, boot = NULL, mc = NULL, lavoptions = NULL, ...)# set/get free parameters lav_model_set_parameters(lavmodel, x = NULL) lav_model_get_parameters(lavmodel, glist = NULL, type = "free", extra = TRUE, ...) # compute model-implied statistics lav_model_implied(lavmodel, glist = NULL, delta = TRUE, ...) # compute standard errors lav_model_vcov_se(lavmodel, lavpartable, vcov = NULL, boot = NULL, mc = NULL, lavoptions = NULL, ...)
Arguments
lavmodel |
An internal representation of a lavaan model. |
x |
Numeric. A vector containing the values of all the free model parameters. |
glist |
List. A list of model matrices, similar to the output of
|
type |
Character string. If |
extra |
Logical. If |
delta |
Logical. If |
lavpartable |
A parameter table. |
vcov |
Numeric matrix containing an estimate of the variance covariance matrix of the free model parameters. |
boot |
Numeric matrix containing the bootstrap based parameter estimates (in the columns) for each bootstrap sample (in the rows). |
mc |
Numeric matrix containing the Monte-Carlo based parameter estimates (in the columns) for each Monte-Carlo sample (in the rows). |
lavoptions |
A named list. The Options slot from a lavaan object. |
... |
To accept old argument names with dots or capitals. No other arguments are accepted. |
Examples
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) lavmodel <- fit@Model est <- lav_model_get_parameters(lavmodel) estHS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) lavmodel <- fit@Model est <- lav_model_get_parameters(lavmodel) est
Get model information
Description
Extracts the information from a model that is needed to produce a plot.
Usage
lav_model_plotinfo(model = NULL, infile = NULL, varlv = FALSE)lav_model_plotinfo(model = NULL, infile = NULL, varlv = FALSE)
Arguments
model |
A character vector specifying the model in lavaan syntax or a list
(or data.frame) with at least members lhs, op, rhs, label and fixed or a fitted
lavaan object (in which case the |
infile |
A character string specifying the file that contains the model syntax. |
varlv |
A logical indicating that the (residual) variance of a variable should be plotted as a separate latent variable (with a smaller circle than ordinary latent variables). In this case, a covariance between two such variables is plotted as a covariance between their variance latent variables. |
Value
A structure 'plotinfo', which is a list with members nodes and edges. These are data.frames containing the data needed to create a diagram.
-
nodes
- id
-
character, identification of the node consisting of blok and naam.
- naam
-
character, name of the node as specified in the model. For intercepts the name is "1vanXXXX", with XXXX the name of the regressed variable.
- tiepe
-
character, type of node: ov (observed variable), lv (latent variable), varlv (variance as latent variable), cv (composite variable), wov (within level variable in multilevel model), bov (between level variable in multilevel model), const (intercept of regression).
- blok
-
integer, level (0 if not a multilevel model).
-
edges
- id
-
integer, autoincrement identification of the edge.
- label
-
character, label for the edge, made from the label specified in the model and the fixed (or estimated) value if present.
- van
-
character, id of the starting node.
- naar
-
character, id of the destination node.
- tiepe
-
character, lavaan operator, with two exceptions: a (residual) variance is coded here as '~~~', and a regression introduced by varlv = TRUE is coded as '~.'.
Examples
model <- 'alpha =~ 1 * x1 + x2 + x3 # latent variable beta <~ x4 + x5 + x6 # composite gamma =~ 1 * x7 + x8 + x9 # latent variable Xi =~ 1 * x10 + x11 + x12 + x13 # latent variable # regressions Xi ~ v * alpha + t * beta + cc * 1 alpha ~ tt * beta + ss * gamma + yy * Theta1 # variances and covariances x2 ~~ cc25 * x5 x3 ~~ cc36 * x6 x3 ~~ cc34 * x4 gamma ~~ 0.55 * gamma ' (test <- lav_model_plotinfo(model))model <- 'alpha =~ 1 * x1 + x2 + x3 # latent variable beta <~ x4 + x5 + x6 # composite gamma =~ 1 * x7 + x8 + x9 # latent variable Xi =~ 1 * x10 + x11 + x12 + x13 # latent variable # regressions Xi ~ v * alpha + t * beta + cc * 1 alpha ~ tt * beta + ss * gamma + yy * Theta1 # variances and covariances x2 ~~ cc25 * x5 x3 ~~ cc36 * x6 x3 ~~ cc34 * x4 gamma ~~ 0.55 * gamma ' (test <- lav_model_plotinfo(model))
mplus to lavaan converter
Description
Read in an Mplus input file, convert it to lavaan syntax, and fit the model.
Usage
lav_mplus_lavaan(inpfile, run = TRUE) mplus2lavaan(inpfile, run = TRUE)lav_mplus_lavaan(inpfile, run = TRUE) mplus2lavaan(inpfile, run = TRUE)
Arguments
inpfile |
The filename (including a full path) of the Mplus input file. The data (as referred to in the Mplus input file) should be in the same directory as the Mplus input file. |
run |
Whether to run the specified Mplus input syntax ( |
Value
A lavaan object with the fitted results of the Mplus model. The parsed
and converted Mplus syntax is preserved in the @external slot of the lavaan
object in the $mplus.inp element. If run is FALSE, a list of converted
syntax is returned.
Author(s)
Michael Hallquist
See Also
Examples
## Not run: out <- lav_mplus_lavaan("ex5.1.inp") summary(out) ## End(Not run)## Not run: out <- lav_mplus_lavaan("ex5.1.inp") summary(out) ## End(Not run)
Convert Mplus model syntax to lavaan
Description
Converts Mplus model syntax into lavaan model syntax.
Usage
lav_mplus_syntax_model(syntax) mplus2lavaan.modelSyntax(syntax)lav_mplus_syntax_model(syntax) mplus2lavaan.modelSyntax(syntax)
Arguments
syntax |
A character vector containing Mplus model syntax to be
converted to lavaan model syntax. Note that parsing Mplus syntax often
requires correct usage of newline characters. If |
Value
A character string of converted lavaan model syntax.
Author(s)
Michael Hallquist
See Also
Examples
## Not run: syntax <- ' f1 BY x1*1 x2 x3; x1 WITH x2; x3 (1); x2 (1); ' lavSyntax <- lav_mplus_syntax_model(syntax) cat(lavSyntax) ## End(Not run)## Not run: syntax <- ' f1 BY x1*1 x2 x3; x1 WITH x2; x3 (1); x2 (1); ' lavSyntax <- lav_mplus_syntax_model(syntax) cat(lavSyntax) ## End(Not run)
lavaan partable functions
Description
Utility functions related to the parameter table (partable)
Usage
# extract information from a parameter table lav_pt_df(partable) lav_pt_ndat(partable) lav_pt_npar(partable) lav_pt_ngroups(partable) lav_pt_attributes(partable, pta = NULL) # generate parameter labels lav_pt_labels(partable, blocks = c("group", "level"), group_equal = "", group_partial = "", type = "user") # generate parameter table for specific models lav_pt_independence(lavobject = NULL, lavdata = NULL, lavpta = NULL, lavoptions = NULL, lavsamplestats = NULL, lavh1 = NULL, sample_cov = NULL, sample_mean = NULL, sample_slopes = NULL, sample_th = NULL, sample_th_idx = NULL, sample_cov_x = NULL, sample_mean_x = NULL) lav_pt_unrestricted(lavobject = NULL, lavdata = NULL, lavpta = NULL, lavoptions = NULL, lavsamplestats = NULL, lavh1 = NULL, sample_cov = NULL, sample_mean = NULL, sample_slopes = NULL, sample_th = NULL, sample_th_idx = NULL, sample_cov_x = NULL, sample_mean_x = NULL) lav_pt_from_lm(object, est = FALSE, label = FALSE, as_data_frame = FALSE) # complete a parameter table only containing a few columns (lhs,op,rhs) lav_pt_complete(partable = NULL, start = TRUE) # merge two parameter tables lav_pt_merge(pt1 = NULL, pt2 = NULL, remove_duplicated = FALSE, from_last = FALSE, warn = TRUE) # add a single parameter to an existing parameter table lav_pt_add(partable = NULL, add = list())# extract information from a parameter table lav_pt_df(partable) lav_pt_ndat(partable) lav_pt_npar(partable) lav_pt_ngroups(partable) lav_pt_attributes(partable, pta = NULL) # generate parameter labels lav_pt_labels(partable, blocks = c("group", "level"), group_equal = "", group_partial = "", type = "user") # generate parameter table for specific models lav_pt_independence(lavobject = NULL, lavdata = NULL, lavpta = NULL, lavoptions = NULL, lavsamplestats = NULL, lavh1 = NULL, sample_cov = NULL, sample_mean = NULL, sample_slopes = NULL, sample_th = NULL, sample_th_idx = NULL, sample_cov_x = NULL, sample_mean_x = NULL) lav_pt_unrestricted(lavobject = NULL, lavdata = NULL, lavpta = NULL, lavoptions = NULL, lavsamplestats = NULL, lavh1 = NULL, sample_cov = NULL, sample_mean = NULL, sample_slopes = NULL, sample_th = NULL, sample_th_idx = NULL, sample_cov_x = NULL, sample_mean_x = NULL) lav_pt_from_lm(object, est = FALSE, label = FALSE, as_data_frame = FALSE) # complete a parameter table only containing a few columns (lhs,op,rhs) lav_pt_complete(partable = NULL, start = TRUE) # merge two parameter tables lav_pt_merge(pt1 = NULL, pt2 = NULL, remove_duplicated = FALSE, from_last = FALSE, warn = TRUE) # add a single parameter to an existing parameter table lav_pt_add(partable = NULL, add = list())
Arguments
partable |
A parameter table. See |
blocks |
Character vector. Which columns in the parameter table should be
taken to distinguish between different blocks of parameters (and hence
be given different labels)? If |
group_equal |
The same options can be used here as in the fitting functions. Parameters that are constrained to be equal across groups will be given the same label. |
group_partial |
A vector of character strings containing the labels of the parameters which should be free in all groups. |
type |
Character string. Either ‘user’ to select all entries, or ‘free’ to select only the free parameters from the parameter table. |
lavobject |
An object of class ‘lavaan’. If this argument is provided, it should be the only argument. All the values for the other arguments are extracted from this object. |
lavdata |
An object of class ‘lavData’. The Data slot from a lavaan object. |
lavoptions |
A named list. The Options slot from a lavaan object. |
lavsamplestats |
An object of class ‘lavSampleStats’. The SampleStats slot from a lavaan object. |
lavh1 |
A named list. The h1 slot from a lavaan object. |
lavpta |
The pta (parameter table attributes) slot from a lavaan object. |
sample_cov |
Optional list of numeric matrices. Each list element contains a sample variance-covariance matrix for this group. If provided, these values will be used as starting values. |
sample_mean |
Optional list of numeric vectors. Each list element contains a sample mean vector for this group. If provided, these values will be used as starting values. |
sample_slopes |
Optional list of numeric matrices.
Each list element contains the sample slopes for this group (only used
when |
sample_th |
Optional list of numeric vectors. Each list element contains a vector of sample thresholds for this group. If provided (and also sample.th.idx is provided), these values will be used as starting values. |
sample_th_idx |
Optional list of integers. Each list contains the threshold indices for this group. |
sample_cov_x |
Optional list of numeric matrices. Each list element
contains a sample variance-covariance matrix for the exogenous variables
for this group (only used when |
sample_mean_x |
Optional list of numeric vectors.
Each list element contains a sample mean vector for the exogenous variables
for this group (only used when |
est |
Logical. If TRUE, include the fitted estimates in the parameter table. |
label |
Logical. If TRUE, include parameter labels in the parameter table. |
as_data_frame |
Logical. If TRUE, return the parameter table as a data.frame. |
object |
An object of class |
start |
Logical. If TRUE, include a start column, based on the simple method for generating starting values. |
pta |
A list containing parameter attributes. |
pt1 |
A parameter table. |
pt2 |
A parameter table. |
remove_duplicated |
Logical. If |
from_last |
Logical. If |
warn |
Logical. If |
add |
A named list. A single row of a parameter table as a named list. |
Examples
# generate syntax for an independence model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) lav <- lav_pt_independence(fit) as.data.frame(lav, stringsAsFactors = FALSE) # how many free parameters? lav_pt_npar(lav) # how many sample statistics? lav_pt_ndat(lav)# generate syntax for an independence model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) lav <- lav_pt_independence(fit) as.data.frame(lav, stringsAsFactors = FALSE) # how many free parameters? lav_pt_npar(lav) # how many sample statistics? lav_pt_ndat(lav)
Create diagram code for tikz or svg, or produce an R plot
Description
Creates code to draw a diagram in tikz or svg, plots the diagram, or stores the diagram in a png file.
Usage
lav_plot(model = NULL, infile = NULL, varlv = FALSE, placenodes = NULL, edgelabelsbelow = NULL, group_covar_indicators = FALSE, common_opts = list(sloped_labels = TRUE, mlovcolors = c("lightgreen", "lightblue"), italic = TRUE, lightness = 1, auto_subscript = TRUE), rplot = list(outfile = "", addgrid = TRUE), tikz = list(outfile = "", cex = 1.3, standalone = FALSE), svg = list(outfile = "", stroke_width = 2L, font_size = 20L, idx_font_size = 15L, dy = 5L, font_family = "Latin Modern Math, arial, Arial, sans", standalone = FALSE) )lav_plot(model = NULL, infile = NULL, varlv = FALSE, placenodes = NULL, edgelabelsbelow = NULL, group_covar_indicators = FALSE, common_opts = list(sloped_labels = TRUE, mlovcolors = c("lightgreen", "lightblue"), italic = TRUE, lightness = 1, auto_subscript = TRUE), rplot = list(outfile = "", addgrid = TRUE), tikz = list(outfile = "", cex = 1.3, standalone = FALSE), svg = list(outfile = "", stroke_width = 2L, font_size = 20L, idx_font_size = 15L, dy = 5L, font_family = "Latin Modern Math, arial, Arial, sans", standalone = FALSE) )
Arguments
model |
A character vector specifying the model in lavaan syntax or a list
(or data.frame) with at least members lhs, op, rhs, label and fixed or a fitted
lavaan object (in which case the |
infile |
A character string specifying the file that contains the model syntax. |
varlv |
A logical indicating that the (residual) variance of a variable should be plotted as a separate latent variable (with a smaller circle than ordinary latent variables). In this case, a covariance between two such variables is plotted as a covariance between their variance latent variables. |
placenodes |
optional list with members |
edgelabelsbelow |
optional list with members |
group_covar_indicators |
logical, should items with indicators which have an explicit covariance link be placed in the same group, i.e. forced to be on the same side of the diagram? |
common_opts |
options common to the three types of generated plots. |
rplot |
options for creating Rplot,
see |
tikz |
options for creating code for tikz plot,
see |
svg |
options for creating code for svg plot,
see |
Details
If rplot is specified, or if neither tikz nor svg is
specified, an R plot is generated, and stored in a png file if the outfile
member of rplot is set. If tikz is specified, the code for a tikz
diagram is stored in the specified outfile; the same applies to svg.
The lav_plot command tries to create a nice plot from the input model,
but the variable names should be kept short, and the nodes in the plot may
sometimes need to be rearranged. As an example, the (slightly modified) example
of the sem function in lavaan produces the first plot shown below.
Using the placenodes argument produces the second plot.
More details on the parameters can be found in the help for
the lav_... functions.
Value
NULL, invisible
See Also
lav_model_plotinfo, lav_plotinfo_positions,
lav_plotinfo_rgraph, lav_plotinfo_tikzcode,
lav_plotinfo_svgcode
Examples
model <- 'alpha11 =~ 1 * x1 + x2 + x3 # latent variable alpha12 <~ x4 + x5 + x6 # composite gamma =~ 1 * x7 + x8 + x9 # latent variable xi =~ 1 * x10 + x11 + x12 + x13 # latent variable x1 ~~ x3 x2 ~~ epsilon2 * x2 x12 ~~ epsilon12 * x12 x4 ~~ epsilon4 * x4 x7 ~~ x9 x10 ~~ x11 + x13 gamma ~~ 0.7 * xi # regressions xi ~ v * alpha11 + t * alpha12 + 1 alpha11 ~ yy * Theta1 + tt1 * 0.12 * alpha12 + ss * gamma Theta1 ~~ alpha12 ' lav_plot(model) lav_plot(model, placenodes=list(Theta1 = c(2, 2.5)), tikz = list(outfile=stdout())) modelml <- ' level: 1 fw =~ y_1 + y_2 + y_3 + y_4 level: 2 fb =~ y_1 + y_2 + y_3 + y_5 y_2 ~~ cv24 * y_5 ' tikzcodeml <- lav_plot(modelml, common_opts = list(auto_subscript = FALSE), svg = list(outfile=stdout()) ) ## Not run: # example creating tex file with the above models zz <- file("testtikz.tex", open="w") writeLines(c( '\documentclass{article}', '\usepackage{amsmath, amssymb}', '\usepackage{amsfonts}', '\usepackage[utf8]{inputenc}', '\usepackage[english]{babel}', '\usepackage{xcolor}', '\usepackage{color}', '\usepackage{tikz}', '\usetikzlibrary {shapes.geometric}', '\begin{document}'), zz) lav_plot(model, tikz = list(outfile = "tmp.tex") ) tmp <- readLines("tmp.tex") writeLines(tmp, zz) writeLines(" ", zz) lav_plot(modelml, common_opts = list(sloped_labels = FALSE, mlovcolors = c("lightgreen", "lightblue")), tikz = list(outfile = "tmp.tex", cex = 1.4) ) tmp <- readLines("tmp.tex") writeLines(tmp, zz) writeLines("\end{document}", zz) close(zz) openPDF <- function(f) { os <- .Platform$OS.type if (os=="windows") shell.exec(normalizePath(f)) else { pdf <- getOption("pdfviewer", default='') if (nchar(pdf)==0) stop("The 'pdfviewer' option is not set. Use options(pdfviewer=...)") system2(pdf, args=c(f)) } } tools::texi2dvi("testtikz.tex", pdf = TRUE, clean = TRUE) openPDF("testtikz.pdf") # example creating html file with the above diagrams zz <- file("demosvg.html", open="w") writeLines(c( '<!DOCTYPE html>', '<html>', '<body>', '<h2>SVG diagrams created by lav_plot R package</h2>'), zz) lav_plot(model, svg = list(outfile = "temp.svg") ) tmp <- readLines("tmp.svg") writeLines(tmp, zz) writeLines("<br />", zz) lav_plot(modelml, common_opts = list(sloped_labels = FALSE), tikz = list(outfile = "tmp.svg") ) tmp <- readLines("tmp.svg") writeLines(tmp, zz) writeLines(c("</body>", "</html>"), zz) close(zz) browseURL("demosvg.html") ## End(Not run)model <- 'alpha11 =~ 1 * x1 + x2 + x3 # latent variable alpha12 <~ x4 + x5 + x6 # composite gamma =~ 1 * x7 + x8 + x9 # latent variable xi =~ 1 * x10 + x11 + x12 + x13 # latent variable x1 ~~ x3 x2 ~~ epsilon2 * x2 x12 ~~ epsilon12 * x12 x4 ~~ epsilon4 * x4 x7 ~~ x9 x10 ~~ x11 + x13 gamma ~~ 0.7 * xi # regressions xi ~ v * alpha11 + t * alpha12 + 1 alpha11 ~ yy * Theta1 + tt1 * 0.12 * alpha12 + ss * gamma Theta1 ~~ alpha12 ' lav_plot(model) lav_plot(model, placenodes=list(Theta1 = c(2, 2.5)), tikz = list(outfile=stdout())) modelml <- ' level: 1 fw =~ y_1 + y_2 + y_3 + y_4 level: 2 fb =~ y_1 + y_2 + y_3 + y_5 y_2 ~~ cv24 * y_5 ' tikzcodeml <- lav_plot(modelml, common_opts = list(auto_subscript = FALSE), svg = list(outfile=stdout()) ) ## Not run: # example creating tex file with the above models zz <- file("testtikz.tex", open="w") writeLines(c( '\documentclass{article}', '\usepackage{amsmath, amssymb}', '\usepackage{amsfonts}', '\usepackage[utf8]{inputenc}', '\usepackage[english]{babel}', '\usepackage{xcolor}', '\usepackage{color}', '\usepackage{tikz}', '\usetikzlibrary {shapes.geometric}', '\begin{document}'), zz) lav_plot(model, tikz = list(outfile = "tmp.tex") ) tmp <- readLines("tmp.tex") writeLines(tmp, zz) writeLines(" ", zz) lav_plot(modelml, common_opts = list(sloped_labels = FALSE, mlovcolors = c("lightgreen", "lightblue")), tikz = list(outfile = "tmp.tex", cex = 1.4) ) tmp <- readLines("tmp.tex") writeLines(tmp, zz) writeLines("\end{document}", zz) close(zz) openPDF <- function(f) { os <- .Platform$OS.type if (os=="windows") shell.exec(normalizePath(f)) else { pdf <- getOption("pdfviewer", default='') if (nchar(pdf)==0) stop("The 'pdfviewer' option is not set. Use options(pdfviewer=...)") system2(pdf, args=c(f)) } } tools::texi2dvi("testtikz.tex", pdf = TRUE, clean = TRUE) openPDF("testtikz.pdf") # example creating html file with the above diagrams zz <- file("demosvg.html", open="w") writeLines(c( '<!DOCTYPE html>', '<html>', '<body>', '<h2>SVG diagrams created by lav_plot R package</h2>'), zz) lav_plot(model, svg = list(outfile = "temp.svg") ) tmp <- readLines("tmp.svg") writeLines(tmp, zz) writeLines("<br />", zz) lav_plot(modelml, common_opts = list(sloped_labels = FALSE), tikz = list(outfile = "tmp.svg") ) tmp <- readLines("tmp.svg") writeLines(tmp, zz) writeLines(c("</body>", "</html>"), zz) close(zz) browseURL("demosvg.html") ## End(Not run)
Position the nodes in the diagram
Description
Computes the positions for the nodes and anchors and control points for the edges in the diagram.
Usage
lav_plotinfo_positions(plotinfo, placenodes = NULL, edgelabelsbelow = NULL, group_covar_indicators = FALSE, debug = FALSE)lav_plotinfo_positions(plotinfo, placenodes = NULL, edgelabelsbelow = NULL, group_covar_indicators = FALSE, debug = FALSE)
Arguments
plotinfo |
The plotinfo structure as returned from |
placenodes |
optional list with members |
edgelabelsbelow |
optional list with members |
group_covar_indicators |
logical, should items with indicators which have an explicit covariance link be placed in the same group, i.e. forced to be on the same side of the diagram? |
debug |
logical, print debug information? |
Details
This function tries to arrange the nodes and the anchor points for the
edges in a way that keeps the diagram reasonably compact, while placing the
dependent variable of a regression to the right of the variables it depends on.
If the result is not what you want, you can inspect the plot with the
lav_plotinfo_rgraph or lav_plot functions and then place some
nodes at a different location (placenodes) and/or move some edge labels
to the other side of the edge (labelsbelow).
For multilevel models – maximum two levels – the nodes in block 2 are grouped
at the top of the diagram and those in block 1 at the bottom. The item
mlrij gives the position of the separation between the blocks.
Value
A plotinfo structure with modified nodes and edges
data.frames, and an integer mlrij giving the position at which a line
should be drawn for multilevel models.
The data.frames have new columns defined as follows:
-
nodes- rij
-
index of the row where the node will be placed, initialized NA.
- kolom
-
index of the column where the node will be placed, initialized NA.
-
edges- vananker
-
character, anchor point for starting node, initialized NA.
- naaranker
-
character, anchor point for destination node, initialized NA.
- controlpt.kol
-
real, column position of control point if the edge has to be drawn as a quadratic Bezier curve.
- controlpt.row
-
real, row position of control point if the edge has to be drawn as a quadratic Bezier curve.
- labelbelow
-
logical, TRUE if label has to be positioned under the line, initialized FALSE.
See Also
lav_model_plotinfo, lav_plotinfo_rgraph,
lav_plot
Examples
model <- 'alfa =~ 1 * x1 + x2 + x3 # latent variable beta <~ x4 + x5 + x6 # composite gamma =~ 1 * x7 + x8 + x9 # latent variable Xi =~ 1 * x10 + x11 + x12 + x13 # latent variable # regressions Xi ~ v * alfa + t * beta + cc * 1 alfa ~ tt * beta + ss * gamma + yy * Theta1 # variances and covariances x2 ~~ cc25 * x5 x3 ~~ cc36 * x6 x3 ~~ cc34 * x4 gamma ~~ 0.55 * gamma ' test <- lav_model_plotinfo(model) (test_positioned <- lav_plotinfo_positions(test))model <- 'alfa =~ 1 * x1 + x2 + x3 # latent variable beta <~ x4 + x5 + x6 # composite gamma =~ 1 * x7 + x8 + x9 # latent variable Xi =~ 1 * x10 + x11 + x12 + x13 # latent variable # regressions Xi ~ v * alfa + t * beta + cc * 1 alfa ~ tt * beta + ss * gamma + yy * Theta1 # variances and covariances x2 ~~ cc25 * x5 x3 ~~ cc36 * x6 x3 ~~ cc34 * x4 gamma ~~ 0.55 * gamma ' test <- lav_model_plotinfo(model) (test_positioned <- lav_plotinfo_positions(test))
Plots a graph in R
Description
Creates a graph in R showing a simple diagram of the model.
Usage
lav_plotinfo_rgraph(plotinfo, sloped_labels = TRUE, outfile = "", addgrid = TRUE, mlovcolors = c("lightgreen", "lightblue"), lightness = 1, italic = TRUE, auto_subscript = TRUE )lav_plotinfo_rgraph(plotinfo, sloped_labels = TRUE, outfile = "", addgrid = TRUE, mlovcolors = c("lightgreen", "lightblue"), lightness = 1, italic = TRUE, auto_subscript = TRUE )
Arguments
plotinfo |
A plotinfo structure as returned from |
sloped_labels |
Logical, should labels be sloped above (or below) the edges? |
outfile |
Character string naming the file in which to store the diagram as a PNG, or NA to show the plot in R. |
addgrid |
Logical, add a grid with indicated 'positions' to the graph? |
mlovcolors |
Array of two colors for distinguishing ov nodes with the same name across the levels of a multilevel model. |
lightness |
A scalar factor to modify the distances between nodes. |
italic |
Should labels be in an italic font? Attention: switching to an italic font is only possible if the label value is not an expression! |
auto_subscript |
Logical, see |
Value
NULL (invisible)
See Also
Examples
model <- 'alpha =~ x1 + x2 + x_3 # latent variable beta <~ x4 + x5 + x6 # composite gamma =~ x7 + x8 + x9 # latent variable Xi =~ x10 + x11 + x12 + x13 # latent variable # regressions Xi ~ v * alpha + t * beta + c * 1 alpha ~ yy * Theta1 + tt * beta + ss * gamma ' test <- lav_model_plotinfo(model) test1 <- lav_plotinfo_positions(test) lav_plotinfo_rgraph(test1, lightness = 1.1) # better position for constant in regressen Xi, no sloped labels test2 <- lav_plotinfo_positions(test, placenodes = list(`1vanXi` = c(2, 5))) lav_plotinfo_rgraph(test2, FALSE, lightness = 1.1) modelml <- ' level: 1 fw =~ 1*y_1 + y_2 + y_3 + y_5 level: 2 fb =~ 1*y_1 + y_2 + y_3 + y_4 y_2 ~~ cv24 * y_4 ' test <- lav_model_plotinfo(modelml) test <- lav_plotinfo_positions(test) lav_plotinfo_rgraph(test, sloped_labels = FALSE, addgrid = FALSE, auto_subscript = FALSE) ## Not run: # example where plot is stored in a PNG file lav_plotinfo_rgraph(test, sloped_labels = FALSE, addgrid = FALSE, auto_subscript = FALSE, outfile="demo_rplot.png") ## End(Not run)model <- 'alpha =~ x1 + x2 + x_3 # latent variable beta <~ x4 + x5 + x6 # composite gamma =~ x7 + x8 + x9 # latent variable Xi =~ x10 + x11 + x12 + x13 # latent variable # regressions Xi ~ v * alpha + t * beta + c * 1 alpha ~ yy * Theta1 + tt * beta + ss * gamma ' test <- lav_model_plotinfo(model) test1 <- lav_plotinfo_positions(test) lav_plotinfo_rgraph(test1, lightness = 1.1) # better position for constant in regressen Xi, no sloped labels test2 <- lav_plotinfo_positions(test, placenodes = list(`1vanXi` = c(2, 5))) lav_plotinfo_rgraph(test2, FALSE, lightness = 1.1) modelml <- ' level: 1 fw =~ 1*y_1 + y_2 + y_3 + y_5 level: 2 fb =~ 1*y_1 + y_2 + y_3 + y_4 y_2 ~~ cv24 * y_4 ' test <- lav_model_plotinfo(modelml) test <- lav_plotinfo_positions(test) lav_plotinfo_rgraph(test, sloped_labels = FALSE, addgrid = FALSE, auto_subscript = FALSE) ## Not run: # example where plot is stored in a PNG file lav_plotinfo_rgraph(test, sloped_labels = FALSE, addgrid = FALSE, auto_subscript = FALSE, outfile="demo_rplot.png") ## End(Not run)
Creates code to show a diagram in svg format
Description
Creates svg code to show a diagram of the model.
Usage
lav_plotinfo_svgcode(plotinfo, outfile = "", sloped_labels = TRUE, standalone = FALSE, stroke_width = 2L, font_size = 20L, idx_font_size = 15L, dy = 5L, mlovcolors = c("lightgreen", "lightblue"), lightness= 1, font_family = "Latin Modern Math, arial, Arial, sans", italic = TRUE, auto_subscript = TRUE )lav_plotinfo_svgcode(plotinfo, outfile = "", sloped_labels = TRUE, standalone = FALSE, stroke_width = 2L, font_size = 20L, idx_font_size = 15L, dy = 5L, mlovcolors = c("lightgreen", "lightblue"), lightness= 1, font_family = "Latin Modern Math, arial, Arial, sans", italic = TRUE, auto_subscript = TRUE )
Arguments
plotinfo |
A plotinfo structure as returned from |
outfile |
A connection or a character string, the file to store the code. |
sloped_labels |
logical, sloped labels for the edges. |
standalone |
logical, should code be added to produce an html file with the svg embedded in it? If FALSE (the default), the outfile (if specified) must have the file extension 'svg'; if TRUE, the file extension must be 'htm' or 'html'. |
stroke_width |
Value for stroke-width parameter in svg. |
font_size |
An integer specifying the normal font size to use. |
idx_font_size |
An integer specifying the font size to use for a subscript. |
dy |
An integer specifying the distance by which to move the baseline of the subscript. |
mlovcolors |
Array of two colors for distinguishing ov nodes with the same name across the levels of a multilevel model. |
lightness |
A scalar factor to modify the distances between nodes. |
font_family |
Fonts to be tried for rendering the labels. The first one, Latin Modern Math, is close to the default font used in tikz for mathematical expressions and can be downloaded from CTAN. |
italic |
Should labels be in an italic font? If FALSE, the labels are shown in mathrm font. |
auto_subscript |
Logical, see |
Value
NULL (invisible)
See Also
Examples
model <- 'alpha =~ x1 + x2 + x3 # latent variable beta <~ x4 + x5 + x6 # composite gamma =~ x7 + x8 + x9 # latent variable Xi =~ x10 + x11 + x12 + x13 # latent variable # regressions Xi ~ v * alpha + t * beta + 1 alpha ~ yy * Theta1 + tt * beta + ss * gamma ' test <- lav_model_plotinfo(model) test <- lav_plotinfo_positions(test) lav_plotinfo_svgcode(test) # no file given, so output to R console modelml <- ' level: 1 fw =~ 1*y_1 + y_2 + y_3 + y_5 level: 2 fb =~ 1*y_1 + y_2 + y_3 + y_4 y_2 ~~ cv24 * y_4 ' testml <- lav_model_plotinfo(modelml) testml <- lav_plotinfo_positions(testml) # in the line hereunder no file is given, so output to R console lav_plotinfo_svgcode(testml, sloped_labels = FALSE, standalone = TRUE, auto_subscript = FALSE) ## Not run: # example creating html file with the above diagrams zz <- file("demosvg.html", open="w") writeLines(c( '<!DOCTYPE html>', '<html>', '<body>', '<h2>SVG diagrams created by lav_plot R package</h2>'), zz) lav_plotinfo_svgcode(test, outfile = "temp.svg") tmp <- readLines("tmp.svg") writeLines(tmp, zz) writeLines("<br />", zz) lav_plotinfo_svgcode(testml, outfile = "temp.svg", sloped_labels = FALSE, standalone = TRUE) tmp <- readLines("tmp.svg") writeLines(tmp, zz) writeLines(c("</body>", "</html>"), zz) close(zz) browseURL("demosvg.html") ## End(Not run)model <- 'alpha =~ x1 + x2 + x3 # latent variable beta <~ x4 + x5 + x6 # composite gamma =~ x7 + x8 + x9 # latent variable Xi =~ x10 + x11 + x12 + x13 # latent variable # regressions Xi ~ v * alpha + t * beta + 1 alpha ~ yy * Theta1 + tt * beta + ss * gamma ' test <- lav_model_plotinfo(model) test <- lav_plotinfo_positions(test) lav_plotinfo_svgcode(test) # no file given, so output to R console modelml <- ' level: 1 fw =~ 1*y_1 + y_2 + y_3 + y_5 level: 2 fb =~ 1*y_1 + y_2 + y_3 + y_4 y_2 ~~ cv24 * y_4 ' testml <- lav_model_plotinfo(modelml) testml <- lav_plotinfo_positions(testml) # in the line hereunder no file is given, so output to R console lav_plotinfo_svgcode(testml, sloped_labels = FALSE, standalone = TRUE, auto_subscript = FALSE) ## Not run: # example creating html file with the above diagrams zz <- file("demosvg.html", open="w") writeLines(c( '<!DOCTYPE html>', '<html>', '<body>', '<h2>SVG diagrams created by lav_plot R package</h2>'), zz) lav_plotinfo_svgcode(test, outfile = "temp.svg") tmp <- readLines("tmp.svg") writeLines(tmp, zz) writeLines("<br />", zz) lav_plotinfo_svgcode(testml, outfile = "temp.svg", sloped_labels = FALSE, standalone = TRUE) tmp <- readLines("tmp.svg") writeLines(tmp, zz) writeLines(c("</body>", "</html>"), zz) close(zz) browseURL("demosvg.html") ## End(Not run)
Creates code to show a diagram in tikz format
Description
Creates the code to make a diagram in tikz.
Usage
lav_plotinfo_tikzcode(plotinfo, outfile = "", cex = 1.3, sloped_labels = TRUE, standalone = FALSE, mlovcolors = c("lightgreen", "lightblue"), lightness = 1, italic = TRUE, auto_subscript = TRUE )lav_plotinfo_tikzcode(plotinfo, outfile = "", cex = 1.3, sloped_labels = TRUE, standalone = FALSE, mlovcolors = c("lightgreen", "lightblue"), lightness = 1, italic = TRUE, auto_subscript = TRUE )
Arguments
plotinfo |
A plotinfo structure as returned from |
outfile |
A connection or a character string, the file to store the code. |
cex |
Minimum distance between nodes in cm. |
sloped_labels |
logical, sloped labels for the edges. |
standalone |
logical, should code be added to make the TeX file standalone? |
mlovcolors |
Array of two colors for distinguishing ov nodes with the same name across the levels of a multilevel model. |
lightness |
A scalar factor to modify the distances between nodes. |
italic |
Should labels be in an italic font? If FALSE, the labels are shown in mathrm font. |
auto_subscript |
Logical, see |
Value
NULL, invisible
See Also
Examples
model <- 'alpha =~ x1 + x2 + x3 # latent variable beta <~ x4 + x5 + x6 # composite gamma =~ x7 + x8 + x9 # latent variable Xi =~ x10 + x11 + x12 + x13 # latent variable # regressions Xi ~ v * alpha + t * beta + 1 alpha ~ yy * Theta1 + tt * beta + ss * gamma ' test <- lav_model_plotinfo(model) test <- lav_plotinfo_positions(test) lav_plotinfo_tikzcode(test) # no file given, so output to R console modelml <- ' level: 1 fw =~ 1*y_1 + y_2 + y_3 + y_5 level: 2 fb =~ 1*y_1 + y_2 + y_3 + y_4 y_2 ~~ cv24 * y_4 ' testml <- lav_model_plotinfo(modelml) testml <- lav_plotinfo_positions(testml) # in the line hereunder no file is given, so output to R console lav_plotinfo_tikzcode(testml, cex = 1.4, sloped_labels = FALSE, standalone = TRUE, auto_subscript = FALSE) ## Not run: # example creating tex file with the above diagrams zz <- file("testtikz.tex", open="w") writeLines(c( '\documentclass{article}', '\usepackage{amsmath, amssymb}', '\usepackage{amsfonts}', '\usepackage[utf8]{inputenc}', '\usepackage[english]{babel}', '\usepackage{xcolor}', '\usepackage{color}', '\usepackage{tikz}', '\usetikzlibrary {shapes.geometric}', '\begin{document}'), zz) lav_plotinfo_tikzcode(test, outfile = "temp.tex") tmp <- readLines("tmp.tex") writeLines(tmp, zz) writeLines(" ", zz) lav_plotinfo_tikzcode(testml, outfile = "temp.tex", cex = 1.4, sloped_labels = FALSE, auto_subscript = FALSE) tmp <- readLines("tmp.tex") writeLines(tmp, zz) writeLines("\end{document}", zz) close(zz) openPDF <- function(f) { os <- .Platform$OS.type if (os=="windows") shell.exec(normalizePath(f)) else { pdf <- getOption("pdfviewer", default='') if (nchar(pdf)==0) stop("The 'pdfviewer' option is not set. Use options(pdfviewer=...)") system2(pdf, args=c(f)) } } tools::texi2dvi("testtikz.tex", pdf = TRUE, clean = TRUE) openPDF("testtikz.pdf") ## End(Not run)model <- 'alpha =~ x1 + x2 + x3 # latent variable beta <~ x4 + x5 + x6 # composite gamma =~ x7 + x8 + x9 # latent variable Xi =~ x10 + x11 + x12 + x13 # latent variable # regressions Xi ~ v * alpha + t * beta + 1 alpha ~ yy * Theta1 + tt * beta + ss * gamma ' test <- lav_model_plotinfo(model) test <- lav_plotinfo_positions(test) lav_plotinfo_tikzcode(test) # no file given, so output to R console modelml <- ' level: 1 fw =~ 1*y_1 + y_2 + y_3 + y_5 level: 2 fb =~ 1*y_1 + y_2 + y_3 + y_4 y_2 ~~ cv24 * y_4 ' testml <- lav_model_plotinfo(modelml) testml <- lav_plotinfo_positions(testml) # in the line hereunder no file is given, so output to R console lav_plotinfo_tikzcode(testml, cex = 1.4, sloped_labels = FALSE, standalone = TRUE, auto_subscript = FALSE) ## Not run: # example creating tex file with the above diagrams zz <- file("testtikz.tex", open="w") writeLines(c( '\documentclass{article}', '\usepackage{amsmath, amssymb}', '\usepackage{amsfonts}', '\usepackage[utf8]{inputenc}', '\usepackage[english]{babel}', '\usepackage{xcolor}', '\usepackage{color}', '\usepackage{tikz}', '\usetikzlibrary {shapes.geometric}', '\begin{document}'), zz) lav_plotinfo_tikzcode(test, outfile = "temp.tex") tmp <- readLines("tmp.tex") writeLines(tmp, zz) writeLines(" ", zz) lav_plotinfo_tikzcode(testml, outfile = "temp.tex", cex = 1.4, sloped_labels = FALSE, auto_subscript = FALSE) tmp <- readLines("tmp.tex") writeLines(tmp, zz) writeLines("\end{document}", zz) close(zz) openPDF <- function(f) { os <- .Platform$OS.type if (os=="windows") shell.exec(normalizePath(f)) else { pdf <- getOption("pdfviewer", default='') if (nchar(pdf)==0) stop("The 'pdfviewer' option is not set. Use options(pdfviewer=...)") system2(pdf, args=c(f)) } } tools::texi2dvi("testtikz.tex", pdf = TRUE, clean = TRUE) openPDF("testtikz.pdf") ## End(Not run)
lavaan samplestats functions
Description
Utility functions related to the sample statistics
Usage
# generate samplestats object from full data lav_samp_from_data(lavdata = NULL, lavoptions = NULL, wls_v = NULL, nacov = NULL)# generate samplestats object from full data lav_samp_from_data(lavdata = NULL, lavoptions = NULL, wls_v = NULL, nacov = NULL)
Arguments
lavdata |
A lavdata object. |
lavoptions |
A named list. The Options slot from a lavaan object. |
wls_v |
A user provided weight matrix. |
nacov |
A user provided matrix containing the elements of (N times) the asymptotic variance-covariance matrix of the sample statistics. For a multiple group analysis, a list with an asymptotic variance-covariance matrix for each group. |
Examples
# generate syntax for an independence model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) # extract data slot and options lavdata <- fit@Data lavoptions <- lavInspect(fit, "options") # generate sample statistics object sampleStats <- lav_samp_from_data(lavdata = lavdata, lavoptions = lavoptions)# generate syntax for an independence model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) # extract data slot and options lavdata <- fit@Data lavoptions <- lavInspect(fit, "options") # generate sample statistics object sampleStats <- lav_samp_from_data(lavdata = lavdata, lavoptions = lavoptions)
Fit a Latent Variable Model
Description
Fit a latent variable model.
Usage
lavaan(model = NULL, data = NULL, ordered = NULL, aux = NULL, sampling_weights = NULL, sample_cov = NULL, sample_mean = NULL, sample_th = NULL, sample_nobs = NULL, group = NULL, cluster = NULL, constraints = "", wls_v = NULL, nacov = NULL, ov_order = "model", slot_options = NULL, slot_par_table = NULL, slot_sample_stats = NULL, slot_data = NULL, slot_model = NULL, slot_cache = NULL, sloth1 = NULL, ...)lavaan(model = NULL, data = NULL, ordered = NULL, aux = NULL, sampling_weights = NULL, sample_cov = NULL, sample_mean = NULL, sample_th = NULL, sample_nobs = NULL, group = NULL, cluster = NULL, constraints = "", wls_v = NULL, nacov = NULL, ov_order = "model", slot_options = NULL, slot_par_table = NULL, slot_sample_stats = NULL, slot_data = NULL, slot_model = NULL, slot_cache = NULL, sloth1 = NULL, ...)
Arguments
model |
A description of the user-specified model. Typically, the model
is described using the lavaan model syntax. See
|
data |
An optional data frame containing the observed variables used in the model. If some variables are declared as ordered factors, lavaan will treat them as ordinal variables. |
ordered |
Character vector. Only used if the data is in a data.frame. Treat these variables as ordered (ordinal) variables, if they are endogenous in the model. Importantly, all other variables will be treated as numeric (unless they are declared as ordered in the data.frame.) Since 0.6-4, ordered can also be logical. If TRUE, all observed endogenous variables are treated as ordered (ordinal). If FALSE, all observed endogenous variables are considered to be numeric (again, unless they are declared as ordered in the data.frame.) |
aux |
Character vector. Names of auxiliary observed variables. Auxiliary
variables are not part of the user-specified model; they are used to make
the missing-at-random (MAR) assumption more plausible under missing data.
Only available (for now) with continuous data and one of
|
sampling_weights |
A variable name in the data frame containing
sampling weight information. Currently only available for non-clustered
data. Depending on the |
sample_cov |
Numeric matrix. A sample variance-covariance matrix. The rownames and/or colnames must contain the observed variable names. For a multiple group analysis, a list with a variance-covariance matrix for each group. |
sample_mean |
A sample mean vector. For a multiple group analysis, a list with a mean vector for each group. |
sample_th |
Vector of sample-based thresholds. For a multiple group analysis, a list with a vector of thresholds for each group. |
sample_nobs |
Number of observations if the full data frame is missing and only sample moments are given. For a multiple group analysis, a list or a vector with the number of observations for each group. |
group |
Character. A variable name in the data frame defining the groups in a multiple group analysis. |
cluster |
Character. A (single) variable name in the data frame defining the clusters in a two-level dataset. |
constraints |
Additional (in)equality constraints not yet included in the
model syntax. See |
wls_v |
A user provided weight matrix to be used by estimator |
nacov |
A user provided matrix containing the elements of (N times)
the asymptotic variance-covariance matrix of the sample statistics.
For a multiple group analysis, a list with an asymptotic
variance-covariance matrix for each group. See the |
ov_order |
Character. If |
slot_options |
Options slot from a fitted lavaan object. If provided, no new Options slot will be created by this call. |
slot_par_table |
ParTable slot from a fitted lavaan object. If provided, no new ParTable slot will be created by this call. |
slot_sample_stats |
SampleStats slot from a fitted lavaan object. If provided, no new SampleStats slot will be created by this call. |
slot_data |
Data slot from a fitted lavaan object. If provided, no new Data slot will be created by this call. |
slot_model |
Model slot from a fitted lavaan object. If provided, no new Model slot will be created by this call. |
slot_cache |
Cache slot from a fitted lavaan object. If provided, no new Cache slot will be created by this call. |
sloth1 |
h1 slot from a fitted lavaan object. If provided, no new h1 slot will be created by this call. |
... |
Many more options can be specified, using 'name = value'.
See |
Value
An object of class lavaan, for which several methods
are available, including a summary method.
References
Yves Rosseel (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. doi:10.18637/jss.v048.i02
See Also
Examples
# The Holzinger and Swineford (1939) example HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- lavaan(HS.model, data=HolzingerSwineford1939, auto.var=TRUE, auto.fix.first=TRUE, auto.cov.lv.x=TRUE) summary(fit, fit.measures=TRUE)# The Holzinger and Swineford (1939) example HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- lavaan(HS.model, data=HolzingerSwineford1939, auto.var=TRUE, auto.fix.first=TRUE, auto.cov.lv.x=TRUE) summary(fit, fit.measures=TRUE)
Class For Representing A (Fitted) Latent Variable Model
Description
The lavaan class represents a (fitted) latent variable
model. It contains a description of the model as specified by the user,
a summary of the data, an internal matrix representation, and if the model
was fitted, the fitting results.
Objects from the Class
Objects can be created via the
cfa, sem, growth or
lavaan functions.
Slots
-
version: -
The lavaan package version used to create this object
-
call: -
The function call as returned by
match.call(). -
timing: -
The elapsed time (user+system) for various parts of the program as a list, including the total time.
-
Options: -
Named list of options that were provided by the user, or filled-in automatically.
-
ParTable: -
Named list describing the model parameters. Can be coerced to a data.frame. In the documentation, this is called the ‘parameter table’.
-
pta: -
Named list containing parameter table attributes.
-
Data: -
Object of internal class
"Data": information about the data. -
SampleStats: -
Object of internal class
"SampleStats": sample statistics -
Model: -
Object of internal class
"Model": the internal (matrix) representation of the model -
Cache: -
List of objects that are computed only once and reused many times.
-
Fit: -
Object of internal class
"Fit": the results of fitting the model. No longer used. -
boot: -
List. Results and information about the bootstrap.
-
optim: -
List. Information about the optimization.
-
loglik: -
List. Information about the loglikelihood of the model (if maximum likelihood was used).
-
implied: -
List. Model implied statistics.
-
vcov: -
List. Information about the variance matrix (vcov) of the model parameters.
-
test: -
List. Different test statistics.
-
h1: -
List. Information about the unrestricted h1 model (if available).
-
baseline: -
List. Information about a baseline model (often the independence model) (if available).
-
internal: -
List. For internal use only.
-
external: -
List. Empty slot to be used by add-on packages.
Methods
- coef
-
signature(object = "lavaan", type = "free"): Returns the estimates of the parameters in the model as a named numeric vector. Iftype="free", only the free parameters are returned. Iftype="user", all parameters listed in the parameter table are returned, including constrained and fixed parameters. - fitted.values
-
signature(object = "lavaan"): Returns the implied moments of the model as a list with two elements (per group):covfor the implied covariance matrix, andmeanfor the implied mean vector. If only the covariance matrix was analyzed, the implied mean vector will be zero. - fitted
-
signature(object = "lavaan"): an alias forfitted.values. - residuals
-
signature(object = "lavaan", type="raw"): Iftype = "raw", this function returns the raw (= unscaled) difference between the observed and the expected (model-implied) summary statistics. Iftype = "cor", ortype = "cor.bollen", the observed and model implied covariance matrices are first transformed to a correlation matrix (usingcov2cor()), before the residuals are computed. Iftype = "cor.bentler", both the observed and model implied covariance matrices are rescaled by dividing the elements by the square roots of the corresponding variances of the observed covariance matrix. Iftype="normalized", the residuals are divided by the square root of the asymptotic variance of the corresponding summary statistic (the variance estimate depends on the choice for theseargument). Unfortunately, these normalized residuals are not entirely correct, and this option is retained only for historical interest. Iftype="standardized", the residuals are divided by the square root of the asymptotic variance of these residuals. The resulting standardized residuals can be interpreted as z-scores. Iftype="standardized.mplus", the residuals are divided by the square root of the asymptotic variance of these residuals. However, a simplified formula is used (see the Mplus reference below) which often results in negative estimates for the variances, resulting in manyNAvalues for the standardized residuals. - resid
-
signature(object = "lavaan"): an alias forresiduals - vcov
-
signature(object = "lavaan"): returns the covariance matrix of the estimated parameters. - predict
-
signature(object = "lavaan"): compute factor scores for all cases that are provided in the data frame. For complete data only. - anova
-
signature(object = "lavaan"): returns model comparison statistics. This method is just a wrapper around the functionlavTestLRT. If only a single argument (a fitted model) is provided, this model is compared to the unrestricted model. If two or more arguments (fitted models) are provided, the models are compared in a sequential order. Test statistics are based on the likelihood ratio test. For more details and further options, see thelavTestLRTpage. - update
-
signature(object = "lavaan", model, add, ..., evaluate = TRUE): update a fitted lavaan object and evaluate it (unlessevaluate = FALSE). Note that we use the environment that is stored within the lavaan object, which is not necessarily the parent frame. Theaddargument is analogous to the one described in thelavTestScorepage, and can be used to add parameters to the specified model rather than passing an entirely newmodelargument. - nobs
-
signature(object = "lavaan"): returns the effective number of observations used when fitting the model. In a multiple group analysis, this is the sum of all observations per group. - logLik
-
signature(object = "lavaan"): returns the log-likelihood of the fitted model, if maximum likelihood estimation was used. TheAICandBICmethods automatically work vialogLik(). - show
-
signature(object = "lavaan"): Print a short summary of the model fit - summary
-
signature(object = "lavaan", header = TRUE, fit.measures = FALSE, residuals = FALSE, estimates = TRUE, ci = FALSE, fmi = FALSE, standardized = FALSE, std = standardized, std.nox = FALSE, remove.system.eq = TRUE, remove.eq = TRUE, remove.ineq = TRUE, remove.def = FALSE, remove.nonfree = FALSE, remove.step1 = TRUE, remove.unused = TRUE, plabel = FALSE, cov.std = TRUE, rsquare = FALSE, baseline.model = NULL, h1.model = NULL, fm.args = list(standard.test = "default", scaled.test = "default", rmsea.ci.level = 0.90, rmsea.h0.closefit = 0.05, rmsea.h0.notclosefit = 0.08, robust = TRUE, cat.check.pd = TRUE), modindices = FALSE, srmr.close.h0 = NULL, nd = 3L, cutoff = 0.3, dot.cutoff = 0.1): Print a nice summary of the model estimates. Ifheader = TRUE, the header section (including fit measures) is printed. Iffit.measures = TRUE, additional fit measures are added to the header section.fit.measurescan also be a list, which allows one to set options related to the fit measures. SeefitMeasuresfor more details. Ifresiduals = TRUE, a residuals section is added (the largest residuals and the residual summary, printed as bylavResidualswithoutput = "text"); the underlyinglavResiduals(object, output = "list")result is stored as theresidualselement of the summary object.residualscan also be a list of arguments passed on tolavResiduals(for exampleresiduals = list(type = "raw", n.largest = 10)). If bothfit.measures = TRUEandresiduals = TRUEand the residual summary is the SRMR (the default), the SRMR is removed from the fit measures section to avoid printing it twice. Ifestimates = TRUE, print the parameter estimates section. Ifci = TRUE, add confidence intervals to the parameter estimates section. Iffmi = TRUE, add the fmi (fraction of missing information) column, if it is available. Ifstandardized = TRUEor a character vector, the standardized solution is also printed (seelavParameterEstimates). Note that SEs and tests are still based on unstandardized estimates. UsestandardizedSolutionto obtain SEs and test statistics for standardized estimates. Thestd.noxargument is deprecated; thestandardizedargument allows"std.nox"solution to be specifically requested. Thestandardizedargument may also be a character vector of (observed) variable names (for examplec("x1", "x2")); only the parameters involving these variables are then standardized, and the result is shown in aStd.usrcolumn. This generalizes"std.nox", where the exogenousxvariables are the ones left unstandardized. Ifremove.system.eq = TRUE, the system-generated equality constraints (using plabels) are not shown. Ifremove.eq = TRUEorremove.ineq = TRUE, the user-specified (in)equality constraints are not shown. Ifremove.def = TRUE, the user-specified parameter definitions are not shown. Ifremove.nonfree = TRUE, the nonfree parameters are not shown. Ifremove.step1 = TRUE, the parameters of the measurement part are not shown (only used when usingsam().) Ifremove.unused = TRUE, automatically added parameters that are fixed to their default (0 or 1) values are removed. Ifrsquare = TRUE, the R-Square values for the dependent variables in the model are printed. Thefm.argslist allows one to set options related to the fit measures (seefitMeasures).baseline.modelandh1.modelallow one to specify user-defined baseline and/or h1 models for the fit measures. If the model is an exploratory factor analysis (EFA) model, EFA related information is printed automatically. Thecutoffanddot.cutoffarguments control how the factor loadings are displayed: loadings whose absolute value is at or abovecutoffare shown as numbers; loadings whose absolute value falls betweendot.cutoffandcutoffare replaced by a dot; loadings whose absolute value is belowdot.cutoffare left blank. Ifmodindices = TRUEormodindicesis a list, modification indices are printed for all fixed parameters. The argumentnddetermines the number of digits after the decimal point to be printed (currently only in the parameter estimates section.) Historically, nothing was returned, but since 0.6-12, a list is returned of classlavaan.summaryfor which a print function is available.
References
Yves Rosseel (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. doi:10.18637/jss.v048.i02
Standardized Residuals in Mplus. Document retrieved from URL https://www.statmodel.com/download/StandardizedResiduals.pdf
See Also
cfa, sem,
fitMeasures, standardizedSolution,
lavParameterEstimates, lavInspect,
modindices
Examples
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) summary(fit, standardized = TRUE, fit.measures = TRUE, rsquare = TRUE) fitted(fit) coef(fit) resid(fit, type = "normalized")HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) summary(fit, standardized = TRUE, fit.measures = TRUE, rsquare = TRUE) fitted(fit) coef(fit) resid(fit, type = "normalized")
Deprecated functions in lavaan package
Description
Deprecated functions in lavaan.
Details
The functions listed in the first column below are deprecated; calls to them should be replaced by calls to the corresponding function in the second column.
| # bootstrapLavaan | lavBootstrap |
| char2num | lav_char2num |
| cor2cov | lav_cor2cov |
| getCov | lav_getcov |
| inspectSampleCov | lavInspectSampleCov |
| # lavaanNames | lavNames |
| mplus2lavaan.modelSyntax | lav_mplus_syntax_model |
| mplus2lavaan | lav_Mplus_lavaan |
| parameterestimates | lavParameterEstimates |
| # simulateData | lavSimulateData |
Fit List of Latent Variable Models
Description
Fit the same latent variable model to a (potentially large) number of datasets.
Usage
lavaanList(model = NULL, data_list = NULL, data_function = NULL, data_function_args = list(), ndat = length(data_list), cmd = "lavaan", ..., store_slots = c("partable"), fun = NULL, show_progress = FALSE, store_failed = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 1L, na.rm = TRUE), cl = NULL, iseed = NULL) semList(model = NULL, data_list = NULL, data_function = NULL, data_function_args = list(), ndat = length(data_list), ..., store_slots = c("partable"), fun = NULL, show_progress = FALSE, store_failed = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 1L, na.rm = TRUE), cl = NULL, iseed = NULL) cfaList(model = NULL, data_list = NULL, data_function = NULL, data_function_args = list(), ndat = length(data_list), ..., store_slots = c("partable"), fun = NULL, show_progress = FALSE, store_failed = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 1L, na.rm = TRUE), cl = NULL, iseed = NULL)lavaanList(model = NULL, data_list = NULL, data_function = NULL, data_function_args = list(), ndat = length(data_list), cmd = "lavaan", ..., store_slots = c("partable"), fun = NULL, show_progress = FALSE, store_failed = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 1L, na.rm = TRUE), cl = NULL, iseed = NULL) semList(model = NULL, data_list = NULL, data_function = NULL, data_function_args = list(), ndat = length(data_list), ..., store_slots = c("partable"), fun = NULL, show_progress = FALSE, store_failed = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 1L, na.rm = TRUE), cl = NULL, iseed = NULL) cfaList(model = NULL, data_list = NULL, data_function = NULL, data_function_args = list(), ndat = length(data_list), ..., store_slots = c("partable"), fun = NULL, show_progress = FALSE, store_failed = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 1L, na.rm = TRUE), cl = NULL, iseed = NULL)
Arguments
model |
A description of the user-specified model. Typically, the model
is described using the lavaan model syntax. See
|
data_list |
List. Each element contains a full data frame containing the observed variables used in the model. |
data_function |
Function. A function that generates a full data frame containing the observed variables used in the model. It can also be a matrix, if the columns are named. |
data_function_args |
List. Optional list of arguments that are passed
to the |
ndat |
Integer. The number of datasets that should be generated using
the |
cmd |
Character. The command used to run the SEM models. The possible
choices are |
... |
Other named arguments for the |
store_slots |
Character vector. Which slots (from a lavaan object)
should be stored for each dataset? The possible choices are
|
fun |
Function. A function which when applied to the
|
store_failed |
Logical. If |
parallel |
The type of parallel operation to be used (if any). If
missing, the default is |
ncpus |
Integer. The number of processes to be used in parallel operation: typically one would set this to the number of available CPUs. |
cl |
An optional parallel or snow cluster for use if
|
iseed |
An integer to set the seed. Or NULL if no reproducible seeds are
needed. To make this work, make sure the first
RNGkind() element is |
show_progress |
If |
Value
An object of class lavaanList, for which several methods
are available, including a summary method.
See Also
class lavaanList
Examples
# The Holzinger and Swineford (1939) example HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' # a data generating function generateData <- function() lavSimulateData(HS.model, sample_nobs = 100) set.seed(1234) fit <- semList(HS.model, data_function = generateData, ndat = 5, store_slots = "partable") # show parameter estimates, per dataset coef(fit)# The Holzinger and Swineford (1939) example HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' # a data generating function generateData <- function() lavSimulateData(HS.model, sample_nobs = 100) set.seed(1234) fit <- semList(HS.model, data_function = generateData, ndat = 5, store_slots = "partable") # show parameter estimates, per dataset coef(fit)
Class For Representing A List of (Fitted) Latent Variable Models
Description
The lavaanList class represents a collection of (fitted)
latent variable models, fitted to a (potentially large) number of datasets.
It contains information about the model (which is always the same),
and, for every dataset, a set of (user-specified) slots from a regular
lavaan object.
Objects from the Class
Objects can be created via the
cfaList, semList, or
lavaanList functions.
Slots
-
version: -
The lavaan package version used to create this object
-
call: -
The function call as returned by
match.call(). -
Options: -
Named list of options that were provided by the user, or filled-in automatically.
-
ParTable: -
Named list describing the model parameters. Can be coerced to a data.frame. In the documentation, this is called the ‘parameter table’.
-
pta: -
Named list containing parameter table attributes.
-
Data: -
Object of internal class
"Data": information about the data. -
Model: -
Object of internal class
"Model": the internal (matrix) representation of the model -
meta: -
List containing additional flags. For internal use only.
-
timingList: -
List. Timing slot per dataset.
-
ParTableList: -
List. ParTable slot per dataset.
-
DataList: -
List. Data slot per dataset.
-
SampleStatsList: -
List. SampleStats slot per dataset.
-
CacheList: -
List. Cache slot per dataset.
-
vcovList: -
List. vcov slot per dataset.
-
testList: -
List. test slot per dataset.
-
optimList: -
List. optim slot per dataset.
-
impliedList: -
List. implied slot per dataset.
-
h1List: -
List. h1 slot per dataset.
-
loglikList: -
List. loglik slot per dataset.
-
baselineList: -
List. baseline slot per dataset.
-
funList: -
List. fun slot per dataset.
-
internalList: -
List. internal slot per dataset.
-
external: -
List. Empty slot to be used by add-on packages.
Methods
- coef
-
signature(object = "lavaanList", type = "free"): Returns the estimates of the parameters in the model as the columns in a matrix; each column corresponds to a different dataset. Iftype="free", only the free parameters are returned. Iftype="user", all parameters listed in the parameter table are returned, including constrained and fixed parameters. - summary
-
signature(object = "lavaanList", header = TRUE, estimates = TRUE, print = TRUE, nd = 3L, simulate.args = list(est.bias = TRUE, se.bias = TRUE, se.bias.med = TRUE, prop.sig = TRUE, coverage = TRUE, level = 0.95, trim = 0)): Print a summary of the collection of fitted models. Ifheader = TRUE, the header section is printed. Ifestimates = TRUE, print the parameter estimates section. Ifprint = TRUE, the summary is printed to the screen. The argumentnddetermines the number of digits after the decimal point to be printed (currently only in the parameter estimates section.) The argumentsimulate.argsis only used if the meta slot indicates that the parameter tables are obtained in the context of a simulation. The options switch on/off the columns that are printed, and thetrimoption determines the amount of trimming that is used when taking the average (or standard deviation) across all replications. Ifse.bias.med = TRUE(the default, only relevant whense.bias = TRUE), two additional columns are printed:se.med(the median, rather than the mean, of the computed standard errors across replications) andse.bias.med(the ratiose.med/se.obs). The median is a robust alternative to the mean-basedse.ave/se.bias, which can be dominated by a few outliers for nonlinear defined parameters (e.g. ratios with near-zero denominators in some replications).
See Also
Bootstrapping a Lavaan Model
Description
Bootstrap the LRT, or any other statistic (or vector of statistics) you can extract from a fitted lavaan object.
Usage
lavBootstrap(object, r = 1000L, type = "ordinary", verbose = FALSE, fun = "coef", keep_idx = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 2L, na.rm = TRUE), cl = NULL, iseed = NULL, h0_rmsea = NULL, ...) bootstrapLavaan(object, r = 1000L, type = "ordinary", verbose = FALSE, fun = "coef", keep_idx = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 2L, na.rm = TRUE), cl = NULL, iseed = NULL, h0_rmsea = NULL, ...)lavBootstrap(object, r = 1000L, type = "ordinary", verbose = FALSE, fun = "coef", keep_idx = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 2L, na.rm = TRUE), cl = NULL, iseed = NULL, h0_rmsea = NULL, ...) bootstrapLavaan(object, r = 1000L, type = "ordinary", verbose = FALSE, fun = "coef", keep_idx = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 2L, na.rm = TRUE), cl = NULL, iseed = NULL, h0_rmsea = NULL, ...)
Arguments
object |
An object of class |
r |
Integer. The number of bootstrap draws. |
type |
If |
fun |
A function which when applied to the |
... |
Other named arguments for |
verbose |
If |
keep_idx |
If |
parallel |
The type of parallel operation to be used (if any). If
missing, the default is |
ncpus |
Integer: number of processes to be used in parallel operation.
By default
this is the number of cores (as detected by |
cl |
An optional parallel or snow cluster for use if
|
iseed |
An integer to set the seed. Or NULL if no reproducible results are
needed. This works for both serial (non-parallel) and parallel settings.
Internally, |
h0_rmsea |
Only used if |
Details
The fun function can return either a scalar or a numeric vector.
This function can be an existing function (for example coef) or
can be a custom defined function. For example:
myFUN <- function(x) {
# require(lavaan)
modelImpliedCov <- fitted(x)$cov
vech(modelImpliedCov)
}
If parallel="snow", it is imperative that the require(lavaan)
is included in the custom function.
When the fitted model was estimated with clustered or multilevel data (i.e., a
cluster= argument was used), the bootstrap automatically switches to a
cluster bootstrap: instead of resampling individual observations, whole
(level-2) clusters are resampled with replacement, keeping all level-1
observations within a selected cluster together. The number of clusters is held
fixed (equal to the number of clusters in the original data), while the total
number of observations may vary from one bootstrap sample to the next. A cluster
that is drawn more than once is treated as several distinct clusters. This
resampling scheme preserves the within-cluster dependence and is the
appropriate bootstrap both for two-level models and for single-level models with
cluster-robust standard errors. It is currently only available for a single
cluster (level-2) variable, and the "bca" confidence interval type
(in parameterEstimates) is not supported in this case.
When the fitted model contains rotated exploratory factors (EFA or ESEM; that
is, the model syntax uses the efa() modifier together with a
rotation= method other than "none"), bootstrap standard errors and
confidence intervals (requested via se = "bootstrap" when fitting the
model) are computed for the rotated solution. Each bootstrap sample is
refit and rotated, and its factors are then aligned (reordered and reflected) to
the original (full-sample) rotated solution before their variability is used.
This alignment resolves the rotational indeterminacy (the sign and order of the
exploratory factors), which would otherwise inflate the standard errors. Note
that the raw bootstrap coefficients returned by lavBootstrap(object,
fun = "coef") are not aligned to a reference solution in this way.
Value
For lavBootstrap(), the bootstrap distribution of the value(s)
returned by fun, when the object can be simplified to a vector.
Author(s)
Yves Rosseel and Leonard Vanbrabant. Ed Merkle contributed Yuan's bootstrap. Improvements to Yuan's bootstrap were contributed by Hao Wu and Chuchu Cheng. The handling of iseed was contributed by Shu Fai Cheung.
References
Bollen, K. and Stine, r. (1992) Bootstrapping Goodness of Fit Measures in Structural Equation Models. Sociological Methods and Research, 21, 205–229.
Yuan, K.-H., Hayashi, K., & Yanagihara, H. (2007). A class of population covariance matrices in the bootstrap approach to covariance structure analysis. Multivariate Behavioral Research, 42, 261–281.
Field, C. A., & Welsh, A. H. (2007). Bootstrapping clustered data. Journal of the Royal Statistical Society: Series B, 69, 369–390.
Examples
# fit the Holzinger and Swineford (1939) example HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939, se="none") # get the test statistic for the original sample T.orig <- fitMeasures(fit, "chisq") # bootstrap to get bootstrap test statistics # we only generate 10 bootstrap samples in this example; in practice # you may wish to use a much higher number T.boot <- lavBootstrap(fit, r=10, type="bollen.stine", fun=fitMeasures, fit.measures="chisq") # compute a bootstrap based p-value pvalue.boot <- length(which(T.boot > T.orig))/length(T.boot)# fit the Holzinger and Swineford (1939) example HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939, se="none") # get the test statistic for the original sample T.orig <- fitMeasures(fit, "chisq") # bootstrap to get bootstrap test statistics # we only generate 10 bootstrap samples in this example; in practice # you may wish to use a much higher number T.boot <- lavBootstrap(fit, r=10, type="bollen.stine", fun=fitMeasures, fit.measures="chisq") # compute a bootstrap based p-value pvalue.boot <- length(which(T.boot > T.orig))/length(T.boot)
Polychoric, polyserial and Pearson correlations
Description
Fit an unrestricted model to compute polychoric, polyserial and/or Pearson correlations.
Usage
lavCor(object, ordered = NULL, group = NULL, missing = "listwise", ov_names_x = NULL, sampling_weights = NULL, se = "none", test = "none", estimator = "two.step", baseline = FALSE, ..., cor_smooth = FALSE, cor_smooth_tol = 1e-04, output = "cor")lavCor(object, ordered = NULL, group = NULL, missing = "listwise", ov_names_x = NULL, sampling_weights = NULL, se = "none", test = "none", estimator = "two.step", baseline = FALSE, ..., cor_smooth = FALSE, cor_smooth_tol = 1e-04, output = "cor")
Arguments
object |
Either a |
ordered |
Character vector. Only used if |
group |
Only used if |
missing |
If |
sampling_weights |
Only used if |
ov_names_x |
Only used if |
se |
Only used if |
test |
Only used if output is |
estimator |
If |
baseline |
Only used if output is |
... |
Optional parameters that are passed to the |
cor_smooth |
Logical. Only used if |
cor_smooth_tol |
Numeric. Smallest eigenvalue used when reconstructing the correlation matrix after an eigenvalue decomposition. |
output |
If |
Details
This function is a wrapper around the lavaan function,
but where the model is defined as the unrestricted model. The
following free parameters are included: all covariances/correlations among
the variables, variances for continuous variables, means for continuous
variables, thresholds for ordered variables, and if exogenous variables
are included (ov_names_x is not empty) while some variables
are ordered, also the regression slopes enter the model.
Value
By default, if output = "cor" or output = "cov", a symmetric
matrix (of class "lavaan.matrix.symmetric", which only affects the
way the matrix is printed). If output = "th", a named vector of
thresholds. If output = "fit" or output = "lavaan",
an object of class lavaan.
References
Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika, 44(4), 443-460.
Olsson, U., Drasgow, F., & Dorans, N. J. (1982). The polyserial correlation coefficient. Psychometrika, 47(3), 337-347.
See Also
Examples
# Holzinger and Swineford (1939) example HS9 <- HolzingerSwineford1939[,c("x1","x2","x3","x4","x5", "x6","x7","x8","x9")] # Pearson correlations lavCor(HS9) # ordinal version, with three categories HS9ord <- as.data.frame( lapply(HS9, cut, 3, labels = FALSE) ) # polychoric correlations, two-stage estimation lavCor(HS9ord, ordered=names(HS9ord)) # thresholds only lavCor(HS9ord, ordered=names(HS9ord), output = "th") # polychoric correlations, with standard errors lavCor(HS9ord, ordered=names(HS9ord), se = "standard", output = "est") # polychoric correlations, full output fit.un <- lavCor(HS9ord, ordered=names(HS9ord), se = "standard", output = "fit") summary(fit.un)# Holzinger and Swineford (1939) example HS9 <- HolzingerSwineford1939[,c("x1","x2","x3","x4","x5", "x6","x7","x8","x9")] # Pearson correlations lavCor(HS9) # ordinal version, with three categories HS9ord <- as.data.frame( lapply(HS9, cut, 3, labels = FALSE) ) # polychoric correlations, two-stage estimation lavCor(HS9ord, ordered=names(HS9ord)) # thresholds only lavCor(HS9ord, ordered=names(HS9ord), output = "th") # polychoric correlations, with standard errors lavCor(HS9ord, ordered=names(HS9ord), se = "standard", output = "est") # polychoric correlations, full output fit.un <- lavCor(HS9ord, ordered=names(HS9ord), se = "standard", output = "fit") summary(fit.un)
Indirect and Total Effects
Description
‘lavEffects’ computes various ‘effects’ that are functions of the estimated model parameters of a fitted lavaan object. In this version, the focus is on the classic (LISREL-style) total, indirect and direct effects among the variables that appear in the structural part of the model (that is, the variables that are involved in a regression). Both observed and latent variables are supported.
This avoids the need to pre-specify all indirect (and total) effects manually
in the model syntax (using the := operator), which can be tedious when
there are many of them.
Usage
lavEffects(object, effects = c("total", "indirect"), se.def = NULL, level = 0.95, monte.carlo = NULL, boot.ci.type = "perc", zstat = TRUE, pvalue = TRUE, ci = TRUE, standardized = FALSE, cov.std = TRUE, add.class = TRUE, output = "data.frame")lavEffects(object, effects = c("total", "indirect"), se.def = NULL, level = 0.95, monte.carlo = NULL, boot.ci.type = "perc", zstat = TRUE, pvalue = TRUE, ci = TRUE, standardized = FALSE, cov.std = TRUE, add.class = TRUE, output = "data.frame")
Arguments
object |
An object of class |
effects |
Character vector. One or more of |
se.def |
Character (or If |
level |
Numeric. The confidence level for the confidence intervals. |
monte.carlo |
List (or |
boot.ci.type |
Character. Only used when |
zstat |
Logical. If |
pvalue |
Logical. If |
ci |
Logical. If |
standardized |
Logical, character vector, or vector of (observed) variable
names, behaving as in |
cov.std |
Logical. See |
add.class |
Logical. If |
output |
Character. If |
Details
All effects are derived from the reduced-form matrix
, where is the matrix of (direct) regression
coefficients among the structural variables (the beta matrix in the
LISREL representation that lavaan uses internally). Writing for the
direct effect of variable on variable , we have:
-
the direct effect of
onequals; -
the total effect of
onequals; -
the indirect effect of
onequals the total effect minus the direct effect.
Only effects that are structurally non-zero (that is, for which a directed path
from to exists) are reported. For indirect effects, this means
that at least one path of length two or more must exist.
The delta and Monte Carlo methods only require the parameter estimates and the
estimated covariance matrix of the parameters. The delta method produces
(symmetric) normal-theory confidence intervals; the Monte Carlo method produces
percentile-based confidence intervals, which need not be symmetric around the
point estimate. The Monte Carlo method typically behaves better than the delta
method for effects that are products of parameters (such as indirect effects),
in particular in smaller samples. When the model was fitted with
se = "bootstrap", the bootstrap draws are reused to obtain bootstrap
standard errors and bootstrap percentile confidence intervals (this requires
no additional model fitting).
Models fitted with conditional.x = TRUE are also supported: in that
case the structural model is , where the
exogenous covariates are stored in the gamma matrix. The effects
of these covariates on the endogenous variables are then computed as
(total), (direct) and
(indirect), and reported alongside the effects
among the beta variables.
Value
If output = "data.frame" (the default), a data.frame (of class
lavaan.effects) with the following columns: effect (the type of
effect: total, indirect or direct), lhs (the outcome variable),
op (always "~"), rhs (the predictor variable), and,
depending on the arguments, group/level/block,
est, se, z, pvalue, ci.lower,
ci.upper and (if standardized is requested) one or more of
std.lv, std.all, std.nox and std.user. The effect
in a given row is the effect of rhs on lhs.
If output = "list", a (possibly nested) list of matrices, where element
contains the effect of variable on variable .
See Also
parameterEstimates, standardizedSolution.
Examples
# a simple mediation model set.seed(1234) X <- rnorm(300) M <- 0.5 * X + rnorm(300) Y <- 0.4 * M + 0.3 * X + rnorm(300) Data <- data.frame(X = X, Y = Y, M = M) model <- ' # direct effect Y ~ c*X # mediator M ~ a*X Y ~ b*M ' fit <- sem(model, data = Data) # total and indirect effects, with Monte Carlo standard errors lavEffects(fit) # all effects, using the delta method lavEffects(fit, effects = c("total", "indirect", "direct"), se.def = "delta") # add standardized (total and indirect) effects lavEffects(fit, se.def = "delta", standardized = TRUE)# a simple mediation model set.seed(1234) X <- rnorm(300) M <- 0.5 * X + rnorm(300) Y <- 0.4 * M + 0.3 * X + rnorm(300) Data <- data.frame(X = X, Y = Y, M = M) model <- ' # direct effect Y ~ c*X # mediator M ~ a*X Y ~ b*M ' fit <- sem(model, data = Data) # total and indirect effects, with Monte Carlo standard errors lavEffects(fit) # all effects, using the delta method lavEffects(fit, effects = c("total", "indirect", "direct"), se.def = "delta") # add standardized (total and indirect) effects lavEffects(fit, se.def = "delta", standardized = TRUE)
lavaan Export
Description
Export a fitted lavaan object to an external program.
Usage
lavExport(object, target = "lavaan", prefix = "sem", dir_name = "lav_export", export = TRUE, ...)lavExport(object, target = "lavaan", prefix = "sem", dir_name = "lav_export", export = TRUE, ...)
Arguments
object |
An object of class |
target |
The target program. Current options are |
prefix |
The prefix used to create the input files; the name of the input file has the pattern ‘prefix dot target dot in’; the name of the data file has the pattern ‘prefix dot target dot raw’. |
dir_name |
The directory name (including a full path) where the input files will be written. |
export |
If |
... |
Only to support old argument name 'dir.name'. |
Details
This function was mainly created to quickly generate an Mplus syntax file to
compare the results between Mplus and lavaan. The target "lavaan" can
be useful to create a full model syntax as needed for the lavaan()
function. More targets (perhaps for LISREL or EQS) will be added
in future releases.
Value
If export = TRUE, a directory (called lav_export by default) will
be created, typically containing a data file, and an input file so that the
same analysis can be run using an external program. If export = FALSE, a
character string containing the model syntax only for the target program.
See Also
Examples
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) out <- lavExport(fit, target = "Mplus", export=FALSE) cat(out)HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) out <- lavExport(fit, target = "Mplus", export=FALSE) cat(out)
Inspect or extract information from a fitted lavaan object
Description
The lavInspect() and lavTech() functions can be used to
inspect/extract information that is stored inside (or can be computed from) a
fitted lavaan object. Note: the (older) inspect() function is
now simply a shortcut for lavInspect() with default arguments.
Usage
lavInspect(object, what = "free", add.labels = TRUE, add.class = TRUE, list.by.group = TRUE, drop.list.single.group = TRUE) lavTech(object, what = "free", add.labels = FALSE, add.class = FALSE, list.by.group = FALSE, drop.list.single.group = FALSE) inspect(object, what = "free", ...)lavInspect(object, what = "free", add.labels = TRUE, add.class = TRUE, list.by.group = TRUE, drop.list.single.group = TRUE) lavTech(object, what = "free", add.labels = FALSE, add.class = FALSE, list.by.group = FALSE, drop.list.single.group = FALSE) inspect(object, what = "free", ...)
Arguments
object |
An object of class |
what |
Character. What needs to be inspected/extracted? See Details for a
full list. Note: the |
add.labels |
If |
add.class |
If |
list.by.group |
Logical. Only used when the output are model matrices.
If |
drop.list.single.group |
If |
... |
Additional arguments. Not used by lavaan, but by other packages. |
Details
The lavInspect() and lavTech() functions only differ in the way
they return the results. The lavInspect() function will prettify the
output by default, while the lavTech() will not attempt to prettify the
output by default. The (older) inspect() function is a simplified
version of lavInspect() with only the first two arguments.
Below is a list of possible values for the what argument, organized
in several sections:
Model matrices:
-
"free": -
A list of model matrices. The non-zero integers represent the free parameters. The numbers themselves correspond to the position of the free parameter in the parameter vector. This determines the order of the model parameters in the output of, for example,
coef()andvcov(). -
"partable": -
A list of model matrices. The non-zero integers represent both the fixed parameters (for example, factor loadings fixed at 1.0) and the free parameters (ignoring any equality constraints). They correspond to all entries (fixed or free) in the parameter table. See
parTable. -
"se": -
A list of model matrices. The non-zero numbers represent the standard errors for the free parameters in the model. If two parameters are constrained to be equal, they will share the same standard error. Aliases:
"std.err"and"standard.errors". -
"se.std": -
A list of model matrices. The non-zero numbers represent the standard errors for the (completely) standardized free parameters in the model. Alias:
"std.se". -
"start": -
A list of model matrices. The values represent the starting values for all model parameters. Alias:
"starting.values". -
"est": -
A list of model matrices. The values represent the estimated model parameters. Aliases:
"estimates", and"x". -
"est.unrotated": -
A list of model matrices. The values represent the estimated model parameters before rotation was applied. Only relevant if rotation was used (for example in EFA); otherwise this is identical to
"est". -
"dx.free": -
A list of model matrices. The values represent the gradient (first derivative) values of the model parameters. If two parameters are constrained to be equal, they will have the same gradient value.
-
"dx.all": -
A list of model matrices. The values represent the first derivative with respect to all possible matrix elements. Currently, this is only available when the estimator is
"ML"or"GLS". -
"std": -
A list of model matrices. The values represent the (completely) standardized model parameters (the variances of both the observed and the latent variables are set to unity). Aliases:
"std.all","standardized". -
"std.lv": -
A list of model matrices. The values represent the standardized model parameters (only the variances of the latent variables are set to unity.)
-
"std.nox": -
A list of model matrices. The values represent the (completely) standardized model parameters (the variances of both the observed and the latent variables are set to unity; however, the variances of any observed exogenous variables are not set to unity; hence no-x.)
-
"mm.lambda": -
The estimated factor loading matrix (per group), as extracted from the
@GLISTslot. Alias:"lambda". -
"mm.delta": -
The estimated delta (scaling) matrix (per group), as extracted from the
@GLISTslot. Only available for categorical data or when a correlation structure is used. (Note: this is the delta model matrix, not the delta jacobian that is returned by"delta".)
To extract a single model matrix (from the @GLIST slot), use the
"mm.*" options (for example "mm.lambda" for the factor loading
matrix). For backward compatibility, the (older) bare names are still accepted
as aliases.
Information about the data:
-
"data": -
A matrix containing the observed variables that were used to fit the model. The matrix has no row or column names. The columns correspond to the output of
lav_object_vnames(object), while the rows correspond to the output oflavInspect(object, "case.idx"). -
"ordered": -
A character vector. The ordered variables.
-
"nobs": -
Numeric vector. The effective number of observations in each group that were used in the analysis. If sampling weights were provided, this is the (per group) sum of the weights, consistent with the value returned by the
nobs()method. Use"norig"to obtain the number of rows in the data. -
"norig": -
Integer vector. The original number of observations (rows in the data) in each group.
-
"ntotal": -
Numeric. The total effective number of observations that were used in the analysis. If there is just a single group, this is the same as the
"nobs"option; if there are multiple groups, this is the sum of the"nobs"numbers for each group. If sampling weights were provided, this is the sum of the weights. -
"case.idx": -
Integer vector. The case/observation numbers that were used in the analysis. In the case of multiple groups: a list of numbers.
-
"empty.idx": -
The case/observation numbers of those cases/observations that contained missing values only (at least for the observed variables that were included in the model). In the case of multiple groups: a list of numbers.
-
"th.idx": -
Integer vector. For categorical data, the index of the observed variable that each threshold belongs to. In the case of multiple groups: a list of integer vectors.
-
"patterns": -
A binary matrix. The rows of the matrix are the missing data patterns where 1 and 0 denote non-missing and missing values for the corresponding observed variables respectively (or
TRUEandFALSEiflavTech()is used.) If the data is complete (no missing values), there will be only a single pattern. In the case of multiple groups: a list of pattern matrices. -
"coverage": -
A symmetric matrix in which each element contains the proportion of jointly observed data points for the corresponding pair of observed variables. In the case of multiple groups: a list of coverage matrices.
-
"group": -
A character string. The group variable in the data.frame (if any).
-
"ngroups": -
Integer. The number of groups.
-
"group.label": -
A character vector. The group labels.
-
"level.label": -
A character vector. The level labels.
-
"cluster": -
A character vector. The cluster variable(s) in the data.frame (if any).
-
"nlevels": -
Integer. The number of levels.
-
"nclusters": -
Integer. The number of clusters that were used in the analysis.
-
"ncluster.size": -
Integer. The number of different cluster sizes.
-
"cluster.size": -
Integer vector. The number of observations within each cluster. For multigroup multilevel models, a list of integer vectors, indicating cluster sizes within each group.
-
"cluster.id": -
Integer vector. The cluster IDs identifying the clusters. For multigroup multilevel models, a list of integer vectors, indicating cluster IDs within each group.
-
"cluster.idx": -
Integer vector. The cluster index for each observation. The cluster index ranges from 1 to the number of clusters. For multigroup multilevel models, a list of integer vectors, indicating cluster indices within each group.
-
"cluster.label": -
Integer vector. The cluster ID for each observation. For multigroup multilevel models, a list of integer vectors, indicating the cluster ID for each observation within each group.
-
"cluster.sizes": -
Integer vector. The different cluster sizes that were used in the analysis. For multigroup multilevel models, a list of integer vectors, indicating the different cluster sizes within each group.
-
"average.cluster.size": -
Integer. The average cluster size (using the formula
s = (N^2 - sum(cluster.size^2)) / (N*(nclusters - 1L))). For multigroup multilevel models, a list containing the average cluster size per group.
Observed sample statistics:
-
"sampstat": -
Observed sample statistics. Aliases:
"obs","observed","samp","sample","samplestatistics". Since 0.6-3, we always check if an h1 slot is available (the estimates for the unrestricted model); if present, we extract the sample statistics from this slot. This implies that if the variables are continuous andmissing = "ml"(or"fiml"), we return the covariance matrix (and mean vector) as computed by the EM algorithm under the unrestricted (h1) model. If the h1 slot is not present (for example, because the model was fitted withh1 = FALSE), we return the sample statistics from the SampleStats slot. In that case, pairwise deletion is used for the elements of the covariance matrix (or correlation matrix), and listwise deletion for all univariate statistics (means, intercepts, and thresholds). -
"sampstat.std": -
Standardized observed sample statistics. The covariance matrix is rescaled to a correlation matrix. Aliases:
"obs.std","observed.std","samp.std","sample.std","samplestatistics.std". -
"sampstat.h1": -
Deprecated. Do not use any longer.
-
"wls.obs": -
The observed sample statistics (covariance elements, intercepts/thresholds, etc.) in a single vector.
-
"wls.v": -
The weight vector as used in weighted least squares estimation.
-
"gamma": -
N times the asymptotic variance matrix of the sample statistics. Alias:
"sampstat.nacov".
Model features:
-
"meanstructure": -
Logical.
TRUEif a meanstructure was included in the model. -
"categorical": -
Logical.
TRUEif categorical endogenous variables were part of the model. -
"fixed.x": -
Logical.
TRUEif the exogenous x-covariates are treated as fixed. -
"parameterization": -
Character. Either
"delta"or"theta".
Model-implied sample statistics:
-
"implied": -
The model-implied summary statistics. Alias:
"fitted","expected","exp". -
"resid": -
The difference between observed and model-implied summary statistics. Alias:
"residuals","residual","res". -
"cov.lv": -
The model-implied variance-covariance matrix of the latent variables. Alias:
"veta"[for V(eta)]. -
"cor.lv": -
The model-implied correlation matrix of the latent variables.
-
"mean.lv": -
The model-implied mean vector of the latent variables. Alias:
"eeta"[for E(eta)]. -
"cov.ov": -
The model-implied variance-covariance matrix of the observed variables. Aliases:
"sigma","sigma.hat". -
"cor.ov": -
The model-implied correlation matrix of the observed variables.
-
"mean.ov": -
The model-implied mean vector of the observed variables. Aliases:
"mu","mu.hat". -
"cov.all": -
The model-implied variance-covariance matrix of both the observed and latent variables.
-
"cor.all": -
The model-implied correlation matrix of both the observed and latent variables.
-
"th": -
The model-implied thresholds. Alias:
"thresholds". -
"mm.theta": -
The (residual) variance-covariance matrix of the observed variables (the theta model matrix). Aliases:
"theta","theta.cov". -
"theta.cor": -
The (residual) variance-covariance matrix of the observed variables, expressed in correlation metric.
-
"wls.est": -
The model-implied sample statistics (covariance elements, intercepts/thresholds, etc.) in a single vector.
-
"vy": -
The model-implied unconditional variances of the observed variables.
-
"rsquare": -
The R-square value for all endogenous variables. Aliases:
"r-square","r2". -
"fs.determinacy": -
The factor determinacies (based on regression factor scores). They represent the (estimated) correlation between the factor scores and the latent variable scores.
-
"fs.reliability": -
The factor reliabilities (based on regression factor scores). They are the square of the factor determinacies.
-
"fs.determinacy.Bartlett": -
The factor determinacies (based on Bartlett factor scores). They represent the (estimated) correlation between the factor scores and the latent variable scores.
-
"fs.reliability.Bartlett": -
The factor reliabilities (based on Bartlett factor scores). They are the square of the factor determinacies.
-
"icc": -
The intraclass correlation coefficients for clustered data with multilevel models. Computed from the model-implied (H1) within-group and between-group covariance matrices. Only available for models with clustered data and multiple levels.
-
"ranef": -
The random effects (empirical Bayes predictions of the cluster-level latent variables). Only available for clustered data (in the long format) with multiple levels.
Diagnostics:
-
"mdist2.fs": -
The squared Mahalanobis distances for the (Bartlett) factor scores.
-
"mdist.fs": -
The Mahalanobis distances for the (Bartlett) factor scores.
-
"mdist2.resid": -
The squared Mahalanobis distances for the (Bartlett-based) casewise residuals.
-
"mdist.resid": -
The Mahalanobis distances for the (Bartlett-based) casewise residuals.
Optimizer information:
-
"converged": -
Logical.
TRUEif the optimizer has converged;FALSEotherwise. -
"iterations": -
Integer. The number of iterations used by the optimizer.
-
"optim": -
List. All available information regarding the optimization results.
-
"npar": -
Integer. Number of free parameters (ignoring constraints).
Gradient, Hessian, observed, expected and first.order information matrices:
-
"gradient": -
Numeric vector containing the first derivatives of the discrepancy function with respect to the (free) model parameters.
-
"gradient.logl": -
Numeric vector containing the first derivatives of the loglikelihood with respect to the (free) model parameters.
-
"optim.gradient": -
Numeric vector containing the first derivatives of the objective function (as seen by the optimizer) with respect to the (free) model parameters.
-
"hessian": -
Matrix containing the second derivatives of the discrepancy function with respect to the (free) model parameters.
-
"information": -
Matrix containing either the observed or the expected information matrix (depending on the information option of the fitted model). This is unit-information, not total-information.
-
"information.expected": -
Matrix containing the expected information matrix for the free model parameters.
-
"information.observed": -
Matrix containing the observed information matrix for the free model parameters.
-
"information.first.order": -
Matrix containing the first.order information matrix for the free model parameters. This is the outer product of the gradient elements (the first derivative of the discrepancy function with respect to the (free) model parameters). Alias:
"first.order". -
"augmented.information": -
Matrix containing either the observed or the expected augmented (or bordered) information matrix (depending on the information option of the fitted model). Only relevant if constraints have been used in the model.
-
"augmented.information.expected": -
Matrix containing the expected augmented (or bordered) information matrix. Only relevant if constraints have been used in the model.
-
"augmented.information.observed": -
Matrix containing the observed augmented (or bordered) information matrix. Only relevant if constraints have been used in the model.
-
"augmented.information.first.order": -
Matrix containing the first.order augmented (or bordered) information matrix. Only relevant if constraints have been used in the model.
-
"inverted.information": -
Matrix containing either the observed or the expected inverted information matrix (depending on the information option of the fitted model).
-
"inverted.information.expected": -
Matrix containing the inverted expected information matrix for the free model parameters.
-
"inverted.information.observed": -
Matrix containing the inverted observed information matrix for the free model parameters.
-
"inverted.information.first.order": -
Matrix containing the inverted first.order information matrix for the free model parameters.
-
"h1.information": -
Matrix containing either the observed, expected or first.order information matrix (depending on the information option of the fitted model) of the unrestricted h1 model. This is unit-information, not total-information.
-
"h1.information.expected": -
Matrix containing the expected information matrix for the unrestricted h1 model.
-
"h1.information.observed": -
Matrix containing the observed information matrix for the unrestricted h1 model.
-
"h1.information.first.order": -
Matrix containing the first.order information matrix for the unrestricted h1 model. Alias:
"h1.first.order".
Variance covariance matrix of the model parameters:
-
"vcov": -
Matrix containing the variance covariance matrix of the estimated model parameters.
-
"vcov.std.all": -
Matrix containing the variance covariance matrix of the standardized estimated model parameters. Standardization is done with respect to both observed and latent variables.
-
"vcov.std.lv": -
Matrix containing the variance covariance matrix of the standardized estimated model parameters. Standardization is done with respect to the latent variables only.
-
"vcov.std.nox": -
Matrix containing the variance covariance matrix of the standardized estimated model parameters. Standardization is done with respect to both observed and latent variables, but ignoring any exogenous observed covariates.
-
"vcov.def": -
Matrix containing the variance covariance matrix of the user-defined (using the := operator) parameters.
-
"vcov.def.std.all": -
Matrix containing the variance covariance matrix of the standardized user-defined parameters. Standardization is done with respect to both observed and latent variables.
-
"vcov.def.std.lv": -
Matrix containing the variance covariance matrix of the standardized user-defined parameters. Standardization is done with respect to the latent variables only.
-
"vcov.def.std.nox": -
Matrix containing the variance covariance matrix of the standardized user-defined parameters. Standardization is done with respect to both observed and latent variables, but ignoring any exogenous observed covariates.
-
"vcov.def.joint": -
Matrix containing the joint variance covariance matrix of both the estimated model parameters and the defined (using the := operator) parameters.
-
"vcov.def.joint.std.all": -
Matrix containing the joint variance covariance matrix of both the standardized model parameters and the user-defined parameters. Standardization is done with respect to both observed and latent variables.
-
"vcov.def.joint.std.lv": -
Matrix containing the joint variance covariance matrix of both the standardized model parameters and the user-defined parameters. Standardization is done with respect to the latent variables only.
-
"vcov.def.joint.std.nox": -
Matrix containing the joint variance covariance matrix of both the standardized model parameters and the user-defined parameters. Standardization is done with respect to both observed and latent variables, but ignoring any exogenous observed covariates.
Miscellaneous:
-
"coef.boot": -
Matrix containing estimated model parameters for each bootstrap sample. Only relevant when bootstrapping was used.
-
"monte.carlo": -
Matrix containing the Monte Carlo draws of the model parameters, as used for the Monte Carlo confidence intervals of defined parameters (Preacher & Selig, 2012). Only relevant when these draws were requested. Aliases:
"mc","mc.coef","coef.mc". -
"UGamma": -
Matrix containing the product of 'U' and 'Gamma' matrices as used by the Satorra-Bentler correction. The trace of this matrix, divided by the degrees of freedom, gives the scaling factor.
-
"UfromUGamma": -
Matrix containing the 'U' matrix as used by the Satorra-Bentler correction. Alias:
"U". -
"delta": -
The delta matrix (per group): the Jacobian of the model-implied summary statistics (the rows: means, (co)variances, thresholds, ...) with respect to the free model parameters (the columns). This is the matrix used in the delta method. (Note: this is the delta Jacobian, not the delta model matrix that is returned by
"mm.delta".) In the case of multiple groups: a list of matrices. -
"delta.rownames": -
The row names of the delta matrix (see
"delta"): the labels of the model-implied summary statistics. In the case of multiple groups: a list of character vectors. -
"list": -
The parameter table. The same output as given by
parTable(). -
"fit": -
The fit measures. Aliases:
"fitmeasures","fit.measures","fit.indices". The same output as given byfitMeasures(). -
"mi": -
The modification indices. Alias:
"modindices","modification.indices". The same output as given bymodindices(). -
"loglik.casewise": -
Vector containing the casewise loglikelihood contributions. Only available if estimator =
"ML". -
"options": -
List. The option list.
-
"call": -
List. The call as returned by match.call, coerced to a list.
-
"timing": -
List. The timing (in milliseconds) of various lavaan subprocedures.
-
"test": -
List. All available information regarding the (goodness-of-fit) test statistic(s).
-
"baseline.test": -
List. All available information regarding the (goodness-of-fit) test statistic(s) of the baseline model.
-
"baseline.partable": -
Data.frame. The parameter table of the (internal) baseline model.
-
"post.check": -
Post-fitting check if the solution is admissible. A warning is raised if negative variances are found, or if either
lavInspect(fit, "cov.lv")orlavInspect(fit, "theta")return a non-positive definite matrix. -
"zero.cell.tables": -
List. List of bivariate frequency tables where at least one cell is empty.
-
"iv": -
Data.frame. One row per (transformed) equation, with the (model-implied) instrumental variables that were used for each equation. Columns are
lhs,rhs,lhs.new,rhs.new,type, andinstruments. Only available whenestimator = "IV". Aliases:"ivs","miiv","miivs","instr","instruments". In the case of multiple groups: a list of data.frames. -
"eqs": -
List. The (internal) list of equations that was used for the (MI)IV-based estimation, including the instruments, the coefficients, and the Sargan test per equation. Only available when
estimator = "IV". -
"sargan": -
Data.frame. The per-equation overidentification tests, for each overidentified equation. Columns are
lhs,rhs,df,sargan.stat,sargan.pval,browne.stat, andbrowne.pval. Thesargan.*columns are the classical Sargan test (assumes normality; the p-value isNAfor categorical data, where it is not valid); thebrowne.*columns are a robust residual-based test computed with the distribution-free (ADF) ACOV for continuous data or the polychoric ACOV for categorical data."hansen"is an alias. Only available whenestimator = "IV". In the case of multiple groups: a list of data.frames. -
"version": -
The lavaan version number that was used to construct the fitted lavaan object.
See Also
Examples
# fit model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939, group = "school") # extract information lavInspect(fit, "sampstat") lavTech(fit, "sampstat")# fit model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939, group = "school") # extract information lavInspect(fit, "sampstat") lavTech(fit, "sampstat")
Observed Variable Covariance Matrix from a Model and Data
Description
The lavaan model syntax describes a latent variable model. Often, the user wants to see the sample covariance matrix of the variables in their model for diagnostic purposes. However, their data may contain many more columns than the variables used in the model.
Usage
lavInspectSampleCov(model, data, ...) inspectSampleCov(model, data, ...)lavInspectSampleCov(model, data, ...) inspectSampleCov(model, data, ...)
Arguments
model |
The model that will be fit by lavaan. |
data |
The data frame being used to fit the model. |
... |
Other arguments to |
Details
One must supply both a model, coded with proper model.syntax, and
a data frame from which a covariance matrix will be calculated. This function
essentially calls sem without fitting the model, and then uses
lavInspect to obtain the sample covariance matrix and the
meanstructure.
See also
Author(s)
Jarrett Byrnes
Inspect or extract information from a lavaanList object
Description
The lavListInspect() and lavListTech() functions can be used to
inspect/extract information that is stored inside (or can be computed from) a
lavaanList object.
Usage
lavListInspect(object, what = "free", add.labels = TRUE, add.class = TRUE, list.by.group = TRUE, drop.list.single.group = TRUE) lavListTech(object, what = "free", add.labels = FALSE, add.class = FALSE, list.by.group = FALSE, drop.list.single.group = FALSE)lavListInspect(object, what = "free", add.labels = TRUE, add.class = TRUE, list.by.group = TRUE, drop.list.single.group = TRUE) lavListTech(object, what = "free", add.labels = FALSE, add.class = FALSE, list.by.group = FALSE, drop.list.single.group = FALSE)
Arguments
object |
An object of class |
what |
Character. What needs to be inspected/extracted? See Details for a
full list. Note: the |
add.labels |
If |
add.class |
If |
list.by.group |
Logical. Only used when the output are model matrices.
If |
drop.list.single.group |
If |
Details
The lavListInspect() and lavListTech() functions only differ in
the way they return the results. The lavListInspect() function will
prettify the output by default, while the lavListTech() will not attempt
to prettify the output by default.
Below is a list of possible values for the what argument, organized
in several sections:
Model matrices:
-
"free": -
A list of model matrices. The non-zero integers represent the free parameters. The numbers themselves correspond to the position of the free parameter in the parameter vector. This determines the order of the model parameters in the output of, for example,
coef()andvcov(). -
"partable": -
A list of model matrices. The non-zero integers represent both the fixed parameters (for example, factor loadings fixed at 1.0) and the free parameters (ignoring any equality constraints). They correspond to all entries (fixed or free) in the parameter table. See
parTable. -
"start": -
A list of model matrices. The values represent the starting values for all model parameters. Alias:
"starting.values".
Information about the data (including missing patterns):
-
"group": -
A character string. The group variable in the data.frame (if any).
-
"ngroups": -
Integer. The number of groups.
-
"group.label": -
A character vector. The group labels.
-
"level.label": -
A character vector. The level labels.
-
"cluster": -
A character vector. The cluster variable(s) in the data.frame (if any).
-
"nlevels": -
Integer. The number of levels.
-
"ordered": -
A character vector. The ordered variables.
-
"nobs": -
Integer vector. The number of observations in each group that were used in the analysis (in each dataset).
-
"norig": -
Integer vector. The original number of observations in each group (in each dataset).
-
"ntotal": -
Integer. The total number of observations that were used in the analysis. If there is just a single group, this is the same as the
"nobs"option; if there are multiple groups, this is the sum of the"nobs"numbers for each group (in each dataset).
Model features:
-
"meanstructure": -
Logical.
TRUEif a meanstructure was included in the model. -
"categorical": -
Logical.
TRUEif categorical endogenous variables were part of the model. -
"fixed.x": -
Logical.
TRUEif the exogenous x-covariates are treated as fixed. -
"parameterization": -
Character. Either
"delta"or"theta".
-
"list": -
The parameter table. The same output as given by
parTable(). -
"options": -
List. The option list.
-
"call": -
List. The call as returned by match.call, coerced to a list.
See Also
Examples
# fit model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' # a data generating function generateData <- function() lavSimulateData(HS.model, sample_nobs = 100) set.seed(1234) fit <- semList(HS.model, dataFunction = generateData, ndat = 5, store.slots = "partable") # extract information lavListInspect(fit, "free") lavListTech(fit, "free")# fit model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' # a data generating function generateData <- function() lavSimulateData(HS.model, sample_nobs = 100) set.seed(1234) fit <- semList(HS.model, dataFunction = generateData, ndat = 5, store.slots = "partable") # extract information lavListInspect(fit, "free") lavListTech(fit, "free")
lavaan matrix representation
Description
Extend the parameter table with a matrix representation.
Usage
lavMatrixRepresentation(partable, representation = "LISREL", allow.composites = TRUE, add.attributes = FALSE, as.data.frame. = TRUE)lavMatrixRepresentation(partable, representation = "LISREL", allow.composites = TRUE, add.attributes = FALSE, as.data.frame. = TRUE)
Arguments
partable |
A lavaan parameter table (as extracted by the
|
representation |
Character. The matrix representation style. Currently, only the all-y version of the LISREL representation is supported. |
allow.composites |
Logical. If |
add.attributes |
Logical. If |
as.data.frame. |
Logical. If |
Value
A list or a data.frame containing the original parameter table, plus
three columns: a "mat" column containing matrix names, and
a "row" and "col" column for the row and column indices
of the model parameters in the model matrices.
See Also
Examples
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) # extract partable partable <- parTable(fit) # add matrix representation (and show only a few columns) lavMatrixRepresentation(partable)[,c("lhs","op","rhs","mat","row","col")]HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) # extract partable partable <- parTable(fit) # add matrix representation (and show only a few columns) lavMatrixRepresentation(partable)[,c("lhs","op","rhs","mat","row","col")]
lavaan Names
Description
Extract variable names from a fitted lavaan object.
Usage
lavNames(object, type = "ov", ...)lavNames(object, type = "ov", ...)
Arguments
object |
An object of class |
type |
Character. The type of variables whose names should be extracted. See details for a complete list. |
... |
Additional selection criteria. For example, |
Details
The order of the variable names, as returned by lav_object_vnames,
determines the order in which the variables are listed in the parameter
table, and therefore also in the summary output.
The following variable types are available:
-
"ov": observed variables -
"ov.x": (pure) exogenous observed variables (no mediators) -
"ov.nox": non-exogenous observed variables -
"ov.model": modeled observed variables (joint vs conditional) -
"ov.y": (pure) endogenous variables (dependent only) (no mediators) -
"ov.num": numeric observed variables -
"ov.ord": ordinal observed variables -
"ov.ind": observed indicators of latent variables -
"ov.orphan": isolated observed variables (only their intercepts or variances appear in the model syntax) -
"ov.interaction": interaction terms (defined by the colon operator) -
"th": threshold names (ordinal variables only) -
"th.mean": threshold names (ordinal and numeric variables, if any) -
"lv": latent variables -
"lv.regular": measured latent variables (defined by =~ only) -
"lv.composite": composites (defined by <~ only) -
"lv.x": (pure) exogenous variables -
"lv.y": (pure) endogenous variables -
"lv.nox": non-exogenous latent variables -
"lv.nonnormal": latent variables with non-normal indicators -
"lv.interaction": interaction terms at the latent level -
"eqs.y": variables that appear as dependent variables in a regression formula (but not indicators of latent variables) -
"eqs.x": variables that appear as independent variables in a regression formula
See Also
Examples
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) lavNames(fit, "ov")HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) lavNames(fit, "ov")
lavaan Options
Description
Show the default options used by the lavaan() function. The
options can be changed by passing 'name = value' arguments to the
lavaan() function call, where they are added to the '...'
argument.
Usage
lavOptions(x = NULL, default = NULL, mimic = "lavaan")lavOptions(x = NULL, default = NULL, mimic = "lavaan")
Arguments
x |
Character. A character string holding an option name, or a character string vector holding multiple option names. All option names are converted to lower case. |
default |
If a single option is specified but not available, this value is returned. |
mimic |
Not used for now. |
Details
This is the full list of options that are accepted by the lavaan()
function, organized in several sections:
Model features:
-
meanstructure: -
If
TRUE, the means of the observed variables enter the model. If"default", the value is set based on the user-specified model, and/or the values of other arguments. -
int.ov.free: -
If
FALSE, the intercepts of the observed variables are fixed to zero. -
int.lv.free: -
If
FALSE, the intercepts of the latent variables are fixed to zero. -
conditional.x: -
If
TRUE, we set up the model conditional on the exogenous ‘x’ covariates; the model-implied sample statistics only include the non-x variables. IfFALSE, the exogenous ‘x’ variables are modeled jointly with the other variables, and the model-implied statistics reflect both sets of variables. If"default", the value is set depending on the estimator, and whether or not the model involves categorical endogenous variables. -
fixed.x: -
If
TRUE, the exogenous ‘x’ covariates are considered fixed variables and the means, variances and covariances of these variables are fixed to their sample values. IfFALSE, they are considered random, and the means, variances and covariances are free parameters. If"default", the value is set depending on the mimic option. -
orthogonal: -
If
TRUE, all covariances among latent variables are set to zero. -
orthogonal.y: -
If
TRUE, all covariances among endogenous latent variables only are set to zero. -
orthogonal.x: -
If
TRUE, all covariances among exogenous latent variables only are set to zero. -
std.lv: -
If
TRUE, the metric of each latent variable is determined by fixing their (residual) variances to 1.0. IfFALSE, the metric of each latent variable is determined by fixing the factor loading of the first indicator to 1.0. If there are multiple groups,std.lv = TRUEand"loadings"is included in thegroup.equalargument, then only the latent variances of the first group will be fixed to 1.0, while the latent variances of other groups are set free. -
effect.coding: -
Can be logical or character string. If logical and
TRUE, this implieseffect.coding = c("loadings", "intercepts"). If logical andFALSE, it is set equal to the empty string. If"loadings"is included, equality constraints are used so that the average of the factor loadings (per latent variable) equals 1. Note that this should not be used together withstd.lv = TRUE. If"intercepts"is included, equality constraints are used so that the sum of the intercepts (belonging to the indicators of a single latent variable) equals zero. As a result, the latent mean is freely estimated and usually equals the average of the means of the involved indicators. -
ceq.simple: -
Logical. If
TRUE, and no other general (equality or inequality) constraints are used in the model, simple equality constraints are represented in the parameter table as duplicated free parameters (instead of extra rows withop = "=="). The default isFALSE. -
parameterization: -
Currently only used if data is categorical. If
"delta", the delta parameterization is used. If"theta", the theta parameterization is used. -
correlation: -
Only used for (single-level) continuous data. If
TRUE, analyze a correlation matrix (instead of a (co)variance matrix). This implies that the residual observed variances are no longer free parameters. Instead, they are set to values that ensure the model-implied variances are unity. This also affects the standard errors. The only available estimators are GLS and WLS, which produce correct standard errors and a correct test statistic under normal and non-normal conditions respectively. Bothfixed.x = FALSEandfixed.x = TRUEare supported (the latter affects the way the standard errors are computed). For now, this option always assumesconditional.x = FALSE. Alternatively,correlationmay be a character vector of (observed) variable names (for examplecorrelation = c("x1", "x2", "x3")). In that case only the listed variables are standardized to unit variance (their residual variances are fixed accordingly), while all remaining observed variables keep their original metric (a 'partial' correlation structure). -
composites.cov: -
Character string. Only used if the model contains composites. Controls whether the composite-indicator (co)variances (the elements of the
Tmatrix) are fixed to their sample values or estimated as free parameters. If"fixed", theTmatrix is fixed to the sample (co)variances. If"free", theTmatrix is estimated as free parameters. If"default", the value is resolved to"free"for multilevel models (which makes composites at every level identified) and"fixed"otherwise. For a single-level model, freeingTis fit-invariant (the degrees of freedom are unchanged). -
auto.fix.first: -
If
TRUE, the factor loading of the first indicator is set to 1.0 for every latent variable. -
bad.marker.crit: -
Only used if
auto.fix.first = TRUE. A single number (default 0.1). If larger than zero, lavaan checks – once the unrestricted (h1) sample statistics are available – whether the first indicator of each latent variable is a poor item, in the sense that it correlates weakly with the other indicators of the same factor (more precisely: the absolute value of its corrected item-total correlation is belowbad.marker.crit). If so (and a clearly better indicator is available), a warning is issued and the loading of that better indicator is fixed to 1.0 instead, in order to set the metric of that latent variable. The main purpose is to avoid convergence problems caused by a (very) poor marker item. The check is based on the (pooled) unrestricted (h1) covariance matrix, so it behaves consistently with or without missing data, categorical data, multiple groups, etc. Larger values make the switching more aggressive; a value of 0 disables the check and always keeps the first indicator as the marker. -
auto.fix.single: -
If
TRUE, the residual variance (if included) of an observed indicator is set to zero if it is the only indicator of a latent variable. - auto.var
-
If
TRUE, the (residual) variances of both observed and latent variables are set free. -
auto.cov.lv.x: -
If
TRUE, the covariances of exogenous latent variables are included in the model and set free. -
auto.cov.y: -
If
TRUE, the covariances of dependent variables (both observed and latent) are included in the model and set free. -
auto.th: -
If
TRUE, thresholds for limited dependent variables are included in the model and set free. -
auto.delta: -
If
TRUE, response scaling parameters for limited dependent variables are included in the model and set free. -
auto.efa: -
If
TRUE, the necessary constraints are imposed to make the (unrotated) exploratory factor analysis blocks identifiable: for each block, factor variances are set to 1, factor covariances are constrained to be zero, and factor loadings are constrained to follow an echelon pattern.
Data options:
-
std.ov: -
If
TRUE, observed variables are standardized before entering the analysis. By default, these are only the non-exogenous observed variables, unlessfixed.x = FALSE. Use this option with caution; it can be used to test whether (for example) nonconvergence was due to scaling issues. Note that this is still a covariance-based analysis: no constraints are imposed to ensure the model-implied (co)variance matrix has unit variances, and the standard errors still assume that the input was unstandardized. See also thecorrelationoption. -
missing: -
The default setting is
"listwise": all cases with missing values are removed listwise from the data before the analysis starts. This is only valid if the data are missing completely at random (MCAR). Therefore, it may not be the optimal choice, but it can be useful for a first run. If the estimator belongs to the ML family, another option is"ml"(alias:"fiml"or"direct"). This corresponds to the so-called full information maximum likelihood approach (fiml), where we compute the likelihood case by case, using all available data from that case. Note that if the model contains exogenous observed covariates, andfixed.x = TRUE(the default), all cases with any missing values on these covariates will be deleted first. The option"ml.x"(alias:"fiml.x"or"direct.x") is similar to"ml", but does not delete any cases with missing values for the exogenous covariates, even iffixed.x = TRUE. (Note: all lavaan versions < 0.6 used"ml.x"instead of"ml"). If you wish to use multiple imputation, you need to use an external package (e.g., mice) to generate imputed datasets, which can then be analyzed using thesemListfunction. The semTools package contains several functions to do this automatically. Another option (with continuous data) is to use"two.stage"or"robust.two.stage". In this approach, we first estimate the sample statistics (mean vector, variance-covariance matrix) using an EM algorithm. Then, we use these estimated sample statistics as input for a regular analysis (as if the data were complete). The standard errors and test statistics are adjusted correctly to reflect the two-step procedure. The"robust.two.stage"option produces standard errors and a test statistic that are robust against non-normality. Both options are available for the ML estimator, and also for the (continuous-data) least-squares estimators"ULS","GLS","WLS"and"DLS"; for the latter, lavaan automatically switches tose = "robust.sem"andtest = "satorra.bentler", using the two-stage variance-covariance matrix of the EM-based sample statistics. In addition, for these least-squares estimators, requestingmissing = "ml"(or"fiml") is interpreted as a generic request to handle the missing values, and is silently treated asmissing = "two.stage". If (part of) the data is categorical, and the estimator is from the (W)LS family, the only option (besides listwise deletion) is"pairwise". In this three-step approach, missingness is only an issue in the first two steps. In the first step, we compute thresholds (for categorical variables) and means or intercepts (for continuous variables) using univariate information only. In this step, we simply ignore the missing values just like in mean(x, na.rm = TRUE). In the second step, we compute polychoric/polyserial/pearson correlations using (only) two variables at a time. Here we use pairwise deletion: we only keep those observations for which both values are observed (not missing), and this set may change from pair to pair. By default, in the categorical case we useconditional.x = TRUE. Therefore, any cases with missing values on the exogenous covariates will be deleted listwise from the data first. Finally, if the estimator is"PML", the available options are"pairwise","available.cases"and"doubly.robust". See the PML tutorial on the lavaan website for more information about these approaches. -
sampling.weights.normalization: -
If
"none", the sampling weights (if provided) will not be transformed. If"total", the sampling weights are normalized by dividing by the total sum of the weights, and multiplying again by the total sample size. If"group", the sampling weights are normalized per group: by dividing by the sum of the weights (in each group), and multiplying again by the group size. The default is"group". (For a single group,"group"and"total"are identical; they only differ when there are multiple groups, in which case"group"keeps each group's relative contribution proportional to its sample size, matching the behavior of Mplus.) -
sampling.weights.type: -
Only used when sampling weights are provided and the estimator relies on a weight matrix or sandwich variance: the least-squares family (GLS/WLS/DWLS/ULS/DLS, both continuous and categorical) and PML. Determines how the sampling weights enter the asymptotic variance (the Gamma / NACOV matrix, or the PML first-order information), and hence the (robust) standard errors and the scaled test statistic. For GLS and ULS only the standard errors are affected; for WLS/DWLS/DLS the Gamma also feeds the weight matrix, so the point estimates shift as well. If
"design"(the default), the weights are treated as sampling (design) weights and a design-based sandwich is used (the meat is weighted by the sum of the squared weights), matching the behavior of Mplus. If"frequency", the weights are treated as frequency (replication) counts (the meat is weighted by the sum of the weights), so that the results match a fit on the row-replicated data. Without sampling weights the two are identical. -
samplestats: -
Logical. If
FALSE, no sample statistics will be computed (and no estimation can take place). This can be useful when only a dummy lavaan object is requested, without any computations. The default isTRUE.
Data summary options:
-
sample.cov.rescale: -
If
TRUE, the sample covariance matrix provided by the user is internally rescaled by multiplying it with a factor (N-1)/N. If"default", the value is set depending on the estimator and the likelihood option: it is set toTRUEif maximum likelihood estimation is used andlikelihood="normal", andFALSEotherwise. -
ridge: -
Logical. If
TRUE, a small constant value is added to the diagonal elements of the covariance (or correlation) matrix before analysis. The value can be set using theridge.constantoption. -
ridge.constant: -
Numeric. Small constant used for ridging. The default value is 1e-05.
Multiple group options:
-
group.label: -
A character vector. The user can specify which group (or factor) levels need to be selected from the grouping variable, and in which order. If missing, all grouping levels are selected, in the order as they appear in the data.
-
group.equal: -
A vector of character strings. Only used in a multiple group analysis. Can be one or more of the following:
"loadings","composite.weights","intercepts","means","thresholds","regressions","residuals","residual.covariances","lv.variances"or"lv.covariances", specifying the pattern of equality constraints across multiple groups. As a shortcut, the single value"all"can be used to constrain all (free) parameters to be equal across groups; it is equivalent to listing all of the values above. When the model is not the same across groups (for example when thegroup:modifier is used to specify a different model per group), only parameters that are present in two or more groups are constrained to be equal; a parameter that occurs in a single group only is always left free. The constraints are symmetric and do not depend on the first group: a parameter that is shared by (say) the second and third group is constrained to be equal across those two groups, even if it does not appear in the first group. -
group.partial: -
A vector of character strings containing the labels of the parameters which should be free in all groups (thereby overriding the group.equal argument for some specific parameters).
-
group.w.free: -
Logical. If
TRUE, the group frequencies are considered to be free parameters in the model. In this case, a Poisson model is fitted to estimate the group frequencies. IfFALSE(the default), the group frequencies are fixed to their observed values.
Estimation options:
-
estimator: -
The estimator to be used. Can be one of the following:
"ML"for maximum likelihood,"GLS"for (normal theory) generalized least squares,"WLS"for weighted least squares (sometimes called ADF estimation),"ULS"for unweighted least squares,"DWLS"for diagonally weighted least squares, and"DLS"for distributionally-weighted least squares. These are the main options that affect the estimation. For convenience, the"ML"option can be extended as"MLM","MLMV","MLMVS","MLF", and"MLR". The estimation will still be plain"ML", but now with robust standard errors and a robust (scaled) test statistic. For"MLM","MLMV","MLMVS", classic robust standard errors are used (se="robust.sem"); for"MLF", standard errors are based on first-order derivatives (information = "first.order"); for"MLR", ‘Huber-White’ robust standard errors are used (se="robust.huber.white"). In addition,"MLM"will compute a Satorra-Bentler scaled (mean adjusted) test statistic (test="satorra.bentler"),"MLMVS"will compute a mean and variance adjusted test statistic (Satterthwaite style) (test="mean.var.adjusted"),"MLMV"will compute a mean and variance adjusted test statistic (scaled and shifted) (test="scaled.shifted"), and"MLR"will compute a test statistic which is asymptotically equivalent to the Yuan-Bentler T2-star test statistic (test="yuan.bentler.mplus"). Analogously, the estimators"WLSM"and"WLSMV"imply the"DWLS"estimator (not the"WLS"estimator) with robust standard errors and a mean or mean and variance adjusted test statistic. Estimators"ULSM"and"ULSMV"imply the"ULS"estimator with robust standard errors and a mean or mean and variance adjusted test statistic. Finally,"RBM"requests reduced-bias M-estimation (penalized maximum likelihood; continuous-outcome models for now). By default sandwich standard errors are used (se = "robust.huber.white"). The type of bias reduction is controlled by therbm.methodelement ofestimator.args(either"implicit"(default) or"explicit"), for exampleestimator = list(estimator = "RBM", rbm.method = "explicit"). The"explicit"method is much faster for models with many parameters (it requires a single ML fit plus a one-step correction), and is recommended in that case. -
likelihood: -
Only relevant for ML estimation. If
"wishart", the Wishart likelihood approach is used. In this approach, the covariance matrix has been divided by N-1, and both standard errors and test statistics are based on N-1. If"normal", the normal likelihood approach is used. Here, the covariance matrix has been divided by N, and both standard errors and test statistics are based on N. If"default", it depends on the mimic option: ifmimic="lavaan"ormimic="Mplus", normal likelihood is used; otherwise, Wishart likelihood is used. -
link: -
Not used yet. This is just a placeholder until the MML estimator is back.
-
information: -
If
"expected", the expected information matrix is used (to compute the standard errors). If"observed", the observed information matrix is used. If"first.order", the information matrix is based on the outer product of the casewise scores. See also the options"h1.information"and"observed.information"for further control. If"default", the value is set depending on the estimator, the missing argument, and the mimic option. If the argument is a vector with two elements, the first element is used for the computation of the standard errors, while the second element is used for the (robust) test statistic. -
h1.information: -
If
"structured"(the default), the unrestricted (h1) information part of the (expected, first.order or observed if h1 is used) information matrix is based on the structured, or model-implied statistics (model-implied covariance matrix, model-implied mean vector, etc.). If"unstructured", the unrestricted (h1) information part is based on sample-based statistics (observed covariance matrix, observed mean vector, etc.) If the argument is a vector with two elements, the first element is used for the computation of the standard errors, while the second element is used for the (robust) test statistic. -
observed.information: -
If
"hessian", the observed information matrix is based on the hessian of the objective function. If"h1", an approximation is used that is based on the observed information matrix of the unrestricted (h1) model. If the argument is a vector with two elements, the first element is used for the computation of the standard errors, while the second element is used for the (robust) test statistic. -
se: -
If
"standard", conventional standard errors are computed based on inverting the (expected, observed or first.order) information matrix. If"robust.sem", conventional robust standard errors are computed. If"robust.huber.white", standard errors are computed based on the 'mlr' (aka pseudo ML, Huber-White) approach. If"robust", either"robust.sem"or"robust.huber.white"is used depending on the estimator, the mimic option, and whether the data are complete or not. If"boot"or"bootstrap", bootstrap standard errors are computed using standard bootstrapping (unless Bollen-Stine bootstrapping is requested for the test statistic; in this case bootstrap standard errors are computed using model-based bootstrapping). If"none", no standard errors are computed. -
test: -
Character vector. See the documentation of the
lavTestfunction for a full list. Multiple names of test statistics can be provided. If"default", the value depends on the values of other arguments. See also thelavTestfunction to extract (alternative) test statistics from a fitted lavaan object. FMG test names such as"peba4","pols3","pall", and"all"can be requested here for supported ML-family models. The convenience value"fmg"resolves to"peba4_rls"for one-model tests. -
standard.test: -
Character. Choose the test statistic that will be used to compute fit measures (like CFI or RMSEA). The default is
"standard", but it could also be (for example)"Browne.residual.nt", or an FMG test name such as"peba4"or"fmg". -
scaled.test: -
Character. Choose the test statistic that will be scaled (if a scaled test statistic is requested). The default is
"standard", but it could also be (for example)"Browne.residual.nt". gamma.n.minus.one-
Logical. If
TRUE, we divide the Gamma matrix by N-1 (instead of the default N). gamma.unbiased-
Logical. If
TRUE, we compute an unbiased version for the Gamma matrix. Only available for single-level complete data and whenconditional.x = FALSEandfixed.x = FALSE(for now). Suffixless FMG test names use this option to choose between biased and unbiased Gamma. se.delta.second.order-
Logical. If
FALSE(the default), the standard errors of defined parameters (introduced with the:=operator) and of standardized parameters (as returned bystandardizedSolution()orlavInspect(., "vcov.std.*")) are computed using the first-order delta method. IfTRUE, the second-order delta method is used, which adds the term(whereis the Hessian of the transformed parameter andis the parameter covariance matrix) to the first-order variance approximation. This may improve accuracy when the transformation is a strongly non-linear function of the model parameters. Has no effect when standard errors are obtained by bootstrapping or by the Monte Carlo method. se.def-
Character. Method for computing standard errors (and confidence intervals) of defined parameters (introduced with the
:=operator). The default is"default"(or equivalently"delta"), which uses the delta method (respectingse.delta.second.order). Set to"monte.carlo"to use the Monte Carlo method of Preacher and Selig (2012). Under this method,Rdraws are taken from, the defined parameter is evaluated for each draw, and standard errors are obtained as the standard deviation of these realizations. Confidence intervals (inparameterEstimates()andstandardizedSolution()) are based on percentile bounds of the Monte Carlo distribution, and therefore can be asymmetric (just like bootstrap intervals). Has no effect whense = "bootstrap". monte.carlo-
List of settings for the Monte Carlo method (used when
se.def = "monte.carlo"). Currently recognizes:R(integer; number of Monte Carlo draws; default 20000) andseed(integer orNULL; optional seed for reproducibility). -
bootstrap: -
Number of bootstrap draws, if bootstrapping is used.
-
do.fit: -
If
FALSE, the model is not fit, and the current starting values of the model parameters are preserved.
Optimization options:
-
control: -
A list containing control parameters passed to the external optimizer. By default, lavaan uses
"nlminb". See the manpage ofnlminbfor an overview of the control parameters. If another (external) optimizer is selected, see the manpage for that optimizer to see the possible control parameters. -
optim.method: -
Character. The optimizer that should be used. For unconstrained optimization or models with only linear equality constraints (i.e., the model syntax does not include any "==", ">" or "<" operators), the available options are
"nlminb"(the default),"BFGS","L-BFGS-B". These are all quasi-newton methods. A basic implementation of Gauss-Newton is also available (optim.method = "GN"). The latter is the default whenestimator = "DLS". For constrained optimization, the only available option is"nlminb_constr", which uses an augmented Lagrangian minimization algorithm. -
optim.force.converged: -
Logical. If
TRUE, pretend the model has converged, no matter what. optim.dx.tol-
Numeric. Tolerance used for checking if the elements of the (unscaled) gradient are all zero (in absolute value). The default value is 0.001.
-
optim.gn.tol.x: -
Numeric. Only used when
optim.method = "GN". Optimization stops when the root mean square of the difference between the old and new parameter values is smaller than this tolerance value. Default is1e-05for DLS estimation and1e-07otherwise. -
optim.gn.iter.max: -
Integer. Only used when
optim.method = "GN". The maximum number of GN iterations. The default is 200. -
bounds: -
Only used if
optim.method = "nlminb". If logical:FALSEimplies no bounds are imposed on the parameters. IfTRUE, this impliesbounds = "wide". If character, possible options are"none"(the default),"standard","wide","pos.var","pos.ov.var", and"pos.lv.var". Ifbounds = "pos.ov.var", the observed variances are forced to be nonnegative. Ifbounds = "pos.lv.var", the latent variances are forced to be nonnegative. Ifbounds = "pos.var", both observed and latent variances are forced to be nonnegative. Ifbounds = "standard", lower and upper bounds are computed for observed and latent variances, and factor loadings. Ifbounds = "wide", lower and upper bounds are computed for observed and latent variances, and factor loadings; but the range of the bounds is enlarged (allowing again for slightly negative variances). -
optim.bounds: -
List. This can be used instead of the
boundsargument to allow more control. Possible elements of the list arelower,upper,lower.factorandupper.factor. All of these accept a vector. Thelowerandupperelements indicate for which type of parameters bounds should be computed. Possible choices are"ov.var","lv.var","loadings"and"covariances". Thelower.factorandupper.factorelements should have the same length as thelowerandupperelements respectively. They indicate the factor by which the range of the bounds should be enlarged (for example, 1.1 or 1.2; the default is 1.0). Other elements aremin.reliability.markerwhich sets the lower bound for the reliability of the marker indicator (if any) of each factor (default is 0.1). Finally, themin.var.lv.endoelement indicates the lower bound of the variance of any endogenous latent variable (default is 0.0).
Parallelization options (currently only used for bootstrapping):
- parallel
-
The type of parallel operation to be used (if any). If missing, the default is
"no". - ncpus
-
Integer: number of processes to be used in parallel operation: typically one would set this to the number of available CPUs. By default this is the number of cores (as detected by
parallel::detectCores()) minus one. - cl
-
An optional parallel or snow cluster for use if
parallel = "snow". If not supplied, a cluster on the local machine is created for the duration of thelavBootstrapcall. - iseed
-
An integer to set the seed. Or NULL if no reproducible results are needed. This works for both serial (non-parallel) and parallel settings. Internally,
RNGkind()is set to"L'Ecuyer-CMRG"ifparallel = "multicore". Ifparallel = "snow"(under windows),parallel::clusterSetRNGStream()is called which automatically switches to"L'Ecuyer-CMRG". Wheniseedis not NULL,.Random.seed(if it exists) in the global environment is left untouched.
Categorical estimation options:
-
zero.add: -
A numeric vector containing two values. These values affect the calculation of polychoric correlations when some frequencies in the bivariate table are zero. The first value only applies for 2x2 tables. The second value for larger tables. This value is added to the zero frequency in the bivariate table. If
"default", the value is set depending on the"mimic"option. By default, lavaan useszero.add = c(0.5, 0.0). -
zero.keep.margins: -
Logical. This argument only affects the computation of polychoric correlations for 2x2 tables with an empty cell, and where a value is added to the empty cell. If
TRUE, the other values of the frequency table are adjusted so that all margins are unaffected. If"default", the value is set depending on the"mimic"option. The default isTRUE. -
zero.cell.warn: -
Logical. Only used if some observed endogenous variables are categorical. If
TRUE, give a warning if one or more cells of a bivariate frequency table are empty. -
allow.empty.cell: -
Logical. If
TRUE, ignore situations where an ordinal variable has fewer categories than expected, or where a category is empty in a specific group. This argument is currently used by the blavaan package (which uses lavaan to set up the model). The argument is not expected to salvage a lavaan model that results in errors.
Starting values options:
-
start: -
If it is a character string, the two options are currently
"simple"and"default". In the first case, all parameter values are set to zero, except the factor loadings and (residual) variances, which are set to 0.7 and 1.0 respectively. Whenstartis"default", the factor loadings are estimated using the fabin3 estimator (tsls) per factor. The residual variances of observed variables are set to half the observed variance, and all other (residual) variances are set to 0.05. The remaining parameters (regression coefficients, covariances) are set to zero. Ifstartis a numerical vector, it should contain the starting values for all the free parameters (in the same order as the parameter table). Ifstartis a fitted object of classlavaan, the estimated values of the corresponding parameters will be extracted. If it is a parameter table, for example the output of theparameterEstimates()function, the values of theestorstartorustartcolumn (whichever is found first) will be extracted. -
rstarts: -
Integer. The number of refits that lavaan should try with random starting values. Random starting values are computed by drawing random numbers from a uniform distribution. Correlations are drawn from the interval [-0.5, +0.5] and then converted to covariances. Lower and upper bounds for (residual) variances are computed just like the standard bounds in bounded estimation. Random starting values are not computed for regression coefficients (which are always zero) and factor loadings of higher-order constructs (which are always unity). From all the runs that converged, the final solution is the one that resulted in the smallest value for the discrepancy function.
Check options:
-
check.start: -
Logical. If
TRUE, the starting values are checked for possibly inconsistent values (for example values implying correlations larger than one). If needed, a warning is given. -
check.sigma.pd: -
Character. If
"chol", a Cholesky decomposition is used to check if the model implied covariance matrix (Sigma) is positive definite. If"eigen", an eigen decomposition is used to check if Sigma is positive definite. The latter was the default until 0.6-20. From 0.6-21 onwards,"chol"became the default (as it is much faster). -
check.gradient: -
Logical. If
TRUE, and the model converged, a warning is given if the optimizer reported a (local) solution while not all elements of the (unscaled) gradient (as seen by the optimizer) are (near) zero, as they should be (the tolerance used is 0.001). -
check.post: -
Logical. If
TRUE, and the model converged, a check is performed after (post) fitting, to verify if the solution is admissible. This implies that all variances are non-negative, and all the model-implied covariance matrices are positive (semi-)definite. For the latter test, we tolerate a tiny negative eigenvalue that is smaller than .Machine$double.eps^(3/4), treating it as being zero. -
check.vcov: -
Logical. If
TRUE, and the model converged, we check if the variance-covariance matrix of the free parameters is positive definite. We take into account possible equality and active inequality constraints. If needed, a warning is given. -
check.lv.names: -
Logical. If
TRUE, and latent variables are defined in the model, lavaan will stop with an error message if a latent variable name also occurs in the data (implying it is also an observed variable).
Verbosity options:
-
verbose: -
If
TRUE, show what lavaan is doing. During estimation, the function value is printed out during each iteration. -
warn: -
If
FALSE, suppress all lavaan-specific warning messages. -
debug: -
If
TRUE, debugging information is printed out.
Miscellaneous:
-
model.type: -
Set the model type: possible values are
"cfa","sem"or"growth". This may affect how starting values are computed, and may be used to alter the terminology used in the summary output, or the layout of path diagrams that are based on a fitted lavaan object. -
mimic: -
If
"Mplus", an attempt is made to mimic the Mplus program. If"EQS", an attempt is made to mimic the EQS program. If"default", the value is (currently) set to"lavaan", which is very close to"Mplus". Seemimicfor the list of options that are affected by each setting. -
representation: -
If
"LISREL"the classical LISREL matrix representation is used to represent the model (using the all-y variant). No other options are available (for now). -
implied: -
Logical. If
TRUE, compute the model-implied statistics, and store them in the implied slot. -
h1: -
Logical. If
TRUE, compute the unrestricted model and store the unrestricted summary statistics (and perhaps a loglikelihood) in the h1 slot. baseline:-
Logical. If
TRUE, compute a baseline model (currently always the independence model, assuming all variables are uncorrelated) and store the results in the baseline slot. -
baseline.conditional.x.free.slopes: -
Logical. If
TRUE, andconditional.x = TRUE, the (default) baseline model will allow the slope structure to be unrestricted. store.vcov-
Logical. If
TRUE, andse=is not set to"none", store the full variance-covariance matrix of the model parameters in the vcov slot of the fitted lavaan object. parser-
Character. If
"new"(the default), the new parser is used to parse the model syntax. If"old", the original (pre 0.6-18) parser is used.
See Also
Examples
lavOptions() lavOptions("std.lv") lavOptions(c("std.lv", "orthogonal"))lavOptions() lavOptions("std.lv") lavOptions(c("std.lv", "orthogonal"))
Parameter Estimates
Description
Parameter estimates of a latent variable model.
Usage
lavParameterEstimates(object, se = TRUE, zstat = TRUE, pvalue = TRUE, ci = TRUE, standardized = FALSE, fmi = FALSE, plabel = FALSE, level = 0.95, boot.ci.type = "perc", cov.std = TRUE, fmi.options = list(), rsquare = FALSE, remove.system.eq = TRUE, remove.eq = TRUE, remove.ineq = TRUE, remove.def = FALSE, remove.nonfree = FALSE, remove.step1 = TRUE, remove.unused = FALSE, remove.aux = TRUE, add.attributes = FALSE, output = "data.frame", header = FALSE) parameterEstimates(object, se = TRUE, zstat = TRUE, pvalue = TRUE, ci = TRUE, standardized = FALSE, fmi = FALSE, plabel = FALSE, level = 0.95, boot.ci.type = "perc", cov.std = TRUE, fmi.options = list(), rsquare = FALSE, remove.system.eq = TRUE, remove.eq = TRUE, remove.ineq = TRUE, remove.def = FALSE, remove.nonfree = FALSE, remove.step1 = TRUE, remove.unused = FALSE, remove.aux = TRUE, add.attributes = FALSE, output = "data.frame", header = FALSE)lavParameterEstimates(object, se = TRUE, zstat = TRUE, pvalue = TRUE, ci = TRUE, standardized = FALSE, fmi = FALSE, plabel = FALSE, level = 0.95, boot.ci.type = "perc", cov.std = TRUE, fmi.options = list(), rsquare = FALSE, remove.system.eq = TRUE, remove.eq = TRUE, remove.ineq = TRUE, remove.def = FALSE, remove.nonfree = FALSE, remove.step1 = TRUE, remove.unused = FALSE, remove.aux = TRUE, add.attributes = FALSE, output = "data.frame", header = FALSE) parameterEstimates(object, se = TRUE, zstat = TRUE, pvalue = TRUE, ci = TRUE, standardized = FALSE, fmi = FALSE, plabel = FALSE, level = 0.95, boot.ci.type = "perc", cov.std = TRUE, fmi.options = list(), rsquare = FALSE, remove.system.eq = TRUE, remove.eq = TRUE, remove.ineq = TRUE, remove.def = FALSE, remove.nonfree = FALSE, remove.step1 = TRUE, remove.unused = FALSE, remove.aux = TRUE, add.attributes = FALSE, output = "data.frame", header = FALSE)
Arguments
object |
An object of class |
se |
Logical. If |
zstat |
Logical. If |
pvalue |
Logical. If |
ci |
If |
level |
The confidence level required. |
plabel |
Logical. If |
boot.ci.type |
If bootstrapping was used, the type of interval required.
The value should be one of |
standardized |
Logical or character. If |
cov.std |
Logical. If TRUE, the (residual) observed covariances are scaled by the square root of the ‘Theta’ diagonal elements, and the (residual) latent covariances are scaled by the square root of the ‘Psi’ diagonal elements. If FALSE, the (residual) observed covariances are scaled by the square root of the diagonal elements of the observed model-implied covariance matrix (Sigma), and the (residual) latent covariances are scaled by the square root of diagonal elements of the model-implied covariance matrix of the latent variables. |
fmi |
Logical. If |
fmi.options |
List. If non-empty, arguments can be provided to alter the default options when the model is fitted with the complete(d) data; otherwise, the same options are used as the original model. |
remove.eq |
Logical. If |
remove.system.eq |
Logical. If |
remove.ineq |
Logical. If |
remove.def |
Logical. If |
remove.nonfree |
Logical. If |
remove.step1 |
Logical. Only used by |
remove.unused |
Logical. If |
remove.aux |
Logical. If |
rsquare |
Logical. If |
add.attributes |
Deprecated argument. Please use output= instead. |
output |
Character. If |
header |
Logical. Only used if |
Value
A data.frame containing the estimated parameters, standard errors, and (by default) z-values, p-values, and the lower and upper values of the confidence intervals. If requested, extra columns are added with standardized versions of the parameter estimates.
References
Savalei, V. & Rhemtulla, M. (2012). On obtaining estimates of the fraction of missing information from FIML. Structural Equation Modeling: A Multidisciplinary Journal, 19(3), 477-494.
Examples
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) lavParameterEstimates(fit) lavParameterEstimates(fit, output = "text")HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) lavParameterEstimates(fit) lavParameterEstimates(fit, output = "text")
Predict the values of latent variables (and their indicators)
Description
The main purpose of the lavPredict() function is to compute (or
‘predict’) individual scores for the latent variables in the model
(‘factor scores’). NOTE: the goal of this
function is NOT to predict future values of dependent variables as in the
regression framework! (For models with only continuous observed variables, the function lavPredictY() supports this.)
Usage
lavPredict(object, newdata = NULL, type = "lv", method = "EBM", transform = FALSE, se = "none", acov = "none", label = TRUE, fsm = FALSE, mdist = FALSE, rel = FALSE, append.data = FALSE, assemble = FALSE, level = 1L, optim.method = "bfgs", ETA = NULL, parallel = c("auto", "no", "multicore", "snow"), ncpus = NULL, cl = NULL, drop.list.single.group = TRUE)lavPredict(object, newdata = NULL, type = "lv", method = "EBM", transform = FALSE, se = "none", acov = "none", label = TRUE, fsm = FALSE, mdist = FALSE, rel = FALSE, append.data = FALSE, assemble = FALSE, level = 1L, optim.method = "bfgs", ETA = NULL, parallel = c("auto", "no", "multicore", "snow"), ncpus = NULL, cl = NULL, drop.list.single.group = TRUE)
Arguments
object |
An object of class |
newdata |
An optional data.frame, containing the same variables as the data.frame used when fitting the model in object. |
type |
A character string. If |
method |
A character string. In the linear case (when the indicators are
continuous), the possible options are |
transform |
Logical. If |
se |
Character. If |
acov |
Similar to the |
label |
Logical. If TRUE, the columns in the output are labeled. |
fsm |
Logical. If TRUE, return the factor score matrix as an attribute. Only for numeric data. |
mdist |
Logical. If TRUE, the (squared)
Mahalanobis distances of the factor scores (if |
rel |
Logical. Only used if |
append.data |
Logical. Only used when |
assemble |
Logical. If TRUE, the separate groups are reassembled into a single data.frame with a group column, having the same dimensions as the original (or newdata) dataset. |
level |
Integer. Only used in a multilevel SEM.
If |
optim.method |
Character string. Only used in the categorical case.
If |
ETA |
An optional matrix or list, containing latent variable values
for each observation. Used for computations when |
parallel |
Character. Only used in the categorical case, where factor
scores are computed by a per-observation numerical optimization. The options
are |
ncpus |
Integer. The number of processes to use in parallel computation. The default is to use all available cores, minus two. |
cl |
An optional parallel or snow cluster for use when
|
drop.list.single.group |
Logical. If |
Details
The predict() function calls the lavPredict() function
with its default options.
If there are no latent variables in the model, type = "ov" will
simply return the values of the observed variables. Note that this function
can not be used to ‘predict’ values of dependent variables, given the
values of independent variables (in the regression sense). In other words,
the structural component is completely ignored (for now).
References
For an overview (and evaluation) of the various factor score methods, see:
Grice, J. W. (2001). Computing and evaluating factor scores. Psychological Methods, 6(4), 430-450. doi:10.1037/1082-989X.6.4.430
For the (continuous) regression and Bartlett methods, see:
Bartlett, M. S. (1937). The statistical conception of mental factors. British Journal of Psychology, 28, 97-104. doi:10.1111/j.2044-8295.1937.tb00863.x
Bentler, P. M., & Yuan, K.-H. (1997). Optimal conditionally unbiased equivariant factor score estimators. In M. Berkane (Ed.), Latent variable modeling and applications to causality (pp. 259-281). New York: Springer-Verlag. doi:10.1007/978-1-4612-1842-5_14
For the (categorical) Empirical Bayes Modal (EBM) and Maximum Likelihood (ML) methods, see:
Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models. Boca Raton, FL: Chapman & Hall/CRC.
For the correlation-preserving factor scores (transform = TRUE), see:
ten Berge, J. M. F., Krijnen, W. P., Wansbeek, T., & Shapiro, A. (1999). Some new results on correlation-preserving factor scores prediction methods. Linear Algebra and its Applications, 289(1-3), 311-318. doi:10.1016/S0024-3795(97)10007-6
See Also
lavPredictY to predict y-variables given x-variables.
Examples
data(HolzingerSwineford1939) ## fit model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) head(lavPredict(fit)) head(lavPredict(fit, type = "ov")) ## --------------------------------------------- ## standard errors for the factor scores (se =) ## --------------------------------------------- ## the standard errors are returned as the "se" attribute (a list, one ## (nobs x nfactor) matrix per group) ## for continuous indicators, the (naive) standard errors are the same ## for every observation fscores <- lavPredict(fit, se = "standard") attr(fscores, "se")[[1]] ## for categorical indicators, the factor scores are obtained by numerical ## optimization, and their standard errors differ from one response pattern ## (observation) to the next HS.ord <- HolzingerSwineford1939 HS.ord[ , paste0("x", 1:9)] <- lapply(HS.ord[ , paste0("x", 1:9)], function(x) ordered(cut(x, 3))) fit.ord <- cfa(HS.model, data = HS.ord, ordered = paste0("x", 1:9)) fscores <- lavPredict(fit.ord, se = "standard") head(attr(fscores, "se")[[1]]) ## ------------------------------------------ ## merge factor scores to original data.frame ## ------------------------------------------ idx <- lavInspect(fit, "case.idx") fscores <- lavPredict(fit) ## loop over factors for (fs in colnames(fscores)) { HolzingerSwineford1939[idx, fs] <- fscores[ , fs] } head(HolzingerSwineford1939) ## multigroup models return a list of factor scores (one per group) data(HolzingerSwineford1939) mgfit <- update(fit, group = "school", group.equal = c("loadings","intercepts")) idx <- lavInspect(mgfit, "case.idx") # list: 1 vector per group fscores <- lavPredict(mgfit) # list: 1 matrix per group ## loop over groups and factors for (g in seq_along(fscores)) { for (fs in colnames(fscores[[g]])) { HolzingerSwineford1939[ idx[[g]], fs] <- fscores[[g]][ , fs] } } head(HolzingerSwineford1939) ## ------------------------------------- ## Use factor scores in subsequent models ## ------------------------------------- ## see Examples in semTools package: ?plausibleValuesdata(HolzingerSwineford1939) ## fit model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) head(lavPredict(fit)) head(lavPredict(fit, type = "ov")) ## --------------------------------------------- ## standard errors for the factor scores (se =) ## --------------------------------------------- ## the standard errors are returned as the "se" attribute (a list, one ## (nobs x nfactor) matrix per group) ## for continuous indicators, the (naive) standard errors are the same ## for every observation fscores <- lavPredict(fit, se = "standard") attr(fscores, "se")[[1]] ## for categorical indicators, the factor scores are obtained by numerical ## optimization, and their standard errors differ from one response pattern ## (observation) to the next HS.ord <- HolzingerSwineford1939 HS.ord[ , paste0("x", 1:9)] <- lapply(HS.ord[ , paste0("x", 1:9)], function(x) ordered(cut(x, 3))) fit.ord <- cfa(HS.model, data = HS.ord, ordered = paste0("x", 1:9)) fscores <- lavPredict(fit.ord, se = "standard") head(attr(fscores, "se")[[1]]) ## ------------------------------------------ ## merge factor scores to original data.frame ## ------------------------------------------ idx <- lavInspect(fit, "case.idx") fscores <- lavPredict(fit) ## loop over factors for (fs in colnames(fscores)) { HolzingerSwineford1939[idx, fs] <- fscores[ , fs] } head(HolzingerSwineford1939) ## multigroup models return a list of factor scores (one per group) data(HolzingerSwineford1939) mgfit <- update(fit, group = "school", group.equal = c("loadings","intercepts")) idx <- lavInspect(mgfit, "case.idx") # list: 1 vector per group fscores <- lavPredict(mgfit) # list: 1 matrix per group ## loop over groups and factors for (g in seq_along(fscores)) { for (fs in colnames(fscores[[g]])) { HolzingerSwineford1939[ idx[[g]], fs] <- fscores[[g]][ , fs] } } head(HolzingerSwineford1939) ## ------------------------------------- ## Use factor scores in subsequent models ## ------------------------------------- ## see Examples in semTools package: ?plausibleValues
Predict the values of y-variables given the values of x-variables
Description
This function can be used to predict the values of (observed) y-variables given the values of (observed) x-variables in a structural equation model.
Usage
lavPredictY(object, newdata = NULL, ynames = lav_object_vnames(object, "ov.y"), xnames = lav_object_vnames(object, "ov.x"), method = "conditional.mean", label = TRUE, assemble = TRUE, force.zero.mean = FALSE, lambda = 0)lavPredictY(object, newdata = NULL, ynames = lav_object_vnames(object, "ov.y"), xnames = lav_object_vnames(object, "ov.x"), method = "conditional.mean", label = TRUE, assemble = TRUE, force.zero.mean = FALSE, lambda = 0)
Arguments
object |
An object of class |
newdata |
An optional data.frame, containing the same variables as
the data.frame that was used when fitting the model in |
ynames |
The names of the observed variables that should be treated as the y-variables. It is for these variables that the function will predict the (model-based) values for each observation. Can also be a list to allow for a separate set of variable names per group (or block). |
xnames |
The names of the observed variables that should be treated as the x-variables. Can also be a list to allow for a separate set of variable names per group (or block). |
method |
A character string. The only available option for now is
|
label |
Logical. If TRUE, the columns of the output are labeled. |
assemble |
Logical. If TRUE, the predictions for the separate groups in the output are reassembled into a single data.frame with a group column, having the same dimensions as the original (or newdata) dataset. |
force.zero.mean |
Logical. Only relevant if there is no mean structure.
If |
lambda |
Numeric. A lambda regularization penalty term. |
Details
This function can be used for (SEM-based) out-of-sample predictions of
outcome (y) variables, given the values of predictor (x) variables. This
is in contrast to the lavPredict() function which (historically)
only ‘predicts’ the (factor) scores for latent variables, ignoring the
structural part of the model.
When method = "conditional.mean", predictions (for y given x)
are based on the (joint y and x) model-implied variance-covariance (Sigma)
matrix and mean vector (Mu), and the standard expression for the
conditional mean of a multivariate normal distribution. Note that if the
model is saturated (and hence df = 0), the SEM-based predictions are identical
to ordinary least squares predictions.
Lambda is a regularization penalty term to improve prediction accuracy that can
be determined using the lavPredictY_cv function.
References
de Rooij, M., Karch, J.D., Fokkema, M., Bakk, Z., Pratiwi, B.C, and Kelderman, H. (2022) SEM-Based Out-of-Sample Predictions, Structural Equation Modeling: A Multidisciplinary Journal. doi:10.1080/10705511.2022.2061494
Molina, M. D., Molina, L., & Zappaterra, M. W. (2024). Aspects of Higher Consciousness: A Psychometric Validation and Analysis of a New Model of Mystical Experience. doi:10.31219/osf.io/cgb6e
See Also
lavPredict to compute scores for latent variables.
lavPredictY_cv to determine an optimal lambda to increase
prediction accuracy.
Examples
model <- ' # latent variable definitions ind60 =~ x1 + x2 + x3 dem60 =~ y1 + a*y2 + b*y3 + c*y4 dem65 =~ y5 + a*y6 + b*y7 + c*y8 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 # residual correlations y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 ' fit <- sem(model, data = PoliticalDemocracy) lavPredictY(fit, ynames = c("y5", "y6", "y7", "y8"), xnames = c("x1", "x2", "x3", "y1", "y2", "y3", "y4"))model <- ' # latent variable definitions ind60 =~ x1 + x2 + x3 dem60 =~ y1 + a*y2 + b*y3 + c*y4 dem65 =~ y5 + a*y6 + b*y7 + c*y8 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 # residual correlations y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 ' fit <- sem(model, data = PoliticalDemocracy) lavPredictY(fit, ynames = c("y5", "y6", "y7", "y8"), xnames = c("x1", "x2", "x3", "y1", "y2", "y3", "y4"))
Determine an optimal lambda penalty value through cross-validation
Description
This function can be used to determine an optimal lambda value for the
lavPredictY function, based on cross-validation.
Usage
lavPredictY_cv(object, data = NULL, xnames = lav_object_vnames(object, "ov.x"), ynames = lav_object_vnames(object, "ov.y"), n.folds = 10L, lambda.seq = seq(0, 1, 0.1))lavPredictY_cv(object, data = NULL, xnames = lav_object_vnames(object, "ov.x"), ynames = lav_object_vnames(object, "ov.y"), n.folds = 10L, lambda.seq = seq(0, 1, 0.1))
Arguments
object |
An object of class |
data |
A data.frame, containing the same variables as the data.frame that
was used when fitting the model in |
xnames |
The names of the observed variables that should be treated as the x-variables. Can also be a list to allow for a separate set of variable names per group (or block). |
ynames |
The names of the observed variables that should be treated as the y-variables. It is for these variables that the function will predict the (model-based) values for each observation. Can also be a list to allow for a separate set of variable names per group (or block). |
n.folds |
Integer. The number of folds to be used during cross-validation. |
lambda.seq |
An R |
Details
This function determines an optimal lambda value for use with
lavPredictY, in order to improve prediction accuracy.
References
de Rooij, M., Karch, J.D., Fokkema, M., Bakk, Z., Pratiwi, B.C, and Kelderman, H. (2022) SEM-Based Out-of-Sample Predictions, Structural Equation Modeling: A Multidisciplinary Journal. doi:10.1080/10705511.2022.2061494
Molina, M. D., Molina, L., & Zappaterra, M. W. (2024). Aspects of Higher Consciousness: A Psychometric Validation and Analysis of a New Model of Mystical Experience. doi:10.31219/osf.io/cgb6e
See Also
lavPredictY to predict the values of (observed) y-variables given
the values of (observed) x-variables in a structural equation model.
Examples
colnames(PoliticalDemocracy) <- c("z1", "z2", "z3", "z4", "y1", "y2", "y3", "y4", "x1", "x2", "x3") model <- ' # latent variable definitions ind60 =~ x1 + x2 + x3 dem60 =~ z1 + z2 + z3 + z4 dem65 =~ y1 + y2 + y3 + y4 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 # residual correlations z1 ~~ y1 z2 ~~ z4 + y2 z3 ~~ y3 z4 ~~ y4 y2 ~~ y4 ' fit <- sem(model, data = PoliticalDemocracy, meanstructure = TRUE) percent <- 0.5 nobs <- lavInspect(fit, "ntotal") idx <- sort(sample(x = nobs, size = floor(percent*nobs))) xnames = c("z1", "z2", "z3", "z4", "x1", "x2", "x3") ynames = c("y1", "y2", "y3", "y4") reg.results <- lavPredictY_cv( fit, PoliticalDemocracy[-idx, ], xnames = xnames, ynames = ynames, n.folds = 10L, lambda.seq = seq(from = .6, to = 2.5, by = .1) ) lam <- reg.results$lambda.min lavPredictY(fit, newdata = PoliticalDemocracy[idx,], ynames = ynames, xnames = xnames, lambda = lam)colnames(PoliticalDemocracy) <- c("z1", "z2", "z3", "z4", "y1", "y2", "y3", "y4", "x1", "x2", "x3") model <- ' # latent variable definitions ind60 =~ x1 + x2 + x3 dem60 =~ z1 + z2 + z3 + z4 dem65 =~ y1 + y2 + y3 + y4 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 # residual correlations z1 ~~ y1 z2 ~~ z4 + y2 z3 ~~ y3 z4 ~~ y4 y2 ~~ y4 ' fit <- sem(model, data = PoliticalDemocracy, meanstructure = TRUE) percent <- 0.5 nobs <- lavInspect(fit, "ntotal") idx <- sort(sample(x = nobs, size = floor(percent*nobs))) xnames = c("z1", "z2", "z3", "z4", "x1", "x2", "x3") ynames = c("y1", "y2", "y3", "y4") reg.results <- lavPredictY_cv( fit, PoliticalDemocracy[-idx, ], xnames = xnames, ynames = ynames, n.folds = 10L, lambda.seq = seq(from = .6, to = 2.5, by = .1) ) lam <- reg.results$lambda.min lavPredictY(fit, newdata = PoliticalDemocracy[idx,], ynames = ynames, xnames = xnames, lambda = lam)
Residuals
Description
‘lavResiduals’ provides model residuals and standardized residuals from a fitted lavaan object, as well as various summaries of these residuals.
The ‘residuals()’ (and ‘resid()’) methods are just shortcuts to this function with a limited set of arguments.
Usage
lavResiduals(object, type = "cor.bentler", h1 = NULL, se = FALSE, zstat = TRUE, summary = TRUE, elementwise = TRUE, combine = FALSE, usrmr.ci.level = 0.90, usrmr.close.h0 = 0.05, h1.acov = "unstructured", add.type = TRUE, add.labels = TRUE, add.class = TRUE, drop.list.single.group = TRUE, maximum.number = 0L, n.largest = 5L, output = "list")lavResiduals(object, type = "cor.bentler", h1 = NULL, se = FALSE, zstat = TRUE, summary = TRUE, elementwise = TRUE, combine = FALSE, usrmr.ci.level = 0.90, usrmr.close.h0 = 0.05, h1.acov = "unstructured", add.type = TRUE, add.labels = TRUE, add.class = TRUE, drop.list.single.group = TRUE, maximum.number = 0L, n.largest = 5L, output = "list")
Arguments
object |
An object of class |
type |
Character.
If |
h1 |
Optional. A user-provided saturated (unrestricted) model supplying
the observed summary statistics against which the model-implied statistics are
compared. It can be a fitted |
se |
Logical. If |
zstat |
Logical. If |
summary |
Logical. If The two versions are reported with different inferential statistics, and this asymmetry is intentional. The sample RMR/SRMR/CRMR overestimate (are positively biased for) their population values. For these (biased) statistics, we report a standard error and a test of exact fit (the null hypothesis that the population value equals zero). This test relies on the known sampling distribution of the (biased) sample statistic under exact fit (Maydeu-Olivares, 2017, Eqs. 28–30), where the bias is explicitly accounted for. For the (approximately) unbiased URMR/USRMR/UCRMR, we report a standard error, a confidence interval, and a test of close fit (the null hypothesis that the population value equals a small nonzero cutoff, e.g. 0.05). The confidence interval and the close-fit test require an (approximately) unbiased and normally distributed estimator, which is precisely why the unbiased version is used here. Conversely, no test of exact fit is reported for the unbiased estimator: because it is truncated at zero, its sampling distribution is degenerate at the exact-fit boundary, so the test of exact fit is (correctly) only based on the biased statistic. |
elementwise |
Logical. If |
combine |
Logical. Only relevant when multiple blocks are
involved (multiple groups, or multiple levels). If |
usrmr.ci.level |
Numeric. The confidence level of the confidence interval that is reported (in the summary) for the unbiased URMR/USRMR/UCRMR. The default is 0.90. |
usrmr.close.h0 |
Numeric. The value of the population URMR/USRMR/UCRMR under the null hypothesis of the test of close fit that is reported (in the summary) for the unbiased estimator. The default is 0.05. |
h1.acov |
Character. If |
add.type |
Logical. If |
add.labels |
If |
add.class |
If |
drop.list.single.group |
If |
maximum.number |
Integer. Only used if |
n.largest |
Integer. Only used if |
output |
Character. By default, |
Value
If drop.list.single.group = TRUE, a list of (residualized) summary
statistics, including type, standardized residuals, and summaries. If
drop.list.single.group = FALSE, the list of summary statistics is nested
within a list for each group.
References
Bentler, P.M. and Dijkstra, T. (1985). Efficient estimation via linearization in structural models. In Krishnaiah, P.R. (Ed.), Multivariate analysis - VI, (pp. 9–42). New York, NY: Elsevier.
Ogasawara, H. (2001). Standard errors of fit indices using residuals in structural equation modeling. Psychometrika, 66(3), 421–436. doi:10.1007/BF02294443
Maydeu-Olivares, A. (2017). Assessing the size of model misfit in structural equation models. Psychometrika, 82(3), 533–558. doi:10.1007/s11336-016-9552-7
Standardized Residuals in Mplus. Document retrieved from URL http://www.statmodel.com/download/StandardizedResiduals.pdf
Examples
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) lavResiduals(fit)HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) lavResiduals(fit)
Extract Empirical Estimating Functions
Description
A function for extracting the empirical estimating functions of a fitted lavaan model. This is the derivative of the objective function with respect to the parameter vector, evaluated at the observed (case-wise) data. In other words, this function returns the case-wise scores, evaluated at the fitted model parameters.
Usage
estfun.lavaan(object, scaling = FALSE, ignore_constraints = FALSE, remove_duplicated = TRUE, remove_empty_cases = TRUE, ...) lavScores(object, scaling = FALSE, ignore_constraints = FALSE, remove_duplicated = TRUE, remove_empty_cases = TRUE, ...)estfun.lavaan(object, scaling = FALSE, ignore_constraints = FALSE, remove_duplicated = TRUE, remove_empty_cases = TRUE, ...) lavScores(object, scaling = FALSE, ignore_constraints = FALSE, remove_duplicated = TRUE, remove_empty_cases = TRUE, ...)
Arguments
object |
An object of class |
scaling |
Only used for the ML estimator. If |
ignore_constraints |
Logical. If |
remove_duplicated |
If |
remove_empty_cases |
If |
... |
To accept old argument names with dots. No other arguments are accepted. |
Value
A n x k matrix corresponding to n observations and k parameters.
Author(s)
Ed Merkle for the ML case; the remove.duplicated,
ignore.constraints and remove.empty.cases arguments were added by
Yves Rosseel; Franz Classe for the WLS case.
Examples
## The famous Holzinger and Swineford (1939) example HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) head(lavScores(fit))## The famous Holzinger and Swineford (1939) example HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) head(lavScores(fit))
Simulate Data From a Lavaan Model Syntax
Description
Simulate data starting from a lavaan model syntax.
Usage
lavSimulateData(model = NULL, model.type = "sem", meanstructure = FALSE, int.ov.free = TRUE, int.lv.free = FALSE, marker.int.zero = FALSE, conditional.x = FALSE, composites = TRUE, fixed.x = FALSE, orthogonal = FALSE, std.lv = TRUE, auto.fix.first = FALSE, auto.fix.single = FALSE, auto.var = TRUE, auto.cov.lv.x = TRUE, auto.cov.y = TRUE, ..., sample.nobs = 500L, ov.var = NULL, group.label = NULL, skewness = NULL, kurtosis = NULL, cluster.idx = NULL, seed = NULL, empirical = FALSE, mass = FALSE, ordered.center = TRUE, return.type = "data.frame", return.fit = FALSE, debug = FALSE, standardized = FALSE) simulateData(model = NULL, model.type = "sem", meanstructure = FALSE, int.ov.free = TRUE, int.lv.free = FALSE, marker.int.zero = FALSE, conditional.x = FALSE, composites = TRUE, fixed.x = FALSE, orthogonal = FALSE, std.lv = TRUE, auto.fix.first = FALSE, auto.fix.single = FALSE, auto.var = TRUE, auto.cov.lv.x = TRUE, auto.cov.y = TRUE, ..., sample.nobs = 500L, ov.var = NULL, group.label = NULL, skewness = NULL, kurtosis = NULL, cluster.idx = NULL, seed = NULL, empirical = FALSE, mass = FALSE, ordered.center = TRUE, return.type = "data.frame", return.fit = FALSE, debug = FALSE, standardized = FALSE) lav_data_simulate_old(..., ordered.center = FALSE)lavSimulateData(model = NULL, model.type = "sem", meanstructure = FALSE, int.ov.free = TRUE, int.lv.free = FALSE, marker.int.zero = FALSE, conditional.x = FALSE, composites = TRUE, fixed.x = FALSE, orthogonal = FALSE, std.lv = TRUE, auto.fix.first = FALSE, auto.fix.single = FALSE, auto.var = TRUE, auto.cov.lv.x = TRUE, auto.cov.y = TRUE, ..., sample.nobs = 500L, ov.var = NULL, group.label = NULL, skewness = NULL, kurtosis = NULL, cluster.idx = NULL, seed = NULL, empirical = FALSE, mass = FALSE, ordered.center = TRUE, return.type = "data.frame", return.fit = FALSE, debug = FALSE, standardized = FALSE) simulateData(model = NULL, model.type = "sem", meanstructure = FALSE, int.ov.free = TRUE, int.lv.free = FALSE, marker.int.zero = FALSE, conditional.x = FALSE, composites = TRUE, fixed.x = FALSE, orthogonal = FALSE, std.lv = TRUE, auto.fix.first = FALSE, auto.fix.single = FALSE, auto.var = TRUE, auto.cov.lv.x = TRUE, auto.cov.y = TRUE, ..., sample.nobs = 500L, ov.var = NULL, group.label = NULL, skewness = NULL, kurtosis = NULL, cluster.idx = NULL, seed = NULL, empirical = FALSE, mass = FALSE, ordered.center = TRUE, return.type = "data.frame", return.fit = FALSE, debug = FALSE, standardized = FALSE) lav_data_simulate_old(..., ordered.center = FALSE)
Arguments
model |
A description of the user-specified model. Typically, the model
is described using the lavaan model syntax. See
|
model.type |
Set the model type: possible values
are |
meanstructure |
If |
int.ov.free |
If |
int.lv.free |
If |
marker.int.zero |
Logical. Only relevant if the metric of each latent
variable is set by fixing the first factor loading to unity.
If |
conditional.x |
If |
composites |
If |
fixed.x |
If |
orthogonal |
If |
std.lv |
If |
auto.fix.first |
If |
auto.fix.single |
If |
auto.var |
If |
auto.cov.lv.x |
If |
auto.cov.y |
If |
... |
additional arguments passed to the |
sample.nobs |
Number of observations. If a vector, multiple datasets
are created. If |
ov.var |
The user-specified variances of the observed variables. |
group.label |
The group labels that should be used if multiple groups are created. |
skewness |
Numeric vector. The skewness values for the observed variables. Defaults to zero. |
kurtosis |
Numeric vector. The kurtosis values for the observed variables. Defaults to zero. |
cluster.idx |
Optional. Only used (and only available via
|
seed |
Set random seed. |
empirical |
Logical. If |
mass |
Logical. If |
ordered.center |
Logical. Only relevant for categorical data, which is
generated by the (new) multilevel-aware engine. If |
return.type |
If |
return.fit |
If |
debug |
If |
standardized |
If |
Details
Model parameters can be specified by fixed values in the lavaan model syntax. If no fixed values are specified, the value zero will be assumed, except for factor loadings and variances, which are set to 0.7 and 1.0 respectively. By default, multivariate normal data are generated. However, by providing skewness and/or kurtosis values, nonnormal multivariate data can be generated, using the Vale & Maurelli (1983) method.
There is a single data-simulation engine. Multilevel data (model syntax
containing level: blocks, or when the cluster.idx argument is
provided) are generated by an internal multilevel worker; all single-level data
(continuous and categorical, including the ov.var, skewness,
kurtosis, standardized and mass options) are generated by
the historical single-level worker, so that the continuous, single-level output
remains byte-identical to previous versions. For multilevel data, the
ov.var, skewness, kurtosis, standardized and
mass arguments are not (yet) supported and are ignored (with a warning).
lav_data_simulate_old() is a deprecated wrapper kept for backward
compatibility; it forwards to the unified engine (with ordered.center =
FALSE by default, reproducing the historical threshold cut).
Value
The generated data. Either as a data.frame
(if return.type="data.frame"),
a numeric matrix (if return.type="matrix"),
or a covariance matrix (if return.type="cov").
Examples
# specify population model population.model <- ' f1 =~ x1 + 0.8*x2 + 1.2*x3 f2 =~ x4 + 0.5*x5 + 1.5*x6 f3 =~ x7 + 0.1*x8 + 0.9*x9 f3 ~ 0.5*f1 + 0.6*f2 ' # generate data set.seed(1234) myData <- lavSimulateData(population.model, sample.nobs=100L) # population moments fitted(sem(population.model)) # sample moments round(cov(myData), 3) round(colMeans(myData), 3) # fit model myModel <- ' f1 =~ x1 + x2 + x3 f2 =~ x4 + x5 + x6 f3 =~ x7 + x8 + x9 f3 ~ f1 + f2 ' fit <- sem(myModel, data=myData) summary(fit)# specify population model population.model <- ' f1 =~ x1 + 0.8*x2 + 1.2*x3 f2 =~ x4 + 0.5*x5 + 1.5*x6 f3 =~ x7 + 0.1*x8 + 0.9*x9 f3 ~ 0.5*f1 + 0.6*f2 ' # generate data set.seed(1234) myData <- lavSimulateData(population.model, sample.nobs=100L) # population moments fitted(sem(population.model)) # sample moments round(cov(myData), 3) round(colMeans(myData), 3) # fit model myModel <- ' f1 =~ x1 + x2 + x3 f2 =~ x4 + x5 + x6 f3 =~ x7 + x8 + x9 f3 ~ f1 + f2 ' fit <- sem(myModel, data=myData) summary(fit)
lavaan frequency tables
Description
Frequency tables for categorical variables and related statistics.
Usage
lavTables(object, dimension = 2L, type = "cells", categorical = NULL, group = NULL, statistic = "default", G2.min = 3, X2.min = 3, p.value = FALSE, output = "data.frame", patternAsString = TRUE)lavTables(object, dimension = 2L, type = "cells", categorical = NULL, group = NULL, statistic = "default", G2.min = 3, X2.min = 3, p.value = FALSE, output = "data.frame", patternAsString = TRUE)
Arguments
object |
Either a |
dimension |
Integer. If 0L, display all response patterns. If 1L,
display one-dimensional (one-way) tables; if 2L, display two-dimensional
(two-way or pairwise) tables. For the latter, the information shown
per row can be changed: if |
type |
If |
categorical |
Only used if |
group |
Only used if |
statistic |
Either a character string, or a vector of character strings
requesting one or more statistics for each cell, pattern or table. Always
available are |
G2.min |
Numeric. All cells with a G2 statistic larger than this number
are considered ‘large’, as reflected in the (optional) |
X2.min |
Numeric. All cells with a X2 statistic larger than this number
are considered ‘large’, as reflected in the (optional) |
p.value |
Logical. If |
output |
If |
patternAsString |
Logical. Only used for response patterns (dimension = 0L). If |
Value
If output = "data.frame", the output is presented as a data.frame
where each row is either a cell, a table, or a response pattern, depending on
the "type" argument.
If output = "table" (only for two-way tables), the output is
a list of tables (if type = "cells") in which each list element
corresponds to a pairwise table, or a single table per group (if
type = "table"). In both cases, the table entries are determined by the
(single) statistic argument.
References
Joreskog, K.G. & Moustaki, I. (2001). Factor analysis of ordinal variables: A comparison of three approaches. Multivariate Behavioral Research, 36, 347-387.
See Also
Examples
HS9 <- HolzingerSwineford1939[,c("x1","x2","x3","x4","x5", "x6","x7","x8","x9")] HSbinary <- as.data.frame( lapply(HS9, cut, 2, labels=FALSE) ) # using the data only lavTables(HSbinary, dim = 0L, categorical = names(HSbinary)) lavTables(HSbinary, dim = 1L, categorical = names(HSbinary), stat=c("th.un")) lavTables(HSbinary, dim = 2L, categorical = names(HSbinary), type = "table") # fit a model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HSbinary, ordered=names(HSbinary)) lavTables(fit, 1L) lavTables(fit, 2L, type="cells") lavTables(fit, 2L, type="table", stat=c("cor.un", "G2", "cor")) lavTables(fit, 2L, type="table", output="table", stat="X2")HS9 <- HolzingerSwineford1939[,c("x1","x2","x3","x4","x5", "x6","x7","x8","x9")] HSbinary <- as.data.frame( lapply(HS9, cut, 2, labels=FALSE) ) # using the data only lavTables(HSbinary, dim = 0L, categorical = names(HSbinary)) lavTables(HSbinary, dim = 1L, categorical = names(HSbinary), stat=c("th.un")) lavTables(HSbinary, dim = 2L, categorical = names(HSbinary), type = "table") # fit a model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HSbinary, ordered=names(HSbinary)) lavTables(fit, 1L) lavTables(fit, 2L, type="cells") lavTables(fit, 2L, type="table", stat=c("cor.un", "G2", "cor")) lavTables(fit, 2L, type="table", output="table", stat="X2")
Pairwise maximum likelihood fit statistics
Description
Three measures of fit for the pairwise maximum likelihood estimation method that are based on likelihood ratios (LR) are defined:
, , and . Subscript signifies a comparison of model-implied proportions of full response
patterns with observed sample proportions, subscript signifies a comparison of model-implied proportions of full response
patterns with the proportions implied by the assumption of multivariate normality, and subscript signifies
a comparison of model-implied proportions of pairs of item responses with the observed proportions of pairs of item responses.
Usage
lavTablesFitCf(object) lavTablesFitCp(object, alpha = 0.05) lavTablesFitCm(object)lavTablesFitCf(object) lavTablesFitCp(object, alpha = 0.05) lavTablesFitCm(object)
Arguments
object |
An object of class |
alpha |
The nominal level of significance of global fit. |
Details
The statistic compares the log-likelihood of the model-implied proportions () with the observed proportions ()
of the full multivariate responses patterns:
which asymptotically has a chi-square distribution with
where denotes the number of items with discrete response scales, denotes the number of response options, and denotes
the number of parameters to be estimated. Notice that results may be biased because of large numbers of empty cells in the multivariate
contingency table.
The statistic is based on the statistic, and compares the proportions implied by the model of interest (Model 1)
with proportions implied by the assumption of an underlying multivariate normal distribution (Model 0):
where is for Model 0 and is for Model 1. Statistic has a chi-square distribution with
degrees of freedom
where denotes the number of items with discrete response scales, denotes the number of response options, and
denotes the number of polychoric correlations, denotes the number of thresholds, and is the number of parameters of the
model of interest. Notice that results may be biased because of large numbers of empty cells in the multivariate contingency table. However,
bias may cancel out as both Model 1 and Model 0 contain the same pattern of empty responses.
With the statistic we only consider pairs of responses, and compare observed sample proportions () with model-implied proportions
of pairs of responses (). For items and we obtain a pairwise likelihood ratio test statistic
where denotes the number of response options and denotes sample size. The statistic has an asymptotic chi-square distribution
with degrees of freedom equal to the information minus the number of parameters (2(m-1) thresholds and 1 correlation),
As denotes the number of items, there are possible pairs of items. The statistic should therefore be applied with
a Bonferroni adjusted level of significance , with
to keep the family-wise error rate at . The hypothesis of overall goodness-of-fit is tested at and rejected as
soon as is significant at for at least one pair of items. Notice that with dichotomous items, ,
and , so that the hypothesis cannot be tested.
References
Barendse, M. T., Ligtvoet, R., Timmerman, M. E., & Oort, F. J. (2016). Structural Equation Modeling of Discrete data: Model Fit after Pairwise Maximum Likelihood. Frontiers in psychology, 7, 1-8.
Joreskog, K. G., & Moustaki, I. (2001). Factor analysis of ordinal variables: A comparison of three approaches. Multivariate Behavioral Research, 36, 347-387.
See Also
Examples
# Data HS9 <- HolzingerSwineford1939[,c("x1","x2","x3","x4","x5", "x6","x7","x8","x9")] HSbinary <- as.data.frame( lapply(HS9, cut, 2, labels=FALSE) ) # Single group example with one latent factor HS.model <- ' trait =~ x1 + x2 + x3 + x4 ' fit <- cfa(HS.model, data=HSbinary[,1:4], ordered=names(HSbinary[,1:4]), estimator="PML") lavTablesFitCm(fit) lavTablesFitCp(fit) lavTablesFitCf(fit)# Data HS9 <- HolzingerSwineford1939[,c("x1","x2","x3","x4","x5", "x6","x7","x8","x9")] HSbinary <- as.data.frame( lapply(HS9, cut, 2, labels=FALSE) ) # Single group example with one latent factor HS.model <- ' trait =~ x1 + x2 + x3 + x4 ' fit <- cfa(HS.model, data=HSbinary[,1:4], ordered=names(HSbinary[,1:4]), estimator="PML") lavTablesFitCm(fit) lavTablesFitCp(fit) lavTablesFitCf(fit)
Test of exact fit
Description
Compute a variety of test statistics evaluating the global fit of the model.
Usage
lavTest(lavobject, test = "standard", scaled.test = "standard", output = "list", drop.list.single = TRUE)lavTest(lavobject, test = "standard", scaled.test = "standard", output = "list", drop.list.single = TRUE)
Arguments
lavobject |
An object of class |
test |
Character vector. Multiple names of test statistics can be provided.
If |
scaled.test |
Character. Choose the test statistic
that will be scaled (if a scaled test statistic is requested).
The default is |
output |
Character. If |
drop.list.single |
Logical. Only used when |
Value
If output = "list": a nested list with test statistics, or if
only a single test statistic is requested (and
drop.list.single = TRUE), a list with details for this test
statistic. If output = "text": the text is printed, and a
nested list of test statistics (including an info attribute) is
returned.
Examples
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) lavTest(fit, test = "browne.residual.adf") lavTest(fit, test = "peba4", output = "text") lavTest(fit, test = "pols3", scaled.test = "RLS", output = "text")HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) lavTest(fit, test = "browne.residual.adf") lavTest(fit, test = "peba4", output = "text") lavTest(fit, test = "pols3", scaled.test = "RLS", output = "text")
LRT test
Description
LRT test for comparing (nested) lavaan models.
Usage
lavTestLRT(object, ..., method = "default", test = "default", A.method = "delta", scaled.shifted = TRUE, type = "Chisq", model.names = NULL) anova(object, ...)lavTestLRT(object, ..., method = "default", test = "default", A.method = "delta", scaled.shifted = TRUE, type = "Chisq", model.names = NULL) anova(object, ...)
Arguments
object |
An object of class |
... |
additional objects of class |
method |
Character string. The possible options are
|
test |
Character string specifying which scaled test statistics to use,
in case multiple scaled |
A.method |
Character string. The possible options are |
scaled.shifted |
Logical. Only used when method = |
type |
Character. If |
model.names |
Character vector. If provided, use these model names in the first column of the anova table. |
Details
The anova function for lavaan objects simply calls the
lavTestLRT function, which has a few additional arguments.
The only test= options that currently have actual consequences are
"satorra.bentler", "yuan.bentler", or "yuan.bentler.mplus"
because "mean.var.adjusted" and "scaled.shifted" are
currently distinguished by the scaled.shifted argument.
See lavOptions for details about the test= options
implied by robust estimator= options. The "default" is to
select the first available scaled statistic, if any. To check which test(s)
were computed when fitting your model(s), use
lavInspect(fit, "options")$test.
If type = "Chisq" and the test statistics are scaled, a
special scaled difference test statistic is computed. If method is
"satorra.bentler.2001", a simple approximation is used
described in Satorra & Bentler (2001). In some settings,
this can lead to a negative test statistic. To ensure a positive
test statistic, we can use the method proposed by
Satorra & Bentler (2010). Alternatively, when method="satorra.2000",
the original formulas of Satorra (2000) are used. The latter is used for
model comparison when ... contains additional (nested) models.
Even when test statistics are scaled in object or ...,
users may request the method="standard" test statistic,
without a robust adjustment.
FMG nested tests are available when type = "Chisq" and
test is an FMG test name. The supported nested FMG methods are
"pall", "all", "peba" and "pols" variants.
The convenience value "fmg" resolves to "pall_ug_rls" for
single-group comparisons and "pall_ug_ml" for multiple-group
comparisons.
They use the Satorra (2000) UGamma projection; method may be left
at "default" or set to "standard" or
"satorra.2000". Other nested LRT methods are not used for FMG
tests.
Value
An object of class anova. When given a single argument, it simply returns the test statistic of this model. When given a sequence of objects, this function tests the models against one another, after reordering the models according to their degrees of freedom.
Note
If there is a lavaan model stored in
object@external$h1.model, it will be added to ...
References
Satorra, A. (2000). Scaled and adjusted restricted tests in multi-sample analysis of moment structures. In Heijmans, R.D.H., Pollock, D.S.G. & Satorra, A. (eds.), Innovations in multivariate statistical analysis: A Festschrift for Heinz Neudecker (pp.233-247). London, UK: Kluwer Academic Publishers.
Satorra, A., & Bentler, P. M. (2001). A scaled difference chi-square test statistic for moment structure analysis. Psychometrika, 66(4), 507-514. doi:10.1007/BF02296192
Satorra, A., & Bentler, P. M. (2010). Ensuring positiveness of the scaled difference chi-square test statistic. Psychometrika, 75(2), 243-248. doi:10.1007/s11336-009-9135-y
Foldnes, N., Moss, J., & Gronneberg, S. (2024). Improved goodness of fit procedures for structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 1-13. doi:10.1080/10705511.2024.2372028
Foldnes, N., Gronneberg, S., & Moss, J. (2026). Penalized eigenvalue block averaging: Extension to nested model comparison and Monte Carlo evaluations. Behavior Research Methods, 58(4). doi:10.3758/s13428-026-02968-4
Examples
HS.model <- ' visual =~ x1 + b1*x2 + x3 textual =~ x4 + b2*x5 + x6 speed =~ x7 + b3*x8 + x9 ' fit1 <- cfa(HS.model, data = HolzingerSwineford1939) fit0 <- cfa(HS.model, data = HolzingerSwineford1939, orthogonal = TRUE) lavTestLRT(fit1, fit0) ## When multiple test statistics are selected when the model is fitted, ## use the type= and test= arguments to select a test for comparison. ## refit models, requesting 6 test statistics (in addition to "standard") t6.1 <- cfa(HS.model, data = HolzingerSwineford1939, test = c("browne.residual.adf","scaled.shifted","mean.var.adjusted", "satorra.bentler", "yuan.bentler", "yuan.bentler.mplus")) t6.0 <- cfa(HS.model, data = HolzingerSwineford1939, orthogonal = TRUE, test = c("browne.residual.adf","scaled.shifted","mean.var.adjusted", "satorra.bentler", "yuan.bentler", "yuan.bentler.mplus")) ## By default (test="default", type="Chisq"), the first scaled statistic ## requested will be used. Here, that is "scaled.shifted" lavTestLRT(t6.1, t6.0) ## But even if "satorra.bentler" were requested first, method="satorra.2000" ## provides the scaled-shifted chi-squared difference test: lavTestLRT(t6.1, t6.0, method = "satorra.2000") ## == lavTestLRT(update(t6.1, test = "scaled.shifted"), update(t6.0, test = "scaled.shifted")) ## The mean- and variance-adjusted (Satterthwaite) statistic implies ## scaled.shifted = FALSE lavTestLRT(t6.1, t6.0, method = "satorra.2000", scaled.shifted = FALSE) ## Because "satorra.bentler" is not the first scaled test in the list, ## we MUST request it explicitly: lavTestLRT(t6.1, t6.0, test = "satorra.bentler") # method="satorra.bentler.2001" ## == lavTestLRT(update(t6.1, test = "satorra.bentler"), ## update(t6.0, test = "satorra.bentler")) ## The "strictly-positive test" is necessary when the above test is < 0: lavTestLRT(t6.1, t6.0, test = "satorra.bentler", method = "satorra.bentler.2010") ## Likewise, other scaled statistics can be selected: lavTestLRT(t6.1, t6.0, test = "yuan.bentler") ## == lavTestLRT(update(t6.1, test = "yuan.bentler"), ## update(t6.0, test = "yuan.bentler")) lavTestLRT(t6.1, t6.0, test = "yuan.bentler.mplus") ## == lavTestLRT(update(t6.1, test = "yuan.bentler.mplus"), ## update(t6.0, test = "yuan.bentler.mplus")) ## To request the difference between Browne's (1984) residual-based statistics, ## rather than statistics based on the fitted model's discrepancy function, ## use the type= argument: lavTestLRT(t6.1, t6.0, type = "browne.residual.adf") ## Despite requesting multiple robust tests, it is still possible to obtain ## the standard chi-squared difference test (i.e., without a robust correction) lavTestLRT(t6.1, t6.0, method = "standard") ## == lavTestLRT(update(t6.1, test = "standard"), update(t6.0, test = "standard")) ## FMG nested p-values use the Satorra (2000) UGamma projection lavTestLRT(fit1, fit0, method = "satorra.2000", test = "pall")HS.model <- ' visual =~ x1 + b1*x2 + x3 textual =~ x4 + b2*x5 + x6 speed =~ x7 + b3*x8 + x9 ' fit1 <- cfa(HS.model, data = HolzingerSwineford1939) fit0 <- cfa(HS.model, data = HolzingerSwineford1939, orthogonal = TRUE) lavTestLRT(fit1, fit0) ## When multiple test statistics are selected when the model is fitted, ## use the type= and test= arguments to select a test for comparison. ## refit models, requesting 6 test statistics (in addition to "standard") t6.1 <- cfa(HS.model, data = HolzingerSwineford1939, test = c("browne.residual.adf","scaled.shifted","mean.var.adjusted", "satorra.bentler", "yuan.bentler", "yuan.bentler.mplus")) t6.0 <- cfa(HS.model, data = HolzingerSwineford1939, orthogonal = TRUE, test = c("browne.residual.adf","scaled.shifted","mean.var.adjusted", "satorra.bentler", "yuan.bentler", "yuan.bentler.mplus")) ## By default (test="default", type="Chisq"), the first scaled statistic ## requested will be used. Here, that is "scaled.shifted" lavTestLRT(t6.1, t6.0) ## But even if "satorra.bentler" were requested first, method="satorra.2000" ## provides the scaled-shifted chi-squared difference test: lavTestLRT(t6.1, t6.0, method = "satorra.2000") ## == lavTestLRT(update(t6.1, test = "scaled.shifted"), update(t6.0, test = "scaled.shifted")) ## The mean- and variance-adjusted (Satterthwaite) statistic implies ## scaled.shifted = FALSE lavTestLRT(t6.1, t6.0, method = "satorra.2000", scaled.shifted = FALSE) ## Because "satorra.bentler" is not the first scaled test in the list, ## we MUST request it explicitly: lavTestLRT(t6.1, t6.0, test = "satorra.bentler") # method="satorra.bentler.2001" ## == lavTestLRT(update(t6.1, test = "satorra.bentler"), ## update(t6.0, test = "satorra.bentler")) ## The "strictly-positive test" is necessary when the above test is < 0: lavTestLRT(t6.1, t6.0, test = "satorra.bentler", method = "satorra.bentler.2010") ## Likewise, other scaled statistics can be selected: lavTestLRT(t6.1, t6.0, test = "yuan.bentler") ## == lavTestLRT(update(t6.1, test = "yuan.bentler"), ## update(t6.0, test = "yuan.bentler")) lavTestLRT(t6.1, t6.0, test = "yuan.bentler.mplus") ## == lavTestLRT(update(t6.1, test = "yuan.bentler.mplus"), ## update(t6.0, test = "yuan.bentler.mplus")) ## To request the difference between Browne's (1984) residual-based statistics, ## rather than statistics based on the fitted model's discrepancy function, ## use the type= argument: lavTestLRT(t6.1, t6.0, type = "browne.residual.adf") ## Despite requesting multiple robust tests, it is still possible to obtain ## the standard chi-squared difference test (i.e., without a robust correction) lavTestLRT(t6.1, t6.0, method = "standard") ## == lavTestLRT(update(t6.1, test = "standard"), update(t6.0, test = "standard")) ## FMG nested p-values use the Satorra (2000) UGamma projection lavTestLRT(fit1, fit0, method = "satorra.2000", test = "pall")
Score test
Description
Score test (or Lagrange Multiplier test) for releasing one or more fixed or constrained parameters in the model.
Usage
lavTestScore(object, add = NULL, release = NULL, univariate = TRUE, cumulative = FALSE, epc = FALSE, standardized = epc, cov.std = epc, verbose = FALSE, warn = TRUE, information = "expected")lavTestScore(object, add = NULL, release = NULL, univariate = TRUE, cumulative = FALSE, epc = FALSE, standardized = epc, cov.std = epc, verbose = FALSE, warn = TRUE, information = "expected")
Arguments
object |
An object of class |
add |
Either a character string (typically between single quotes) or a parameter table containing additional (currently fixed-to-zero) parameters for which the score test must be computed. |
release |
Vector of integers. The indices of the constraints that should be released. The indices correspond to the order in which the equality constraints appear in the parameter table. |
univariate |
Logical. If |
cumulative |
Logical. If |
epc |
Logical. If |
standardized |
If |
cov.std |
Logical. See |
verbose |
Logical. Not used for now. |
warn |
Logical. If |
information |
|
Details
This function can be used to compute both multivariate and univariate
score tests. There are two modes: 1) releasing fixed-to-zero parameters
(using the add argument), and 2) releasing existing equality
constraints (using the release argument). The two modes cannot
be used simultaneously.
When adding new parameters, they should not already be part of the model (i.e. not listed in the parameter table). If you want to test for a parameter that was explicitly fixed to a constant (say to zero), it is better to label the parameter, and use an explicit equality constraint.
Value
A list containing at least one data.frame:
-
$test: The total score test, with columns for the score test statistic (X2), the degrees of freedom (df), and a p value under thedistribution (p.value). -
$uni: Optional (ifunivariate=TRUE). Each 1-df score test, equivalent to modification indices. Ifepc=TRUEwhenadding parameters (not when releasing constraints), an unstandardized EPC is provided for each added parameter, as would be returned bymodificationIndices. -
$cumulative: Optional (ifcumulative=TRUE). Cumulative score tests. -
$epc: Optional (ifepc=TRUE). Parameter estimates, expected parameter changes, and expected parameter values if all the tested constraints were freed.
References
Bentler, P. M., & Chou, C. P. (1993). Some new covariance structure model improvement statistics. Sage Focus Editions, 154, 235-255.
Examples
HS.model <- ' visual =~ x1 + b1*x2 + x3 textual =~ x4 + b2*x5 + x6 speed =~ x7 + b3*x8 + x9 b1 == b2 b2 == b3 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) # test 1: release both two equality constraints lavTestScore(fit, cumulative = TRUE) # test 2: the score test for adding two (currently fixed # to zero) cross-loadings newpar = ' visual =~ x9 textual =~ x3 ' lavTestScore(fit, add = newpar) # equivalently, "add" can be a parameter table specifying parameters to free, # but must include some additional information: PT.add <- data.frame(lhs = c("visual","textual"), op = c("=~","=~"), rhs = c("x9","x3"), user = 10L, # needed to identify new parameters free = 1, # arbitrary numbers > 0 start = 0) # null-hypothesized value PT.add lavTestScore(fit, add = PT.add) # same result as aboveHS.model <- ' visual =~ x1 + b1*x2 + x3 textual =~ x4 + b2*x5 + x6 speed =~ x7 + b3*x8 + x9 b1 == b2 b2 == b3 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) # test 1: release both two equality constraints lavTestScore(fit, cumulative = TRUE) # test 2: the score test for adding two (currently fixed # to zero) cross-loadings newpar = ' visual =~ x9 textual =~ x3 ' lavTestScore(fit, add = newpar) # equivalently, "add" can be a parameter table specifying parameters to free, # but must include some additional information: PT.add <- data.frame(lhs = c("visual","textual"), op = c("=~","=~"), rhs = c("x9","x3"), user = 10L, # needed to identify new parameters free = 1, # arbitrary numbers > 0 start = 0) # null-hypothesized value PT.add lavTestScore(fit, add = PT.add) # same result as above
Wald test
Description
Wald test for testing a linear hypothesis about the parameters of a fitted lavaan object.
Usage
lavTestWald(object, constraints = NULL, verbose = FALSE)lavTestWald(object, constraints = NULL, verbose = FALSE)
Arguments
object |
An object of class |
constraints |
A character string (typically between single quotes) containing one or more equality constraints. See examples for more details. |
verbose |
Logical. If |
Details
The constraints are specified using the "==" operator. Both
the left-hand side and the right-hand side of the equality can contain
a linear combination of model parameters, or a constant (like zero).
The model parameters must be specified by their user-specified labels.
Names of defined parameters (using the ":=" operator) can be
included too.
Value
A list containing three elements: the Wald test statistic (stat), the degrees of freedom (df), and a p-value under the chi-square distribution (p.value).
Examples
HS.model <- ' visual =~ x1 + b1*x2 + x3 textual =~ x4 + b2*x5 + x6 speed =~ x7 + b3*x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) # test 1: test about a single parameter # this is the 'chi-square' version of the # z-test from the summary() output lavTestWald(fit, constraints = "b1 == 0") # test 2: several constraints con = ' 2*b1 == b3 b2 - b3 == 0 ' lavTestWald(fit, constraints = con)HS.model <- ' visual =~ x1 + b1*x2 + x3 textual =~ x4 + b2*x5 + x6 speed =~ x7 + b3*x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) # test 1: test about a single parameter # this is the 'chi-square' version of the # z-test from the summary() output lavTestWald(fit, constraints = "b1 == 0") # test 2: several constraints con = ' 2*b1 == b3 b2 - b3 == 0 ' lavTestWald(fit, constraints = con)
The mimic= option
Description
The mimic= argument of the lavaan function (and its
wrappers cfa, sem and growth)
controls a collection of primarily technical default settings, with the aim of
making lavaan's output as similar as possible to that of other SEM software.
This applies in particular to a few key results, such as the value of the
Satorra-Bentler scaled test statistic.
The mimic= option was originally introduced to demonstrate that
differences between lavaan and other SEM programs were often due to technical
implementation details rather than errors in lavaan. Nevertheless, the scope of
the mimic= option is intentionally limited. It is designed to reproduce
a small number of important results and does not attempt to replicate every
quantity reported by alternative SEM software packages.
This help page documents which options are affected by the
mimic= argument.
Details
The mimic= argument does not change the model that is fitted, nor the
estimator that is used. Instead, it overwrites the default values of a number
of (mostly technical) options that are otherwise estimator-dependent. The
user can always override these defaults by setting the corresponding option
explicitly in the lavaan call.
The argument is case-insensitive and accepts a number of aliases. After normalization, only four values remain:
-
"lavaan": -
the native lavaan defaults (also selected by the value
"default"); this is the default. -
"Mplus": -
mimic the
Mplusprogram (also selected by the value"mplus"). -
"EQS": -
mimic the
EQSprogram (also selected by the values"eqs","LISREL"and"lisrel"). -
"lm": -
a minimal setting used internally for plain regression (also selected by the value
"regression"); not intended for general use.
mimic = "lavaan" (the default)
This is the reference setting. For maximum likelihood (ML) estimation, the following defaults are used:
-
likelihood = "normal": -
the sample covariance matrix is rescaled by a factor
(N-1)/N, so the loglikelihood and standard errors are based on a division byN(rather thanN-1). -
conditional.x = FALSE: -
the exogenous
xcovariates are regressed out first, and a conditional (on x) model is fitted. -
fixed.x = TRUE: -
the means, variances and covariances of the exogenous
xcovariates are fixed to their sample values (for the ML, MML and IV estimator groups, unlessstart = "simple"). -
zero.keep.margins = TRUE: -
for categorical data, the (one-way) margins are preserved when adding a small constant to empty cells.
In addition, the various Mplus-specific technical options
(information.expected.mplus, gamma.vcov.mplus,
gamma.wls.mplus and gls.v11.mplus) are all set to
FALSE.
mimic = "Mplus"
Starting from the lavaan defaults, the following options are changed in an
attempt to reproduce the output of Mplus:
-
information.expected.mplus = TRUE: -
use the Mplus variant of the expected information matrix. This affects the standard errors (when
information = "expected") and the scaled (Satorra-Bentler and Yuan-Bentler) test statistics. -
gamma.vcov.mplus = TRUE: -
use the Mplus way of computing the
matrix (the asymptotic covariance matrix of the sample statistics) that enters the robust (sandwich) standard errors. -
gamma.wls.mplus = TRUE: -
use the Mplus way of computing the
matrix used as the weight matrix in (D)WLS estimation. -
gls.v11.mplus = TRUE: -
use the Mplus variant of the weight matrix used in GLS estimation (when there is a meanstructure and
conditional.x = FALSE). -
missing = "ml": -
for continuous data and the ML or MLR estimator, the default missing-data handling becomes full information maximum likelihood (FIML), rather than listwise deletion.
-
meanstructure = TRUE: -
a meanstructure is added by default (unless the estimator is PML).
-
group.equal: -
in a multiple-group analysis, if no equality constraints are requested, a default set is imposed:
"loadings"and"thresholds"for categorical data;"loadings"for continuous data without a meanstructure; and"loadings"and"intercepts"for continuous data with a meanstructure. -
baseline.conditional.x.free.slopes = FALSE: -
when
conditional.x = TRUE, the baseline (independence) model does not free the slope structure.
The likelihood, conditional.x, fixed.x and
zero.keep.margins defaults are the same as for
mimic = "lavaan".
mimic = "EQS"
Starting from the lavaan defaults, the following options are changed in an
attempt to reproduce the output of EQS (the value "LISREL" is
treated as an alias for "EQS"):
-
likelihood = "wishart": -
for ML estimation, the Wishart likelihood is used. The sample covariance matrix is divided by
N-1(instead ofN), which affects the chi-square test statistic, the loglikelihood and the standard errors. -
baseline.fixed.x.free.cov = FALSE: -
when
fixed.x = TRUE, the baseline (independence) model does not free the (co)variances of the exogenous covariates.
In addition, for the MLR estimator, the robust test statistic defaults to
"yuan.bentler" (instead of the "yuan.bentler.mplus" variant
that is used for mimic = "lavaan" and mimic = "Mplus").
Note that the mimic= argument only sets defaults: any option
that is set explicitly in the lavaan call takes precedence. The
mimicking is also necessarily incomplete; small numerical differences with
the target program may remain.
See Also
Examples
# default (mimic = "lavaan") fit1 <- cfa(" visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ", test = "satorra.bentler", missing = "listwise", data = HolzingerSwineford1939) fit1 # mimic the Mplus program fit2 <- cfa(" visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ", test = "satorra.bentler", missing = "listwise", data = HolzingerSwineford1939, mimic = "Mplus") fit2 # mimic the EQS program fit3 <- cfa(" visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ", test = "satorra.bentler", missing = "listwise", data = HolzingerSwineford1939, mimic = "EQS") fit3# default (mimic = "lavaan") fit1 <- cfa(" visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ", test = "satorra.bentler", missing = "listwise", data = HolzingerSwineford1939) fit1 # mimic the Mplus program fit2 <- cfa(" visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ", test = "satorra.bentler", missing = "listwise", data = HolzingerSwineford1939, mimic = "Mplus") fit2 # mimic the EQS program fit3 <- cfa(" visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ", test = "satorra.bentler", missing = "listwise", data = HolzingerSwineford1939, mimic = "EQS") fit3
The Lavaan Model Syntax
Description
The lavaan model syntax describes a latent variable model. The
function lavParTable turns it into a table that represents the full
model as specified by the user. We refer to this table as the parameter table.
Usage
lavaanify(model = NULL, meanstructure = FALSE, int_ov_free = FALSE, int_lv_free = FALSE, marker_int_zero = FALSE, orthogonal = FALSE, orthogonal_y = FALSE, orthogonal_x = FALSE, orthogonal_efa = FALSE, std_lv = FALSE, correlation = FALSE, composites = TRUE, composites_cov_free = FALSE, effect_coding = "", conditional_x = FALSE, fixed_x = FALSE, parameterization = "delta", constraints = NULL, ceq_simple = FALSE, auto = FALSE, model_type = "sem", auto_fix_first = FALSE, marker = NULL, auto_fix_single = FALSE, auto_var = FALSE, auto_cov_lv_x = FALSE, auto_cov_y = FALSE, auto_th = FALSE, auto_delta = FALSE, auto_efa = FALSE, var_table = NULL, ngroups = 1L, nthresholds = NULL, group_equal = NULL, group_partial = NULL, group_w_free = FALSE, debug = FALSE, warn = TRUE, as_data_frame = TRUE, ...) lavParTable(model = NULL, meanstructure = FALSE, int_ov_free = FALSE, int_lv_free = FALSE, marker_int_zero = FALSE, orthogonal = FALSE, orthogonal_y = FALSE, orthogonal_x = FALSE, orthogonal_efa = FALSE, std_lv = FALSE, correlation = FALSE, composites = TRUE, composites_cov_free = FALSE, effect_coding = "", conditional_x = FALSE, fixed_x = FALSE, parameterization = "delta", constraints = NULL, ceq_simple = FALSE, auto = FALSE, model_type = "sem", auto_fix_first = FALSE, marker = NULL, auto_fix_single = FALSE, auto_var = FALSE, auto_cov_lv_x = FALSE, auto_cov_y = FALSE, auto_th = FALSE, auto_delta = FALSE, auto_efa = FALSE, var_table = NULL, ngroups = 1L, nthresholds = NULL, group_equal = NULL, group_partial = NULL, group_w_free = FALSE, debug = FALSE, warn = TRUE, as_data_frame = TRUE, ...) lavParseModelString(model_syntax = '', as_data_frame = FALSE, parser = "open", warn = TRUE, debug = FALSE, ...)lavaanify(model = NULL, meanstructure = FALSE, int_ov_free = FALSE, int_lv_free = FALSE, marker_int_zero = FALSE, orthogonal = FALSE, orthogonal_y = FALSE, orthogonal_x = FALSE, orthogonal_efa = FALSE, std_lv = FALSE, correlation = FALSE, composites = TRUE, composites_cov_free = FALSE, effect_coding = "", conditional_x = FALSE, fixed_x = FALSE, parameterization = "delta", constraints = NULL, ceq_simple = FALSE, auto = FALSE, model_type = "sem", auto_fix_first = FALSE, marker = NULL, auto_fix_single = FALSE, auto_var = FALSE, auto_cov_lv_x = FALSE, auto_cov_y = FALSE, auto_th = FALSE, auto_delta = FALSE, auto_efa = FALSE, var_table = NULL, ngroups = 1L, nthresholds = NULL, group_equal = NULL, group_partial = NULL, group_w_free = FALSE, debug = FALSE, warn = TRUE, as_data_frame = TRUE, ...) lavParTable(model = NULL, meanstructure = FALSE, int_ov_free = FALSE, int_lv_free = FALSE, marker_int_zero = FALSE, orthogonal = FALSE, orthogonal_y = FALSE, orthogonal_x = FALSE, orthogonal_efa = FALSE, std_lv = FALSE, correlation = FALSE, composites = TRUE, composites_cov_free = FALSE, effect_coding = "", conditional_x = FALSE, fixed_x = FALSE, parameterization = "delta", constraints = NULL, ceq_simple = FALSE, auto = FALSE, model_type = "sem", auto_fix_first = FALSE, marker = NULL, auto_fix_single = FALSE, auto_var = FALSE, auto_cov_lv_x = FALSE, auto_cov_y = FALSE, auto_th = FALSE, auto_delta = FALSE, auto_efa = FALSE, var_table = NULL, ngroups = 1L, nthresholds = NULL, group_equal = NULL, group_partial = NULL, group_w_free = FALSE, debug = FALSE, warn = TRUE, as_data_frame = TRUE, ...) lavParseModelString(model_syntax = '', as_data_frame = FALSE, parser = "open", warn = TRUE, debug = FALSE, ...)
Arguments
model |
A description of the user-specified model. Typically, the model
is described using the lavaan model syntax; see details for more
information. Alternatively, a parameter table (e.g., the output of
|
model_syntax |
The model syntax specifying the model. Must be a literal string. |
meanstructure |
If |
int_ov_free |
If |
int_lv_free |
If |
marker_int_zero |
Logical. Only relevant if the metric of each latent
variable is set by fixing the first factor loading to unity.
If |
orthogonal |
If |
orthogonal_y |
If |
orthogonal_x |
If |
orthogonal_efa |
If |
std_lv |
If |
correlation |
If |
composites |
Logical. If |
composites_cov_free |
Logical. Only relevant if the model contains
composites. If |
effect_coding |
Can be logical or character string. If
logical and |
conditional_x |
If |
fixed_x |
If |
parameterization |
Currently only used if data is categorical. If
|
constraints |
Additional (in)equality constraints. See details for more information. |
ceq_simple |
If |
auto |
If |
model_type |
Either |
auto_fix_first |
If |
marker |
Optional named character vector mapping a latent variable
(name) to the observed indicator (name) whose loading should be fixed to
1.0 (instead of the first indicator) when |
auto_fix_single |
If |
auto_var |
If |
auto_cov_lv_x |
If |
auto_cov_y |
If |
auto_th |
If |
auto_delta |
If |
auto_efa |
If |
var_table |
The variable table containing information about the observed variables in the model. |
ngroups |
The number of (independent) groups. |
nthresholds |
Either a single integer or a named vector of integers.
If |
group_equal |
A vector of character strings. Only used in
a multiple group analysis. Can be one or more of the following:
|
group_partial |
A vector of character strings containing the labels of the parameters which should be free in all groups (thereby overriding the group_equal argument for some specific parameters). |
group_w_free |
Logical. If |
as_data_frame |
If |
parser |
Character. If |
warn |
If |
debug |
If |
... |
To accept old argument names with dots. No other arguments are accepted. |
Details
The model syntax consists of one or more formula-like expressions, each one
describing a specific part of the model. The model syntax can be read from
a file (using readLines), or can be specified as a literal
string enclosed by single quotes as in the example below.
myModel <- '
# 1. latent variable definitions
f1 =~ y1 + y2 + y3
f2 =~ y4 + y5 + y6
f3 =~ y7 + y8 +
y9 + y10
f4 =~ y11 + y12 + y13
! this is also a comment
# 2. regressions
f1 ~ f3 + f4
f2 ~ f4
y1 + y2 ~ x1 + x2 + x3
# 3. (co)variances
y1 ~~ y1
y2 ~~ y4 + y5
f1 ~~ f2
# 4. intercepts
f1 ~ 1; y5 ~ 1
# 5. thresholds
y11 | t1 + t2 + t3
y12 | t1
y13 | t1 + t2
# 6. scaling factors
y11 ~*~ y11
y12 ~*~ y12
y13 ~*~ y13
# 7. composites
f5 <~ z1 + z2 + z3 + z4
'
Blank lines and comments can be used in between the formulas, and formulas can be split over multiple lines. Both the sharp (#) and the exclamation (!) characters can be used to start a comment. Multiple formulas can be placed on a single line if they are separated by a semicolon (;).
There can be seven types of formula-like expressions in the model syntax:
-
Latent variable definitions: The
"=~"operator can be used to define (continuous) latent variables. The name of the latent variable is on the left of the"=~"operator, while the terms on the right, separated by"+"operators, are the indicators of the latent variable.The operator
"=~"can be read as “is manifested by”. -
Regressions: The
"~"operator specifies a regression. The dependent variable is on the left of a"~"operator and the independent variables, separated by"+"operators, are on the right. These regression formulas are similar to the way ordinary linear regression formulas are used in R, but they may include latent variables. Interaction terms are currently not supported. -
Variance-covariances: The
"~~"(‘double tilde’) operator specifies (residual) variances of an observed or latent variable, or a set of covariances between one variable and several other variables (either observed or latent). Several variables, separated by"+"operators, can appear on the right. In this way, several pairwise (co)variances involving the same left-hand variable can be expressed in a single expression. The distinction between variances and residual variances is made automatically. -
Intercepts: A special case of a regression formula can be used to specify an intercept (or a mean) of either an observed or a latent variable. The variable name is on the left of a
"~"operator, and the only term on the right is the number"1", representing the intercept. Including an intercept formula in the model automatically impliesmeanstructure = TRUE. The distinction between intercepts and means is made automatically. -
Thresholds: The
"|"operator can be used to define the thresholds of categorical endogenous variables (on the left-hand side of the operator). By convention, the thresholds (on the right-hand side, separated by the"+"operator) are named"t1","t2", and so on. -
Scaling factors: The
"~*~"operator defines a scale factor. The variable name on the left hand side must be the same as the variable name on the right hand side. Scale factors are used in the Delta parameterization, in a multiple group analysis when factor indicators are categorical. -
Composites: The
"<~"operator can be used to define a composite (on the right hand side of the operator). A composite is a weighted linear combination of its composite indicators. The name of the composite variable is on the left of the"<~"operator, while the terms on the right, separated by"+"operators, are the indicators of the composite variable.
There are 4 additional operators, also with left- and right-hand sides, that can
be included in model syntax. Three of them are used to specify (in)equality
constraints on estimated parameters (==, >, and <), and
those are demonstrated in a later section about
(In)equality constraints.
The final additional operator (:=) can be used to define “new” parameters
that are functions of one or more other estimated parameters. The :=
operator is demonstrated in a section about User-defined parameters.
Usually, only a single variable name appears on the left side of an
operator. However, if multiple variable names are specified,
separated by the "+" operator, the formula is repeated for each
element on the left side (as for example in the third regression
formula in the example above). The only exception is scaling factors, where
only a single element is allowed on the left-hand side.
In the right-hand side of these formula-like expressions, each element can be
modified (using the "*" operator) by either a numeric constant,
an expression resulting in a numeric constant, an expression resulting
in a character vector, or one
of three special functions: start(), label() and equal().
This provides the user with a mechanism to fix parameters, to provide
alternative starting values, to label the parameters, and to define equality
constraints among model parameters. All "*" expressions are
referred to as modifiers. They are explained in more detail in the
following sections.
Fixing parameters
It is often desirable to fix a model parameter that is otherwise (by default) free. Any parameter in a model can be fixed by using a modifier resulting in a numerical constant. Here are some examples:
-
Fixing the regression coefficient of the predictor
x2:y ~ x1 + 2.4*x2 + x3
-
Specifying an orthogonal (zero) covariance between two latent variables:
f1 ~~ 0*f2
-
Specifying an intercept and a linear slope in a growth model:
i =~ 1*y11 + 1*y12 + 1*y13 + 1*y14 s =~ 0*y11 + 1*y12 + 2*y13 + 3*y14
Instead of a numeric constant, one can use a mathematical function that returns
a numeric constant, for example sqrt(10). Multiplying with NA
will force the corresponding parameter to be free.
Additionally, the == operator can be used to set a labeled parameter
equal to a specific numeric value. This will be demonstrated in the section below
about (In)equality constraints.
Starting values
User-provided starting values can be given by using the special function
start(), containing a numeric constant. For example:
y ~ x1 + start(1.0)*x2 + x3
Note that if a starting value is provided, the parameter is not automatically considered to be free.
Parameter labels and equality constraints
Each free parameter in a model is automatically given a name (or label).
The name given to a model
parameter consists of three parts, coerced to a single character vector.
The first part is the name of the variable in the left-hand side of the
formula where the parameter was
implied. The middle part is based on the special ‘operator’ used in the
formula. This can be either one of "=~", "~" or "~~". The
third part is the name of the variable in the right-hand side of the formula
where the parameter was implied, or "1" if it is an intercept. The three
parts are pasted together in a single string. For example, the name of the
fixed regression coefficient in the regression formula
y ~ x1 + 2.4*x2 + x3 is the string "y~x2".
The name of the parameter
corresponding to the covariance between two latent variables in the
formula f1 ~~ f2 is the string "f1~~f2".
Although this automatic labeling of parameters is convenient, the user may
specify their own labels for specific parameters simply by pre-multiplying
the corresponding term (on the right hand side of the operator only) by
a character string (starting with a letter).
For example, in the formula f1 =~ x1 + x2 + mylabel*x3, the parameter
corresponding with the factor loading of
x3 will be named "mylabel".
An alternative way to specify the label is as follows:
f1 =~ x1 + x2 + label("mylabel")*x3,
where the label is the argument of special function label();
this can be useful if the label contains a space, or an operator (like "~").
There are two ways to constrain a parameter
to be equal to another target parameter. If you
have specified your own labels, you can use the fact that
equal labels imply equal parameter values.
If you rely on automatic parameter labels, you
can use the special function equal(). The argument of
equal() is the (automatic or user-specified) name of the target
parameter. For example, in the confirmatory factor analysis example below, the
intercepts of the three indicators of each latent variable are constrained to
be equal to each other. For the first three, we have used the default
names. For the last three, we have provided a custom label for the
y2a intercept.
model <- '
# two latent variables with fixed loadings
f1 =~ 1*y1a + 1*y1b + 1*y1c
f2 =~ 1*y2a + 1*y2b + 1*y2c
# intercepts constrained to be equal
# using the default names
y1a ~ 1
y1b ~ equal("y1a~1") * 1
y1c ~ equal("y1a~1") * 1
# intercepts constrained to be equal
# using a custom label
y2a ~ int2*1
y2b ~ int2*1
y2c ~ int2*1
'
Multiple groups
In a multiple group analysis, modifiers that contain a single element should be replaced by a vector, having the same length as the number of groups. If you provide a single element, it will be recycled for all the groups. This may be dangerous, in particular when the modifier is a label. In that case, the (same) label is copied across all groups, and this would imply an equality constraint across groups. Therefore, when using modifiers in a multiple group setting, it is always safer (and cleaner) to specify the same number of elements as the number of groups. Consider this example with two groups:
HS.model <- ' visual =~ x1 + 0.5*x2 + c(0.6, 0.8)*x3
textual =~ x4 + start(c(1.2, 0.6))*x5 + x6
speed =~ x7 + x8 + c(x9.group1, x9.group2)*x9 '
In this example, the factor loading of the ‘x2’ indicator is fixed to the value 0.5 for both groups. However, the factor loadings of the ‘x3’ indicator are fixed to 0.6 and 0.8 for group 1 and group 2 respectively. The same logic is used for all modifiers. Note that character vectors can contain unquoted strings.
Multiple modifiers
In the model syntax, you can specify a variable more than once on the right hand side of an operator; therefore, several ‘modifiers’ can be applied simultaneously; for example, if you want to fix the value of a parameter and also label that parameter, you can use something like:
f1 =~ x1 + x2 + 4*x3 + x3.loading*x3
(In)equality constraints
The == operator can be used either to fix a parameter to a specific value,
or to set an estimated parameter equal to another parameter. Adapting the
example in the Parameter labels and equality constraints section, we
could have used different labels for the second factor's intercepts:
y2a ~ int1*1
y2b ~ int2*1
y2c ~ int3*1
Then, we could fix the first intercept to zero by including in the syntax an operation that indicates the parameter's label equals that value:
int1 == 0
Whereas we could still estimate the other two intercepts under an equality constraint by setting their different labels equal to each other:
int2 == int3
Optimization can be less efficient when constraining parameters this way (see
the documentation linked under See also for more information). But the
flexibility might be advantageous. For example, the constraints could be
specified in a separate character-string object, which can be passed to the
lavaan(..., constraints=) argument, enabling users to compare results
with(out) the constraints.
Inequality constraints work in much the same way, using the < or >
operator to indicate which estimated parameter is hypothesized to be greater or
less than either a specific value or another estimated parameter. For example, a
variance can be constrained to be nonnegative:
y1a ~~ var1a*y1a
## hypothesized constraint:
var1a > 0
Or the factor loading of a particular indicator might be expected to exceed other indicators' loadings:
f1 =~ L1*y1a + L2*y1b + L3*y1c
## hypothesized constraints:
L1 > L2
L3 < L1
User-defined parameters
Functions of parameters can be useful to test particular hypotheses. Following
from the Multiple groups example, we might be interested in which group's
factor loading is larger (i.e., an estimate of differential item functioning
(DIF) when the latent scales are linked by anchor items with equal loadings).
speed =~ c(L7, L7)*x7 + c(L8, L8)*x8 + c(L9.group1, L9.group2)*x9 ' ## user-defined parameter: DIF_L9 := L9.group1 - L9.group2
Note that this hypothesis is easily tested without a user-defined parameter by
using the lavTestWald() function. However, a user-defined parameter
additionally provides an estimate of the parameter being tested.
User-defined parameters are particularly useful for specifying indirect effects in models of mediation. For example:
model <- ' # direct effect
Y ~ c*X
# mediator
M ~ a*X
Y ~ b*M
# user defined parameters:
# indirect effect (a*b)
ab := a*b
# total effect (defined using another user-defined parameter)
total := ab + c
'
References
Rosseel, Y. (2012). lavaan: An R package for structural equation
modeling. Journal of Statistical Software, 48(2), 1–36.
doi:10.18637/jss.v048.i02
Modification Indices
Description
Given a fitted lavaan object, compute the modification indices (= univariate score tests) for a selected set of fixed-to-zero parameters.
Usage
modificationIndices(object, standardized = TRUE, cov.std = TRUE, information = "expected", power = FALSE, delta = 0.1, alpha = 0.05, high.power = 0.75, sort. = FALSE, minimum.value = 0, maximum.number = nrow(list_1), free.remove = TRUE, na.remove = TRUE, op = NULL) modindices(object, standardized = TRUE, cov.std = TRUE, information = "expected", power = FALSE, delta = 0.1, alpha = 0.05, high.power = 0.75, sort. = FALSE, minimum.value = 0, maximum.number = nrow(list_1), free.remove = TRUE, na.remove = TRUE, op = NULL)modificationIndices(object, standardized = TRUE, cov.std = TRUE, information = "expected", power = FALSE, delta = 0.1, alpha = 0.05, high.power = 0.75, sort. = FALSE, minimum.value = 0, maximum.number = nrow(list_1), free.remove = TRUE, na.remove = TRUE, op = NULL) modindices(object, standardized = TRUE, cov.std = TRUE, information = "expected", power = FALSE, delta = 0.1, alpha = 0.05, high.power = 0.75, sort. = FALSE, minimum.value = 0, maximum.number = nrow(list_1), free.remove = TRUE, na.remove = TRUE, op = NULL)
Arguments
object |
An object of class |
standardized |
If |
cov.std |
Logical. See |
information |
|
power |
If |
delta |
The value of the effect size, as used in the post-hoc power computation, currently using the unstandardized metric of the epc column. |
alpha |
The significance level used for deciding if the modification index is statistically significant or not. |
high.power |
If the computed power is higher than this cutoff value, the power is considered ‘high’. If not, the power is considered ‘low’. This affects the values in the 'decision' column in the output. |
sort. |
Logical. If TRUE, sort the output by the modification index values. Higher values appear first. |
minimum.value |
Numeric. Filter output and only show rows with a modification index value equal to or higher than this minimum value. |
maximum.number |
Integer. Filter output and only show the first
|
free.remove |
Logical. If TRUE, filter output by removing all rows corresponding to free (unconstrained) parameters in the original model. |
na.remove |
Logical. If TRUE, filter output by removing all rows with NA values for the modification indices. |
op |
Character string. Filter the output by selecting only those rows with
operator |
Details
Modification indices are just 1-df (or univariate) score tests. The
modification index (or score test) for a single parameter reflects
(approximately) the improvement in model fit (in terms of the chi-square
test statistic) if we were to refit the model with this parameter set
free.
This function is a convenience function in the sense that it produces a
(hopefully sensible) table of currently fixed-to-zero (or fixed to another
constant) parameters. For each of these parameters, a modification index
is computed, together with an expected parameter change (epc) value.
It is important to realize that this function will only consider
fixed-to-zero parameters. If you have equality constraints in the model,
and you wish to examine what happens if you release all (or some) of these
equality constraints, use the lavTestScore function.
Value
A data.frame containing modification indices and EPCs.
Examples
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) modindices(fit, minimum.value = 10, sort = TRUE)HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) modindices(fit, minimum.value = 10, sort = TRUE)
The open parser configuration
Description
The lavaan model syntax parser can be extended with new operators, modifiers and groupings. These extensions are only used in the 'open' parser.
Usage
lav_parse_options( pkgname = NULL, operators = NULL, modifiers = NULL, groupings = NULL )lav_parse_options( pkgname = NULL, operators = NULL, modifiers = NULL, groupings = NULL )
Arguments
pkgname |
The name of the package that extends the elements. |
operators |
A character vector with new operators. These operators must start and end with a percentage sign and be at least 3 characters long. |
modifiers |
A data.frame with columns |
groupings |
A character vector with new groupings; they must be in snake_case. |
Value
A list with data.frames containing the currently active parser configuration.
Examples
curconfig <- lav_parse_options("testPKG", operators = c('%w%', '%q%'), modifiers = data.frame(mod = c("linksc", "linksn", "rechtsn"), side = c("l", "l", "r"), expect = c("char", "num", "raw")), groupings = c("color", "colour") ) for (j in seq_along(curconfig)) { cat(names(curconfig)[j], ":\n") print(curconfig[[j]]) } model <- ' ind60 =~ x1 + x2 + x3 dem60 =~ y1 + a*y2 + start(0.3)*b*y3 + upper(0.99)*c*y4 dem65 =~ y5 + a*y6 + b*y7 + rechtsn(2 * pi / 3)*c*y8 dem60 %w% aa *0.2*y4 dem60 ~ ind60 dem65 ~ ind60 + dem60 linksc("klopt") * dem60 =~ aaa * y8 linksn(sqrt(23.5)) * dem60 =~ bbb * y9 efa("efatje") * dem65 =~ xyz * x3 y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 ' print(result <- lavParseModelString(model, TRUE, parser = "open")) print(attributes(result)) model2 <- ' color: green level: 1 fw =~ y1 + y2 + y3 fw ~ x1 + x2 + x3 level: 2 fb =~ y1 + y2 + y3 fb ~ w1 + w2 color: blue level: 1 fw =~ y1 + y2 + y3 fw ~ x1 + x2 + x3 level: 2 fb =~ y1 + y2 + y3 fb ~ w1 + w2 ' print(result2 <- lavParseModelString(model2, TRUE, parser = "open")) print(attributes(result2))curconfig <- lav_parse_options("testPKG", operators = c('%w%', '%q%'), modifiers = data.frame(mod = c("linksc", "linksn", "rechtsn"), side = c("l", "l", "r"), expect = c("char", "num", "raw")), groupings = c("color", "colour") ) for (j in seq_along(curconfig)) { cat(names(curconfig)[j], ":\n") print(curconfig[[j]]) } model <- ' ind60 =~ x1 + x2 + x3 dem60 =~ y1 + a*y2 + start(0.3)*b*y3 + upper(0.99)*c*y4 dem65 =~ y5 + a*y6 + b*y7 + rechtsn(2 * pi / 3)*c*y8 dem60 %w% aa *0.2*y4 dem60 ~ ind60 dem65 ~ ind60 + dem60 linksc("klopt") * dem60 =~ aaa * y8 linksn(sqrt(23.5)) * dem60 =~ bbb * y9 efa("efatje") * dem65 =~ xyz * x3 y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 ' print(result <- lavParseModelString(model, TRUE, parser = "open")) print(attributes(result)) model2 <- ' color: green level: 1 fw =~ y1 + y2 + y3 fw ~ x1 + x2 + x3 level: 2 fb =~ y1 + y2 + y3 fb ~ w1 + w2 color: blue level: 1 fw =~ y1 + y2 + y3 fw ~ x1 + x2 + x3 level: 2 fb =~ y1 + y2 + y3 fb ~ w1 + w2 ' print(result2 <- lavParseModelString(model2, TRUE, parser = "open")) print(attributes(result2))
Parameter Table
Description
Show the parameter table of a fitted model.
Usage
parameterTable(object) parTable(object)parameterTable(object) parTable(object)
Arguments
object |
An object of class |
Value
A data.frame containing the model parameters. This is
simply the output of the lavParTable function
coerced to a data.frame (with stringsAsFactors = FALSE).
See Also
Examples
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) parTable(fit)HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) parTable(fit)
Industrialization And Political Democracy Dataset
Description
The ‘famous’ Industrialization and Political Democracy dataset. This dataset is used throughout Bollen's 1989 book (see pages 12, 17, 36 in chapter 2, pages 228 and following in chapter 7, pages 321 and following in chapter 8). The dataset contains various measures of political democracy and industrialization in developing countries.
Usage
data(PoliticalDemocracy)data(PoliticalDemocracy)
Format
A data frame of 75 observations of 11 variables.
y1-
Expert ratings of the freedom of the press in 1960
y2-
The freedom of political opposition in 1960
y3-
The fairness of elections in 1960
y4-
The effectiveness of the elected legislature in 1960
y5-
Expert ratings of the freedom of the press in 1965
y6-
The freedom of political opposition in 1965
y7-
The fairness of elections in 1965
y8-
The effectiveness of the elected legislature in 1965
x1-
The gross national product (GNP) per capita in 1960
x2-
The inanimate energy consumption per capita in 1960
x3-
The percentage of the labor force in industry in 1960
Source
The dataset was originally retrieved from http://web.missouri.edu/~kolenikovs/Stat9370/democindus.txt (link no longer valid; see discussion on SEMNET 18 Jun 2009). The dataset is part of a larger (public) dataset (ICPSR 2532), see
https://www.icpsr.umich.edu/web/ICPSR/studies/2532.
References
Bollen, K. A. (1989). Structural Equations with Latent Variables. Wiley Series in Probability and Mathematical Statistics. New York: Wiley.
Bollen, K. A. (1979). Political democracy and the timing of development. American Sociological Review, 44, 572-587.
Bollen, K. A. (1980). Issues in the comparative measurement of political democracy. American Sociological Review, 45, 370-390.
Examples
head(PoliticalDemocracy)head(PoliticalDemocracy)
Fit Structural Equation Models using the SAM approach
Description
Fit a Structural Equation Model (SEM) using the Structural After Measurement (SAM) approach.
Usage
sam(model = NULL, data = NULL, aux = NULL, cmd = "sem", se = "twostep", mm_list = NULL, mm_args = list(bounds = "wide.zerovar"), struc_args = list(estimator = "ML"), sam_method = "local", ..., local_options = list(M.method = "ML", lambda.correction = TRUE, alpha.correction = 0L, twolevel.method = "h1"), global_options = list(), bootstrap = list(R = 1000L, type = "ordinary", show.progress = FALSE), output = "lavaan", bootstrap_args = bootstrap )sam(model = NULL, data = NULL, aux = NULL, cmd = "sem", se = "twostep", mm_list = NULL, mm_args = list(bounds = "wide.zerovar"), struc_args = list(estimator = "ML"), sam_method = "local", ..., local_options = list(M.method = "ML", lambda.correction = TRUE, alpha.correction = 0L, twolevel.method = "h1"), global_options = list(), bootstrap = list(R = 1000L, type = "ordinary", show.progress = FALSE), output = "lavaan", bootstrap_args = bootstrap )
Arguments
model |
A description of the user-specified model. Typically, the model
is described using the lavaan model syntax. See
|
data |
A data frame containing the observed variables used in the model. |
aux |
Character vector. Names of auxiliary observed variables, forwarded
to the underlying measurement and structural model fits. See the
|
cmd |
Character. Which command is used to run the sem models. The possible
choices are |
se |
Character. The type of standard errors that are used in the
final (structural) model. If |
mm_list |
List. Define the measurement blocks. Each element of the list should be either a single name of a latent variable, or a vector of latent variable names. If omitted, a separate measurement block is used for each latent variable. |
mm_args |
List. Optional arguments for the fitting
function(s) of the measurement block(s) only. See |
struc_args |
List. Optional arguments for the fitting function of the
structural part only. See |
sam_method |
Character. Can be set to |
... |
Many more options can be specified, using 'name = value'.
See |
local_options |
List. Options specific for local SAM method (these
options may change over time). If |
global_options |
List. Options specific for global SAM method (not used for now). |
bootstrap |
List. Only used when |
output |
Character. If |
bootstrap_args |
List. Deprecated, use |
Details
The sam function automates the SAM approach by first
estimating the measurement part of the model and then the structural
part of the model. See the reference for more details.
Note that in the current implementation, all indicators of latent variables must be observed. As a result, second-order factor structures are not yet supported.
Value
If output = "lavaan", an object of class
lavaan, for which several methods
are available, including a summary method. If output = "list",
a list.
References
Rosseel and Loh (2021). A structural-after-measurement approach to Structural Equation Modeling. Psychological Methods. Advance online publication. https://dx.doi.org/10.1037/met0000503
See Also
Examples
## The industrialization and Political Democracy Example ## Bollen (1989), page 332 model <- ' # latent variable definitions ind60 =~ x1 + x2 + x3 dem60 =~ y1 + a*y2 + b*y3 + c*y4 dem65 =~ y5 + a*y6 + b*y7 + c*y8 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 # residual correlations y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 ' fit.sam <- sam(model, data = PoliticalDemocracy, mm.list = list(ind = "ind60", dem = c("dem60", "dem65"))) summary(fit.sam)## The industrialization and Political Democracy Example ## Bollen (1989), page 332 model <- ' # latent variable definitions ind60 =~ x1 + x2 + x3 dem60 =~ y1 + a*y2 + b*y3 + c*y4 dem65 =~ y5 + a*y6 + b*y7 + c*y8 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 # residual correlations y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 ' fit.sam <- sam(model, data = PoliticalDemocracy, mm.list = list(ind = "ind60", dem = c("dem60", "dem65"))) summary(fit.sam)
Fit Structural Equation Models
Description
Fit a Structural Equation Model (SEM).
Usage
sem(model = NULL, data = NULL, ordered = NULL, aux = NULL, sampling_weights = NULL, sample_cov = NULL, sample_mean = NULL, sample_th = NULL, sample_nobs = NULL, group = NULL, cluster = NULL, constraints = "", wls_v = NULL, nacov = NULL, ov_order = "model", ...)sem(model = NULL, data = NULL, ordered = NULL, aux = NULL, sampling_weights = NULL, sample_cov = NULL, sample_mean = NULL, sample_th = NULL, sample_nobs = NULL, group = NULL, cluster = NULL, constraints = "", wls_v = NULL, nacov = NULL, ov_order = "model", ...)
Arguments
model |
A description of the user-specified model. Typically, the model
is described using the lavaan model syntax. See
|
data |
An optional data frame containing the observed variables used in the model. If some variables are declared as ordered factors, lavaan will treat them as ordinal variables. |
ordered |
Character vector. Only used if the data is in a data.frame. Treat these variables as ordered (ordinal) variables, if they are endogenous in the model. Importantly, all other variables will be treated as numeric (unless they are declared as ordered in the data.frame.) Since 0.6-4, ordered can also be logical. If TRUE, all observed endogenous variables are treated as ordered (ordinal). If FALSE, all observed endogenous variables are considered to be numeric (again, unless they are declared as ordered in the data.frame.) |
aux |
Character vector. Names of auxiliary observed variables, used to
make the missing-at-random (MAR) assumption more plausible under missing
data (continuous data only). With |
sampling_weights |
A variable name in the data frame containing
sampling weight information. Currently only available for non-clustered
data. Depending on the |
sample_cov |
Numeric matrix. A sample variance-covariance matrix. The rownames and/or colnames must contain the observed variable names. For a multiple group analysis, a list with a variance-covariance matrix for each group. |
sample_mean |
A sample mean vector. For a multiple group analysis, a list with a mean vector for each group. |
sample_th |
Vector of sample-based thresholds. For a multiple group analysis, a list with a vector of thresholds for each group. |
sample_nobs |
Number of observations if the full data frame is missing and only sample moments are given. For a multiple group analysis, a list or a vector with the number of observations for each group. |
group |
Character. A variable name in the data frame defining the groups in a multiple group analysis. |
cluster |
Character. A (single) variable name in the data frame defining the clusters in a two-level dataset. |
constraints |
Additional (in)equality constraints not yet included in the
model syntax. See |
wls_v |
A user provided weight matrix to be used by estimator |
nacov |
A user provided matrix containing the elements of (N times)
the asymptotic variance-covariance matrix of the sample statistics.
For a multiple group analysis, a list with an asymptotic
variance-covariance matrix for each group. See the |
ov_order |
Character. If |
... |
Many more options can be specified, using 'name = value'.
See |
Details
The sem function is a wrapper for the more general
lavaan function, using the following default arguments:
int.ov.free = TRUE, int.lv.free = FALSE,
auto.fix.first = TRUE (unless std.lv = TRUE),
auto.fix.single = TRUE, auto.var = TRUE,
auto.cov.lv.x = TRUE, auto.efa = TRUE,
auto.th = TRUE, auto.delta = TRUE,
and auto.cov.y = TRUE.
Value
An object of class lavaan, for which several methods
are available, including a summary method.
References
Yves Rosseel (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. doi:10.18637/jss.v048.i02
See Also
Examples
## The industrialization and Political Democracy Example ## Bollen (1989), page 332 model <- ' # latent variable definitions ind60 =~ x1 + x2 + x3 dem60 =~ y1 + a*y2 + b*y3 + c*y4 dem65 =~ y5 + a*y6 + b*y7 + c*y8 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 # residual correlations y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 ' fit <- sem(model, data = PoliticalDemocracy) summary(fit, fit.measures = TRUE)## The industrialization and Political Democracy Example ## Bollen (1989), page 332 model <- ' # latent variable definitions ind60 =~ x1 + x2 + x3 dem60 =~ y1 + a*y2 + b*y3 + c*y4 dem65 =~ y5 + a*y6 + b*y7 + c*y8 # regressions dem60 ~ ind60 dem65 ~ ind60 + dem60 # residual correlations y1 ~~ y5 y2 ~~ y4 + y6 y3 ~~ y7 y4 ~~ y8 y6 ~~ y8 ' fit <- sem(model, data = PoliticalDemocracy) summary(fit, fit.measures = TRUE)
Standardized Solution
Description
Standardized solution of a latent variable model.
Usage
standardizedSolution(object, type = "std.all", se = TRUE, zstat = TRUE, pvalue = TRUE, ci = TRUE, level = 0.95, boot.ci.type = "perc", cov.std = TRUE, remove.eq = TRUE, remove.ineq = TRUE, remove.def = FALSE, remove.aux = TRUE, partable = NULL, GLIST = NULL, est = NULL, output = "data.frame")standardizedSolution(object, type = "std.all", se = TRUE, zstat = TRUE, pvalue = TRUE, ci = TRUE, level = 0.95, boot.ci.type = "perc", cov.std = TRUE, remove.eq = TRUE, remove.ineq = TRUE, remove.def = FALSE, remove.aux = TRUE, partable = NULL, GLIST = NULL, est = NULL, output = "data.frame")
Arguments
object |
An object of class |
type |
If |
se |
Logical. If TRUE, standard errors for the standardized parameters will be computed, together with a z-statistic and a p-value. |
zstat |
Logical. If |
pvalue |
Logical. If |
ci |
If |
level |
The confidence level required. |
boot.ci.type |
Character. Only used if the model was fitted with
|
cov.std |
Logical. If TRUE, the (residual) observed covariances are scaled by the square root of the ‘Theta’ diagonal elements, and the (residual) latent covariances are scaled by the square root of the ‘Psi’ diagonal elements. If FALSE, the (residual) observed covariances are scaled by the square root of the diagonal elements of the observed model-implied covariance matrix (Sigma), and the (residual) latent covariances are scaled by the square root of diagonal elements of the model-implied covariance matrix of the latent variables. |
remove.eq |
Logical. If TRUE, filter the output by removing all rows containing equality constraints, if any. |
remove.ineq |
Logical. If TRUE, filter the output by removing all rows containing inequality constraints, if any. |
remove.def |
Logical. If TRUE, filter the output by removing all rows containing parameter definitions, if any. |
remove.aux |
Logical. If TRUE (the default), filter the output by
removing all rows corresponding to auxiliary ( |
GLIST |
List of model matrices. If provided, they will be used
instead of the GLIST inside the object@Model slot. Only works if the
|
est |
Numeric. Parameter values (as in the ‘est’ column of a
parameter table). If provided, they will be used instead of
the parameters that can be extracted from object. Only works if the |
partable |
A custom |
output |
Character. If |
Details
The standardized estimates are functions of the (unstandardized) free
parameters and of (a subset of) the model-implied (co)variances used for
scaling. The standard errors reported by standardizedSolution are
therefore standard errors for the standardized parameters, and they
will in general differ from the standard errors of the unstandardized
parameters reported by parameterEstimates (or in the
summary() output). They are also not the same as the standard errors
that would be obtained by simply rescaling the unstandardized standard errors.
How the standard errors are computed depends on how the model was originally
fitted (in particular on the se= argument of lavaan,
cfa, sem, ...):
-
By default (
se = "standard","robust.sem","robust.huber.white", ...), the standard errors are obtained with the delta method: the Jacobian of the standardization function is computed (numerically) and combined with the variance-covariance matrix of the (unstandardized) parameter estimates. Any robustness present in that variance-covariance matrix (for example robust or sandwich-type standard errors) is automatically propagated to the standardized solution. -
If the model was fitted with
se = "bootstrap"(and the bootstrap draws are available), bootstrap standard errors and bootstrap confidence intervals are reported instead. These are obtained by re-standardizing each bootstrap draw and computing the standard deviation (for the standard error) and the requested interval type (seeboot.ci.type) of the resulting standardized values. Note that, as inparameterEstimates, the p-value is still computed by referring the z-statistic (standardized estimate divided by its bootstrap standard error) to a standard normal distribution.
There is no separate argument to choose the type of standard error
within standardizedSolution: the type always follows the se=
setting that was used when the model was fitted. To obtain, say, robust or
bootstrap standard errors for the standardized solution, refit the model with
the corresponding se= argument.
Value
A data.frame containing standardized model parameters.
Note
The est, GLIST, and partable arguments are not meant for
everyday users, but for authors of external R packages that depend on
lavaan. Only to be used with great caution.
Examples
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) standardizedSolution(fit)HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) standardizedSolution(fit)
Variable Table
Description
Summary information about the variables included in either a data.frame, or a fitted lavaan object.
Usage
varTable(object, ov.names = names(object), ov.names.x = NULL, ordered = NULL, factor = NULL, as.data.frame. = TRUE)varTable(object, ov.names = names(object), ov.names.x = NULL, ordered = NULL, factor = NULL, as.data.frame. = TRUE)
Arguments
object |
Either a data.frame, or an object of class
|
ov.names |
Only used if object is a data.frame. A character vector containing the variables that need to be summarized. |
ov.names.x |
Only used if object is a data.frame. A character vector containing additional variables that need to be summarized. |
ordered |
Character vector. Which variables should be treated as ordered factors? |
factor |
Character vector. Which variables should be treated as (unordered) factors? |
as.data.frame. |
If TRUE, return the list as a data.frame. |
Value
A list or data.frame containing summary information about
variables in a data.frame. If object is a fitted lavaan object,
it displays the summary information about the observed variables that are
included in the model. The summary information includes
variable type (numeric, ordered, ...), the number of non-missing values,
the mean and variance for numeric variables, the number of levels of
ordered variables, and the labels for ordered variables.
Examples
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) varTable(fit)HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) varTable(fit)