| Title: | Latent Variable Analysis |
|---|---|
| Description: | Fit a variety of latent variable models, including confirmatory factor analysis, structural equation modeling and latent growth curve models. |
| Authors: | Yves Rosseel [aut, cre]
 , Terrence D.
Jorgensen [aut] , Luc
De Wilde [aut], Daniel Oberski [ctb], Jarrett Byrnes [ctb],
Leonard Vanbrabant [ctb], Victoria Savalei [ctb], Ed Merkle
[ctb], Michael Hallquist [ctb], Mijke Rhemtulla [ctb], Myrsini
Katsikatsou [ctb], Mariska Barendse [ctb], Nicholas Rockwood
[ctb], Florian Scharf [ctb], Han Du [ctb], Haziq Jamil [ctb]
, Franz Classe [ctb] |
| Maintainer: | Yves Rosseel <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.6-18 |
| Built: | 2024-06-21 13:25:13 UTC |
| Source: | CRAN |
Bootstrap the LRT, or any other statistic (or vector of statistics) you can extract from a fitted lavaan object.
bootstrapLavaan(object, R = 1000L, type = "ordinary", verbose = FALSE, FUN = "coef", keep.idx = FALSE, parallel = c("no", "multicore", "snow"), ncpus = 1L, cl = NULL, iseed = NULL, h0.rmsea = NULL, ...) bootstrapLRT(h0 = NULL, h1 = NULL, R = 1000L, type="bollen.stine", verbose = FALSE, return.LRT = FALSE, double.bootstrap = "no", double.bootstrap.R = 500L, double.bootstrap.alpha = 0.05, parallel = c("no", "multicore", "snow"), ncpus = 1L, cl = NULL, iseed = NULL)bootstrapLavaan(object, R = 1000L, type = "ordinary", verbose = FALSE, FUN = "coef", keep.idx = FALSE, parallel = c("no", "multicore", "snow"), ncpus = 1L, cl = NULL, iseed = NULL, h0.rmsea = NULL, ...) bootstrapLRT(h0 = NULL, h1 = NULL, R = 1000L, type="bollen.stine", verbose = FALSE, return.LRT = FALSE, double.bootstrap = "no", double.bootstrap.R = 500L, double.bootstrap.alpha = 0.05, parallel = c("no", "multicore", "snow"), ncpus = 1L, cl = NULL, iseed = NULL)
object |
An object of class |
h0 |
An object of class |
h1 |
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 |
return.LRT |
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 |
double.bootstrap |
If |
double.bootstrap.R |
Integer. The number of bootstrap draws to be use for the double bootstrap. |
double.bootstrap.alpha |
The significance level to compute the adjusted alpha based on the plugin p-values. |
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.
For bootstrapLavaan(), the bootstrap distribution of the value(s)
returned by FUN, when the object can be simplified to a vector.
For bootstrapLRT(), a bootstrap p value, calculated as the
proportion of bootstrap samples with a LRT statistic at least as large as
the LRT statistic for the original data.
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.
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.
# 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 sample in this example; in practice # you may wish to use a much higher number T.boot <- bootstrapLavaan(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 sample in this example; in practice # you may wish to use a much higher number T.boot <- bootstrapLavaan(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 a Confirmatory Factor Analysis (CFA) model.
cfa(model = NULL, data = NULL, ordered = 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, 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", ...)
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.) |
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 additional options can be defined, using 'name = value'.
See |
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.
An object of class lavaan, for which several methods
are available, including a summary method.
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
## 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)
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).
data(Demo.growth)data(Demo.growth)
A data frame of 400 observations of 10 variables.
t1Measured value at time point 1
t2Measured value at time point 2
t3Measured value at time point 3
t4Measured value at time point 4
x1Predictor 1 influencing intercept and slope
x2Predictor 2 influencing intercept and slope
c1Time-varying covariate time point 1
c2Time-varying covariate time point 2
c3Time-varying covariate time point 3
c4Time-varying covariate time point 4
head(Demo.growth)head(Demo.growth)
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”.
data(Demo.twolevel)data(Demo.twolevel)
A data frame of 2500 observations of 12 variables. clusters.
y1item 1
y2item 2
y3item 3
y4item 4
y5item 5
y6item 6
x1within-level covariate 1
x2within-level covariate 2
x3within-level covariate 3
w1between-level covariate 1
w2between-level covariate 2
clustercluster variable
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)
Fit one or more Exploratory Factor Analysis (EFA) model(s).
efa(data = NULL, nfactors = 1L, sample.cov = NULL, sample.nobs = NULL, rotation = "geomin", rotation.args = list(), ov.names = names(data), bounds = "pos.var", ..., output = "efa")efa(data = NULL, nfactors = 1L, sample.cov = NULL, sample.nobs = NULL, rotation = "geomin", rotation.args = list(), ov.names = names(data), bounds = "pos.var", ..., output = "efa")
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 or Integer vector. 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. 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, 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) are similar to those from the GPArotation package, but have been reimplemented for better control. The promax method is taken from the stats package. |
rotation.args |
List. Options related to the rotation algorithm. The
default options (and their alternatives) are |
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, all the variables in the data are used. |
bounds |
Per default, |
... |
Aditional options to be passed to lavaan, using 'name = value'.
See |
output |
Character. If |
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 as
a single block that should be rotated. The function only supports
a single group. 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.
There is also (limited) support for
twolevel data. The same number of factors is then extracted at the
within and the between level.
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.
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.
summary.efaList for a summary method if the output is
of class efaList.
## The famous Holzinger and Swineford (1939) example fit <- efa(data = HolzingerSwineford1939, ov.names = paste("x", 1:9, sep = ""), nfactors = 1:3, rotation = "geomin", rotation.args = list(geomin.epsilon = 0.01, rstarts = 1)) summary(fit, nd = 3L, cutoff = 0.2, dot.cutoff = 0.05) fitMeasures(fit, fit.measures = "all")## The famous Holzinger and Swineford (1939) example fit <- efa(data = HolzingerSwineford1939, ov.names = paste("x", 1:9, sep = ""), nfactors = 1:3, rotation = "geomin", rotation.args = list(geomin.epsilon = 0.01, rstarts = 1)) summary(fit, nd = 3L, cutoff = 0.2, dot.cutoff = 0.05) fitMeasures(fit, fit.measures = "all")
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.
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)
object |
An object of class |
scaling |
Only used for the ML estimator. If |
ignore.constraints |
Logical. If |
remove.duplicated |
If |
remove.empty.cases |
If |
A n x k matrix corresponding to n observations and k parameters.
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.
## 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))
A dataset from the Dutch burn center (http://www.adbc.nl). The data were used to examine psychosocial functioning in patients with facial burn wounds. Psychosocial functioning was measured by Anxiety and depression symptoms (HADS), and self-esteem (Rosenberg's self-esteem scale).
data(FacialBurns)data(FacialBurns)
A data frame of 77 observations of 6 variables.
SelfesteemRosenberg's self-esteem scale
HADSAnxiety and depression scale
AgeAge measured in years, control variable
TBSATotal Burned Surface Area
RUMRumination, control variable
SexGender, grouping variable
head(FacialBurns)head(FacialBurns)
This function computes a variety of fit measures to assess the global fit of a latent variable model.
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", ...)
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. The
|
output |
Character. If |
... |
Further arguments passed to or from other methods. Not currently
used for |
A named numeric vector of fit measures.
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") ## 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") ## 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)
Convenience functions to deal with covariance and correlation matrices.
getCov(x, lower = TRUE, diagonal = TRUE, sds = NULL, names = paste("V", 1:nvar, sep="")) char2num(s) cor2cov(R, sds, names = NULL)getCov(x, lower = TRUE, diagonal = TRUE, sds = NULL, names = paste("V", 1:nvar, sep="")) char2num(s) cor2cov(R, sds, names = NULL)
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; comma's and semi-colons are ignored. |
R |
A correlation matrix, to be scaled into a covariance matrix. |
The 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 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.
# The classic Wheaton et. al. (1977) model # panel data on he 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 <- 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 he 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 <- 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)
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.
growth(model = NULL, data = NULL, ordered = 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, 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", ...)
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.) |
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 additional options can be defined, using 'name = value'.
See |
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.
An object of class lavaan, for which several methods
are available, including a summary method.
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
## 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)
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).
data(HolzingerSwineford1939)data(HolzingerSwineford1939)
A data frame with 301 observations of 15 variables.
idIdentifier
sexGender
ageyrAge, year part
agemoAge, month part
schoolSchool (Pasteur or Grant-White)
gradeGrade
x1Visual perception
x2Cubes
x3Lozenges
x4Paragraph comprehension
x5Sentence completion
x6Word meaning
x7Speeded addition
x8Speeded counting of dots
x9Speeded discrimination straight and curved capitals
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.
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.
head(HolzingerSwineford1939)head(HolzingerSwineford1939)
Testing order/inequality constrained Hypotheses in SEM
InformativeTesting(model = NULL, data, constraints = NULL, R = 1000L, type = "bollen.stine", return.LRT = TRUE, double.bootstrap = "standard", double.bootstrap.R = 249L, double.bootstrap.alpha = 0.05, parallel = c("no", "multicore", "snow"), ncpus = 1L, cl = NULL, verbose = FALSE, ...)InformativeTesting(model = NULL, data, constraints = NULL, R = 1000L, type = "bollen.stine", return.LRT = TRUE, double.bootstrap = "standard", double.bootstrap.R = 249L, double.bootstrap.alpha = 0.05, parallel = c("no", "multicore", "snow"), ncpus = 1L, cl = NULL, verbose = FALSE, ...)
model |
Model syntax specifying the model. See |
data |
The data frame containing the observed variables being used to fit the model. |
constraints |
The imposed inequality constraints on the model. |
R |
Integer; number of bootstrap draws. The default value is set to 1000. |
type |
If |
return.LRT |
Logical; if |
double.bootstrap |
If |
double.bootstrap.R |
Integer; number of double bootstrap draws. The default value is set to 249. |
double.bootstrap.alpha |
The significance level to compute the adjusted
alpha based on the plugin p-values. Only used if |
parallel |
The type of parallel operation to be used (if any). If missing, the default is set "no". |
ncpus |
Integer: number of processes to be used in parallel operation: typically one would chose this to the number of available CPUs. |
cl |
An optional parallel or snow cluster for use if
|
verbose |
Logical; if |
... |
Other named arguments from the lavaan package which are passed to
the function. For example |
The following hypothesis tests are available:
Type A: Test H0: all restriktions with equalities ("=") active against HA: at least one inequality restriktion (">") strictly true.
Type B: Test H0: all restriktions with inequalities (">") (including some equalities ("=")) active against HA: at least one restriktion false (some equality restriktions may be maintained).
An object of class InformativeTesting for which a print and a plot method is available.
Leonard Vanbrabant [email protected]
Van de Schoot, R., Hoijtink, H., & Dekovic, M. (2010). Testing inequality constrained hypotheses in SEM models. Structural Equation Modeling, 17, 443-463.
Van de Schoot, R., Strohmeier, D. (2011). Testing informative hypotheses in SEM increases power: An illustration contrasting classical. International Journal of Behavioral Development, 35, 180-190.
Silvapulle, M.J. and Sen, P.K. (2005). Constrained Statistical Inference. Wiley, New York.
## Not run: ######################### ### real data example ### ######################### # Multiple group path model for facial burns example. # model syntax with starting values. burns.model <- 'Selfesteem ~ Age + c(m1, f1)*TBSA + HADS + start(-.10, -.20)*TBSA HADS ~ Age + c(m2, f2)*TBSA + RUM + start(.10, .20)*TBSA ' # constraints syntax burns.constraints <- 'f2 > 0 ; m1 < 0 m2 > 0 ; f1 < 0 f2 > m2 ; f1 < m1' # we only generate 2 bootstrap samples in this example; in practice # you may wish to use a much higher number. # the double bootstrap was switched off; in practice you probably # want to set it to "standard". example1 <- InformativeTesting(model = burns.model, data = FacialBurns, R = 2, constraints = burns.constraints, double.bootstrap = "no", group = "Sex") example1 ########################## ### artificial example ### ########################## # Simple ANOVA model with 3 groups (N = 20 per group) set.seed(1234) Y <- cbind(c(rnorm(20,0,1), rnorm(20,0.5,1), rnorm(20,1,1))) grp <- c(rep("1", 20), rep("2", 20), rep("3", 20)) Data <- data.frame(Y, grp) #create model matrix fit.lm <- lm(Y ~ grp, data = Data) mfit <- fit.lm$model mm <- model.matrix(mfit) Y <- model.response(mfit) X <- data.frame(mm[,2:3]) names(X) <- c("d1", "d2") Data.new <- data.frame(Y, X) # model model <- 'Y ~ 1 + a1*d1 + a2*d2' # fit without constraints fit <- sem(model, data = Data.new) # constraints syntax: mu1 < mu2 < mu3 constraints <- ' a1 > 0 a1 < a2 ' # we only generate 10 bootstrap samples in this example; in practice # you may wish to use a much higher number, say > 1000. The double # bootstrap is not necessary in case of an univariate ANOVA model. example2 <- InformativeTesting(model = model, data = Data.new, start = parTable(fit), R = 10L, double.bootstrap = "no", constraints = constraints) example2 ## End(Not run)## Not run: ######################### ### real data example ### ######################### # Multiple group path model for facial burns example. # model syntax with starting values. burns.model <- 'Selfesteem ~ Age + c(m1, f1)*TBSA + HADS + start(-.10, -.20)*TBSA HADS ~ Age + c(m2, f2)*TBSA + RUM + start(.10, .20)*TBSA ' # constraints syntax burns.constraints <- 'f2 > 0 ; m1 < 0 m2 > 0 ; f1 < 0 f2 > m2 ; f1 < m1' # we only generate 2 bootstrap samples in this example; in practice # you may wish to use a much higher number. # the double bootstrap was switched off; in practice you probably # want to set it to "standard". example1 <- InformativeTesting(model = burns.model, data = FacialBurns, R = 2, constraints = burns.constraints, double.bootstrap = "no", group = "Sex") example1 ########################## ### artificial example ### ########################## # Simple ANOVA model with 3 groups (N = 20 per group) set.seed(1234) Y <- cbind(c(rnorm(20,0,1), rnorm(20,0.5,1), rnorm(20,1,1))) grp <- c(rep("1", 20), rep("2", 20), rep("3", 20)) Data <- data.frame(Y, grp) #create model matrix fit.lm <- lm(Y ~ grp, data = Data) mfit <- fit.lm$model mm <- model.matrix(mfit) Y <- model.response(mfit) X <- data.frame(mm[,2:3]) names(X) <- c("d1", "d2") Data.new <- data.frame(Y, X) # model model <- 'Y ~ 1 + a1*d1 + a2*d2' # fit without constraints fit <- sem(model, data = Data.new) # constraints syntax: mu1 < mu2 < mu3 constraints <- ' a1 > 0 a1 < a2 ' # we only generate 10 bootstrap samples in this example; in practice # you may wish to use a much higher number, say > 1000. The double # bootstrap is not necessary in case of an univariate ANOVA model. example2 <- InformativeTesting(model = model, data = Data.new, start = parTable(fit), R = 10L, double.bootstrap = "no", constraints = constraints) example2 ## End(Not run)
The print function shows the results of hypothesis tests Type A and Type B. The plot function plots the distributions of bootstrapped LRT values and plug-in p-values.
## S3 method for class 'InformativeTesting' print(x, digits = max(3, getOption("digits") - 3), ...) ## S3 method for class 'InformativeTesting' plot(x, ..., type = c("lr","ppv"), main = "main", xlab = "xlabel", ylab = "Frequency", freq = TRUE, breaks = 15, cex.main = 1, cex.lab = 1, cex.axis = 1, col = "grey", border = par("fg"), vline = TRUE, vline.col = c("red", "blue"), lty = c(1,2), lwd = 1, legend = TRUE, bty = "o", cex.legend = 1, loc.legend = "topright")## S3 method for class 'InformativeTesting' print(x, digits = max(3, getOption("digits") - 3), ...) ## S3 method for class 'InformativeTesting' plot(x, ..., type = c("lr","ppv"), main = "main", xlab = "xlabel", ylab = "Frequency", freq = TRUE, breaks = 15, cex.main = 1, cex.lab = 1, cex.axis = 1, col = "grey", border = par("fg"), vline = TRUE, vline.col = c("red", "blue"), lty = c(1,2), lwd = 1, legend = TRUE, bty = "o", cex.legend = 1, loc.legend = "topright")
x |
object of class "InformativeTesting". |
digits |
the number of significant digits to use when printing. |
... |
Currently not used. |
type |
If |
main |
The main title(s) for the plot(s). |
xlab |
A label for the x axis, default depends on input type. |
ylab |
A label for the y axis. |
freq |
Logical; if TRUE, the histogram graphic is a representation of
frequencies, the counts component of the result; if |
breaks |
see |
cex.main |
The magnification to be used for main titles relative to the current setting of cex. |
cex.lab |
The magnification to be used for x and y labels relative to the current setting of cex. |
cex.axis |
The magnification to be used for axis annotation relative to the current setting of cex. |
col |
A colour to be used to fill the bars. The default of NULL yields unfilled bars. |
border |
Color for rectangle border(s). The default means par("fg"). |
vline |
Logical; if |
vline.col |
Color(s) for the vline.LRT. |
lty |
The line type. Line types can either be specified as an integer (0=blank, 1=solid (default), 2=dashed, 3=dotted, 4=dotdash, 5=longdash, 6=twodash) or as one of the character strings "blank", "solid", "dashed", "dotted", "dotdash", "longdash", or "twodash", where "blank" uses 'invisible lines' (i.e., does not draw them). |
lwd |
The line width, a positive number, defaulting to 1. |
legend |
Logical; if |
bty |
A character string which determined the type of box which is drawn about plots. If bty is one of "o" (the default), "l", "7", "c", "u", or "]" the resulting box resembles the corresponding upper case letter. A value of "n" suppresses the box. |
cex.legend |
A numerical value giving the amount by which the legend text and symbols should be magnified relative to the default. This starts as 1 when a device is opened, and is reset when the layout is changed. |
loc.legend |
The location of the legend, specified by a single
keyword from the list |
Leonard Vanbrabant [email protected]
## Not run: ######################### ### real data example ### ######################### # Multiple group path model for facial burns example. # model syntax with starting values. burns.model <- 'Selfesteem ~ Age + c(m1, f1)*TBSA + HADS + start(-.10, -.20)*TBSA HADS ~ Age + c(m2, f2)*TBSA + RUM + start(.10, .20)*TBSA ' # constraints syntax burns.constraints <- 'f2 > 0 ; m1 < 0 m2 > 0 ; f1 < 0 f2 > m2 ; f1 < m1' # we only generate 2 bootstrap samples in this example; in practice # you may wish to use a much higher number. # the double bootstrap was switched off; in practice you probably # want to set it to "standard". example1 <- InformativeTesting(model = burns.model, data = FacialBurns, R = 2, constraints = burns.constraints, double.bootstrap = "no", group = "Sex") example1 plot(example1) ########################## ### artificial example ### ########################## # Simple ANOVA model with 3 groups (N = 20 per group) set.seed(1234) Y <- cbind(c(rnorm(20,0,1), rnorm(20,0.5,1), rnorm(20,1,1))) grp <- c(rep("1", 20), rep("2", 20), rep("3", 20)) Data <- data.frame(Y, grp) #create model matrix fit.lm <- lm(Y ~ grp, data = Data) mfit <- fit.lm$model mm <- model.matrix(mfit) Y <- model.response(mfit) X <- data.frame(mm[,2:3]) names(X) <- c("d1", "d2") Data.new <- data.frame(Y, X) # model model <- 'Y ~ 1 + a1*d1 + a2*d2' # fit without constraints fit <- sem(model, data = Data.new) # constraints syntax: mu1 < mu2 < mu3 constraints <- ' a1 > 0 a1 < a2 ' # we only generate 10 bootstrap samples in this example; in practice # you may wish to use a much higher number, say > 1000. The double # bootstrap is not necessary in case of an univariate ANOVA model. example2 <- InformativeTesting(model = model, data = Data.new, start = parTable(fit), R = 10L, double.bootstrap = "no", constraints = constraints) example2 # plot(example2) ## End(Not run)## Not run: ######################### ### real data example ### ######################### # Multiple group path model for facial burns example. # model syntax with starting values. burns.model <- 'Selfesteem ~ Age + c(m1, f1)*TBSA + HADS + start(-.10, -.20)*TBSA HADS ~ Age + c(m2, f2)*TBSA + RUM + start(.10, .20)*TBSA ' # constraints syntax burns.constraints <- 'f2 > 0 ; m1 < 0 m2 > 0 ; f1 < 0 f2 > m2 ; f1 < m1' # we only generate 2 bootstrap samples in this example; in practice # you may wish to use a much higher number. # the double bootstrap was switched off; in practice you probably # want to set it to "standard". example1 <- InformativeTesting(model = burns.model, data = FacialBurns, R = 2, constraints = burns.constraints, double.bootstrap = "no", group = "Sex") example1 plot(example1) ########################## ### artificial example ### ########################## # Simple ANOVA model with 3 groups (N = 20 per group) set.seed(1234) Y <- cbind(c(rnorm(20,0,1), rnorm(20,0.5,1), rnorm(20,1,1))) grp <- c(rep("1", 20), rep("2", 20), rep("3", 20)) Data <- data.frame(Y, grp) #create model matrix fit.lm <- lm(Y ~ grp, data = Data) mfit <- fit.lm$model mm <- model.matrix(mfit) Y <- model.response(mfit) X <- data.frame(mm[,2:3]) names(X) <- c("d1", "d2") Data.new <- data.frame(Y, X) # model model <- 'Y ~ 1 + a1*d1 + a2*d2' # fit without constraints fit <- sem(model, data = Data.new) # constraints syntax: mu1 < mu2 < mu3 constraints <- ' a1 > 0 a1 < a2 ' # we only generate 10 bootstrap samples in this example; in practice # you may wish to use a much higher number, say > 1000. The double # bootstrap is not necessary in case of an univariate ANOVA model. example2 <- InformativeTesting(model = model, data = Data.new, start = parTable(fit), R = 10L, double.bootstrap = "no", constraints = constraints) example2 # plot(example2) ## End(Not run)
The lavaan model syntax describes a latent variable model. Often, the user wants to see the covariance matrix generated by their model for diagnostic purposes. However, their data may have far more columns of information than what is contained in their model.
inspectSampleCov(model, data, ...)inspectSampleCov(model, data, ...)
model |
The model that will be fit by lavaan. |
data |
The data frame being used to fit the model. |
... |
Other arguments to |
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, but doesn't fit the model, then uses
lavInspect to get the sample covariance matrix and meanstructure.
Jarrett Byrnes
Utility functions for equality and inequality constraints.
lav_constraints_parse(partable = NULL, constraints = NULL, theta = NULL, debug = FALSE) lav_partable_constraints_ceq(partable, con = NULL, debug = FALSE, txtOnly = FALSE) lav_partable_constraints_ciq(partable, con = NULL, debug = FALSE, txtOnly = FALSE) lav_partable_constraints_def(partable, con = NULL, debug = FALSE, txtOnly = FALSE)lav_constraints_parse(partable = NULL, constraints = NULL, theta = NULL, debug = FALSE) lav_partable_constraints_ceq(partable, con = NULL, debug = FALSE, txtOnly = FALSE) lav_partable_constraints_ciq(partable, con = NULL, debug = FALSE, txtOnly = FALSE) lav_partable_constraints_def(partable, con = NULL, debug = FALSE, txtOnly = FALSE)
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 ‘:=’ |
txtOnly |
Logical. If TRUE, only the body of the function is returned as a character string. If FALSE, a function is returned. |
This is a collection of lower-level constraint related functions that are used in the lavaan code. They are made public per request of package developers. Below is a brief description of what they do:
The lav_constraints_parse function parses the constraints
specification (provided as a string, see example), and generates
a list with useful information about the constraints.
The lav_partable_constraints_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_partable_constraints_ciq function creates a function
which takes the (unconstrained) parameter vector as input, and
returns the slack values for each inequality constraint.
The lav_partable_constraints_def function creates a function
which takes the (unconstrained) parameter vector as input, and
returns the computed values of the defined parameters.
myModel <- 'x1 ~ a*x2 + b*x3 + c*x4' myParTable <- lavaanify(myModel, as.data.frame. = FALSE) con <- ' a == 2*b b - c == 5 ' conInfo <- lav_constraints_parse(myParTable, constraints = con) myModel2 <- 'x1 ~ a*x2 + b*x3 + c*x4 a == 2*b b - c == 5 ' ceq <- lav_partable_constraints_ceq(partable = lavaanify(myModel2)) ceq( c(2,3,4) )myModel <- 'x1 ~ a*x2 + b*x3 + c*x4' myParTable <- lavaanify(myModel, as.data.frame. = FALSE) con <- ' a == 2*b b - c == 5 ' conInfo <- lav_constraints_parse(myParTable, constraints = con) myModel2 <- 'x1 ~ a*x2 + b*x3 + c*x4 a == 2*b b - c == 5 ' ceq <- lav_partable_constraints_ceq(partable = lavaanify(myModel2)) ceq( c(2,3,4) )
Utility functions related to the Data slot
# update data slot with new data (of the same size) lav_data_update(lavdata = NULL, newX = NULL, BOOT.idx = NULL, lavoptions = NULL)# update data slot with new data (of the same size) lav_data_update(lavdata = NULL, newX = NULL, BOOT.idx = NULL, lavoptions = NULL)
lavdata |
A lavdata object. |
newX |
A list of (new) data matrices (per group) of the same size. They will replace the data stored in the internal dataslot. |
BOOT.idx |
A list of integers. If bootstrapping was used to produce the data in newX, use these indices to adapt the remaining slots. |
lavoptions |
A named list. The Options lsot from a lavaan object. |
# 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, newX = 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, newX = newX, lavoptions = lavoptions)
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.
lav_export_estimation(lavaan_model)lav_export_estimation(lavaan_model)
lavaan_model |
a fitted lavaan model |
List with:
get_coef - When working with equality constraints, lavaan internally uses some transformations. get_coef is a functions that recreates 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
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$par, lavaan_model = fit)
Utility functions for computing the gradient of a scalar-valued function or the Jacobian of a vector-valued function by numerical approximation.
lav_func_gradient_complex(func, x, h = .Machine$double.eps, ..., fallback.simple = TRUE) lav_func_jacobian_complex(func, x, h = .Machine$double.eps, ..., fallback.simple = TRUE) lav_func_gradient_simple(func, x, h = sqrt(.Machine$double.eps), ...) lav_func_jacobian_simple(func, x, h = sqrt(.Machine$double.eps), ...)lav_func_gradient_complex(func, x, h = .Machine$double.eps, ..., fallback.simple = TRUE) lav_func_jacobian_complex(func, x, h = .Machine$double.eps, ..., fallback.simple = TRUE) lav_func_gradient_simple(func, x, h = sqrt(.Machine$double.eps), ...) lav_func_jacobian_simple(func, x, h = sqrt(.Machine$double.eps), ...)
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. |
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 part of the numDeriv package. They were used internally, and made public in 0.5-17 per request of other package developers.
Squire, W. and Trapp, G. (1998). Using Complex Variables to Estimate Derivatives of Real Functions. SIAM Review, 40(1), 110-112.
# very accurate complex method lav_func_gradient_complex(func = exp, x = 1) - exp(1) # less accurate forward method lav_func_gradient_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_gradient_complex(func = exp, x = 1) - exp(1) # less accurate forward method lav_func_gradient_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 Matrix and Vector operations.
# matrix to vector lav_matrix_vec(A) lav_matrix_vecr(A) lav_matrix_vech(S, diagonal = TRUE) lav_matrix_vechr(S, diagonal = TRUE) # matrix/vector indices lav_matrix_vech_idx(n = 1L, diagonal = TRUE) lav_matrix_vech_row_idx(n = 1L, diagonal = TRUE) lav_matrix_vech_col_idx(n = 1L, diagonal = TRUE) lav_matrix_vechr_idx(n = 1L, diagonal = TRUE) lav_matrix_vechru_idx(n = 1L, diagonal = TRUE) lav_matrix_diag_idx(n = 1L) lav_matrix_diagh_idx(n = 1L) lav_matrix_antidiag_idx(n = 1L) # vector to matrix lav_matrix_vech_reverse(x, diagonal = TRUE) lav_matrix_vechru_reverse(x, diagonal = TRUE) lav_matrix_upper2full(x, diagonal = TRUE) lav_matrix_vechr_reverse(x, diagonal = TRUE) lav_matrix_vechu_reverse(x, diagonal = TRUE) lav_matrix_lower2full(x, diagonal = TRUE) # the duplication matrix lav_matrix_duplication(n = 1L) lav_matrix_duplication_pre(A = matrix(0,0,0)) lav_matrix_duplication_post(A = matrix(0,0,0)) lav_matrix_duplication_pre_post(A = matrix(0,0,0)) lav_matrix_duplication_ginv(n = 1L) lav_matrix_duplication_ginv_pre(A = matrix(0,0,0)) lav_matrix_duplication_ginv_post(A = matrix(0,0,0)) lav_matrix_duplication_ginv_pre_post(A = matrix(0,0,0)) # the commutation matrix lav_matrix_commutation(m = 1L, n = 1L) lav_matrix_commutation_pre(A = matrix(0,0,0)) lav_matrix_commutation_post(A = matrix(0,0,0)) lav_matrix_commutation_pre_post(A = matrix(0,0,0)) lav_matrix_commutation_mn_pre(A, m = 1L, n = 1L) # sample statistics lav_matrix_cov(Y, Mu = NULL) # other matrix operations lav_matrix_symmetric_sqrt(S = matrix(0,0,0)) lav_matrix_orthogonal_complement(A = matrix(0,0,0)) lav_matrix_bdiag(...) lav_matrix_trace(..., check = TRUE)# matrix to vector lav_matrix_vec(A) lav_matrix_vecr(A) lav_matrix_vech(S, diagonal = TRUE) lav_matrix_vechr(S, diagonal = TRUE) # matrix/vector indices lav_matrix_vech_idx(n = 1L, diagonal = TRUE) lav_matrix_vech_row_idx(n = 1L, diagonal = TRUE) lav_matrix_vech_col_idx(n = 1L, diagonal = TRUE) lav_matrix_vechr_idx(n = 1L, diagonal = TRUE) lav_matrix_vechru_idx(n = 1L, diagonal = TRUE) lav_matrix_diag_idx(n = 1L) lav_matrix_diagh_idx(n = 1L) lav_matrix_antidiag_idx(n = 1L) # vector to matrix lav_matrix_vech_reverse(x, diagonal = TRUE) lav_matrix_vechru_reverse(x, diagonal = TRUE) lav_matrix_upper2full(x, diagonal = TRUE) lav_matrix_vechr_reverse(x, diagonal = TRUE) lav_matrix_vechu_reverse(x, diagonal = TRUE) lav_matrix_lower2full(x, diagonal = TRUE) # the duplication matrix lav_matrix_duplication(n = 1L) lav_matrix_duplication_pre(A = matrix(0,0,0)) lav_matrix_duplication_post(A = matrix(0,0,0)) lav_matrix_duplication_pre_post(A = matrix(0,0,0)) lav_matrix_duplication_ginv(n = 1L) lav_matrix_duplication_ginv_pre(A = matrix(0,0,0)) lav_matrix_duplication_ginv_post(A = matrix(0,0,0)) lav_matrix_duplication_ginv_pre_post(A = matrix(0,0,0)) # the commutation matrix lav_matrix_commutation(m = 1L, n = 1L) lav_matrix_commutation_pre(A = matrix(0,0,0)) lav_matrix_commutation_post(A = matrix(0,0,0)) lav_matrix_commutation_pre_post(A = matrix(0,0,0)) lav_matrix_commutation_mn_pre(A, m = 1L, n = 1L) # sample statistics lav_matrix_cov(Y, Mu = NULL) # other matrix operations lav_matrix_symmetric_sqrt(S = matrix(0,0,0)) lav_matrix_orthogonal_complement(A = matrix(0,0,0)) lav_matrix_bdiag(...) lav_matrix_trace(..., check = TRUE)
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 column 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 |
These are a collection of lower-level matrix/vector related functions that are used throughout the lavaan code. They are made public per request of package developers. Below is a brief description of what they do:
The lav_matrix_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_matrix_vecr function is similar to the lav_matrix_vec
function but transforms a matrix into a vector by stacking the
rows of the matrix one underneath the other.
The lav_matrix_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_matrix_vechr function is similar to the lav_matrix_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_matrix_vech_idx function returns the vector indices of the lower
triangular elements of a symmetric matrix of size n, column by column.
The lav_matrix_vech_row_idx function returns the row indices of the
lower triangular elements of a symmetric matrix of size n.
The lav_matrix_vech_col_idx function returns the column indices of the
lower triangular elements of a symmetric matrix of size n.
The lav_matrix_vechr_idx function returns the vector indices of the
lower triangular elements of a symmetric matrix of size n, row by row.
The lav_matrix_vechu_idx function returns the vector indices of the
upper triangular elements of a symmetric matrix of size n, column by column.
The lav_matrix_vechru_idx function returns the vector indices
of the upper triangular elements of a symmetric matrix of size n, row by row.
The lav_matrix_diag_idx function returns the vector indices of the
diagonal elements of a symmetric matrix of size n.
The lav_matrix_diagh_idx function returns the vector indices of
the lower part of a symmetric matrix of size n.
The lav_matrix_antidiag_idx function returns the vector indices of
the anti diagonal elements a symmetric matrix of size n.
The lav_matrix_vech_reverse function (alias:
lav_matrix_vechru_reverse and lav_matrix_upper2full) creates a
symmetric matrix, given only upper triangular elements, row by row. If
diagonal = FALSE, an diagonal with zero elements is added.
The lav_matrix_vechr_reverse (alias: lav_matrix_vechu_reverse and
lav_matrix_lower2full) creates a symmetric matrix, given only the lower
triangular elements, row by row. If diagonal = FALSE, an diagonal with zero
elements is added.
The lav_matrix_duplication 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_matrix_duplication_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_matrix_duplication_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_matrix_duplication_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_matrix_duplication_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_matrix_duplication_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_matrix_duplication_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_matrix_duplication_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_matrix_commutation function computes the commutation matrix which
is a permutation matrix which transforms vec(A) (with m rows and n columns)
into vec(t(A)).
The lav_matrix_commutation_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_matrix_commutation_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_matrix_commutation_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_matrix_commutation_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_matrix_cov function computes the sample covariance matrix of
its input matrix, where the elements are divided by N (the number of rows).
The lav_matrix_symmetric_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_matrix_orthogonal_complement function computes an orthogonal
complement of the matrix A, using a qr decomposition.
The lav_matrix_bdiag function constructs a block diagonal matrix from
its arguments.
The lav_matrix_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.
Magnus, J. R. and H. Neudecker (1999). Matrix Differential Calculus with Applications in Statistics and Econometrics, Second Edition, John Wiley.
# 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_matrix_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_matrix_duplication_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_matrix_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_matrix_duplication_ginv_pre_post(S %x% S) Gamma.NT
Utility functions related to internal model representation (lavmodel)
# 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)# 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)
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). |
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
Utility functions related to the parameter table (partable)
# extract information from a parameter table lav_partable_df(partable) lav_partable_ndat(partable) lav_partable_npar(partable) lav_partable_attributes(partable, pta = NULL) # generate parameter labels lav_partable_labels(partable, blocks = c("group", "level"), group.equal = "", group.partial = "", type = "user") # generate parameter table for specific models 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_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_from_lm(object, est = FALSE, label = FALSE, as.data.frame. = FALSE) # complete a parameter table only containing a few columns (lhs,op,rhs) lav_partable_complete(partable = NULL, start = TRUE) # merge two parameter tables lav_partable_merge(pt1 = NULL, pt2 = NULL, remove.duplicated = FALSE, fromLast = FALSE, warn = TRUE) # add a single parameter to an existing parameter table lav_partable_add(partable = NULL, add = list())# extract information from a parameter table lav_partable_df(partable) lav_partable_ndat(partable) lav_partable_npar(partable) lav_partable_attributes(partable, pta = NULL) # generate parameter labels lav_partable_labels(partable, blocks = c("group", "level"), group.equal = "", group.partial = "", type = "user") # generate parameter table for specific models 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_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_from_lm(object, est = FALSE, label = FALSE, as.data.frame. = FALSE) # complete a parameter table only containing a few columns (lhs,op,rhs) lav_partable_complete(partable = NULL, start = TRUE) # merge two parameter tables lav_partable_merge(pt1 = NULL, pt2 = NULL, remove.duplicated = FALSE, fromLast = FALSE, warn = TRUE) # add a single parameter to an existing parameter table lav_partable_add(partable = NULL, add = list())
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. Can be either ‘user’ or ‘free’ to select all entries or only the free parameters from the parameter table respectively. |
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 lsot 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 |
fromLast |
Logical. If |
warn |
Logical. If |
add |
A named list. A single row of a parameter table as a named list. |
# 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_partable_independence(fit) as.data.frame(lav, stringsAsFactors = FALSE) # how many free parameters? lav_partable_npar(lav) # how many sample statistics? lav_partable_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_partable_independence(fit) as.data.frame(lav, stringsAsFactors = FALSE) # how many free parameters? lav_partable_npar(lav) # how many sample statistics? lav_partable_ndat(lav)
Utility functions related to the sample statistics
# generate samplestats object from full data lav_samplestats_from_data(lavdata = NULL, lavoptions = NULL, WLS.V = NULL, NACOV = NULL)# generate samplestats object from full data lav_samplestats_from_data(lavdata = NULL, lavoptions = NULL, WLS.V = NULL, NACOV = NULL)
lavdata |
A lavdata object. |
lavoptions |
A named list. The Options lsot 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. |
# 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_samplestats_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_samplestats_from_data(lavdata = lavdata, lavoptions = lavoptions)
Fit a latent variable model.
lavaan(model = NULL, data = NULL, ordered = 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", slotOptions = NULL, slotParTable = NULL, slotSampleStats = NULL, slotData = NULL, slotModel = NULL, slotCache = NULL, sloth1 = NULL, ...)lavaan(model = NULL, data = NULL, ordered = 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", slotOptions = NULL, slotParTable = NULL, slotSampleStats = NULL, slotData = NULL, slotModel = NULL, slotCache = NULL, sloth1 = NULL, ...)
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.) |
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 |
slotOptions |
Options slot from a fitted lavaan object. If provided, no new Options slot will be created by this call. |
slotParTable |
ParTable slot from a fitted lavaan object. If provided, no new ParTable slot will be created by this call. |
slotSampleStats |
SampleStats slot from a fitted lavaan object. If provided, no new SampleStats slot will be created by this call. |
slotData |
Data slot from a fitted lavaan object. If provided, no new Data slot will be created by this call. |
slotModel |
Model slot from a fitted lavaan object. If provided, no new Model slot will be created by this call. |
slotCache |
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 additional options can be defined, using 'name = value'.
See |
An object of class lavaan, for which several methods
are available, including a summary method.
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
# 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)
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 can be created via the
cfa, sem, growth or
lavaan functions.
version:The lavaan package version used to create this objects
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 using objects that we try to compute only once, and reuse 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.
signature(object = "lavaan", type = "free"): Returns
the estimates of the parameters in the model as a named numeric vector.
If type="free", only the free parameters are returned.
If type="user", all parameters listed in the parameter table
are returned, including constrained and fixed parameters.
signature(object = "lavaan"): Returns the
implied moments of the model as a list with two elements (per group):
cov for the implied covariance matrix,
and mean for the implied mean
vector. If only the covariance matrix was analyzed, the implied mean
vector will be zero.
signature(object = "lavaan"): an alias for
fitted.values.
signature(object = "lavaan", type="raw"):
If type = "raw", this function returns the raw (= unscaled)
difference between the observed and the expected (model-implied) summary
statistics.
If type = "cor", or type = "cor.bollen", the observed and
model implied covariance matrices are first transformed to a correlation
matrix (using cov2cor()), before the residuals are computed.
If type = "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.
If type="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 the se argument).
Unfortunately, the corresponding normalized residuals are not entirely
correct, and this option is only available for historical interest.
If type="standardized", the residuals are divided by the square
root of the asymptotic variance of these residuals. The resulting
standardized residuals elements can be interpreted as z-scores.
If type="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 many
NA values for the standardized residuals.
signature(object = "lavaan"): an alias
for residuals
signature(object = "lavaan"): returns the
covariance matrix of the estimated parameters.
signature(object = "lavaan"): compute
factor scores for all cases that are provided in the data frame. For
complete data only.
signature(object = "lavaan"): returns
model comparison statistics. This method is just a wrapper around
the function lavTestLRT.
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 the lavTestLRT page.
signature(object = "lavaan", model, add, ...,
evaluate=TRUE): update a fitted lavaan object and evaluate it
(unless evaluate=FALSE). Note that we use the environment
that is stored within the lavaan object, which is not necessarily
the parent frame. The add argument is analogous to the one
described in the lavTestScore page, and can be used to
add parameters to the specified model rather than passing an entirely
new model argument.
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.
signature(object = "lavaan"):
returns the log-likelihood of the fitted model, if maximum likelihood estimation
was used. The AIC and BIC
methods automatically work via logLik().
signature(object = "lavaan"): Print a short summary
of the model fit
signature(object = "lavaan", header = TRUE,
fit.measures = FALSE, estimates = TRUE, ci = FALSE, fmi = FALSE,
standardized = FALSE, std.nox = FALSE,
remove.step1 = TRUE, remove.unused = TRUE, cov.std = TRUE, rsquare = FALSE,
modindices = FALSE, ci = FALSE, nd = 3L):
Print a nice summary of the model estimates.
If header = TRUE, the header section (including fit measures) is
printed.
If fit.measures = TRUE, additional fit measures are added to the
header section. The related fm.args list allows to set options
related to the fit measures. See fitMeasures
for more details.
If estimates = TRUE, print the parameter estimates section.
If ci = TRUE, add confidence intervals to the parameter estimates
section.
If fmi = TRUE, add the fmi (fraction of missing information)
column, if it is available.
If standardized=TRUE or a character vector, the standardized
solution is also printed (see parameterEstimates).
Note that SEs and
tests are still based on unstandardized estimates. Use
standardizedSolution to obtain SEs and test
statistics for standardized estimates.
The std.nox argument is deprecated; the standardized
argument allows "std.nox" solution to be specifically requested.
If remove.step1, the parameters of the measurement part are not
shown (only used when using sam().)
If remove.unused, automatically added parameters that are
fixed to their default (0 or 1) values are removed.
If rsquare=TRUE, the R-Square values for the dependent variables
in the model are printed.
If efa = TRUE, EFA related information is printed. The related
efa.args list allows to set options related to the EFA output.
See summary.efaList for more details.
If modindices=TRUE, modification indices
are printed for all fixed parameters.
The argument nd determines 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 class lavaan.summary for which is print
function is available.
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
cfa, sem,
fitMeasures, standardizedSolution,
parameterEstimates, lavInspect,
modindices
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")
Fit the same latent variable model, for a (potentially large) number of datasets.
lavaanList(model = NULL, dataList = NULL, dataFunction = NULL, dataFunction.args = list(), ndat = length(dataList), 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), cl = NULL, iseed = NULL) semList(model = NULL, dataList = NULL, dataFunction = NULL, dataFunction.args = list(), ndat = length(dataList), ..., store.slots = c("partable"), FUN = NULL, show.progress = FALSE, store.failed = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 1L), cl = NULL, iseed = NULL) cfaList(model = NULL, dataList = NULL, dataFunction = NULL, dataFunction.args = list(), ndat = length(dataList), ..., store.slots = c("partable"), FUN = NULL, show.progress = FALSE, store.failed = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 1L), cl = NULL, iseed = NULL)lavaanList(model = NULL, dataList = NULL, dataFunction = NULL, dataFunction.args = list(), ndat = length(dataList), 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), cl = NULL, iseed = NULL) semList(model = NULL, dataList = NULL, dataFunction = NULL, dataFunction.args = list(), ndat = length(dataList), ..., store.slots = c("partable"), FUN = NULL, show.progress = FALSE, store.failed = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 1L), cl = NULL, iseed = NULL) cfaList(model = NULL, dataList = NULL, dataFunction = NULL, dataFunction.args = list(), ndat = length(dataList), ..., store.slots = c("partable"), FUN = NULL, show.progress = FALSE, store.failed = FALSE, parallel = c("no", "multicore", "snow"), ncpus = max(1L, parallel::detectCores() - 1L), cl = NULL, iseed = NULL)
model |
A description of the user-specified model. Typically, the model
is described using the lavaan model syntax. See
|
dataList |
List. Each element contains a full data frame containing the observed variables used in the model. |
dataFunction |
Function. A function that generated a full data frame containing the observed variables used in the model. It can also be a matrix, if the columns are named. |
dataFunction.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. Which command is used to run the sem models. The possible
choices are |
... |
Other named arguments for |
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 chose 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 |
An object of class lavaanList, for which several methods
are available, including a summary method.
class lavaanList
# 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() simulateData(HS.model, sample.nobs = 100) set.seed(1234) fit <- semList(HS.model, dataFunction = 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() simulateData(HS.model, sample.nobs = 100) set.seed(1234) fit <- semList(HS.model, dataFunction = generateData, ndat = 5, store.slots = "partable") # show parameter estimates, per dataset coef(fit)
The lavaanList class represents a collection of (fitted)
latent variable models, for 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 can be created via the
cfaList, semList, or
lavaanList functions.
version:The lavaan package version used to create this objects
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.
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.
If type="free", only the free parameters are returned.
If type="user", all parameters listed in the parameter table
are returned, including constrained and fixed parameters.
signature(object = "lavaanList", header = TRUE, estimates = TRUE, nd = 3L):
Print a summary of the collection of fitted models.
If header = TRUE, the header section is
printed.
If estimates = TRUE, print the parameter estimates section.
The argument nd determines the number of digits after the
decimal point to be printed (currently only in the parameter estimates
section.)
Nothing is returned (use
parameterEstimates or another extractor function
to extract information from this object).
Fit an unrestricted model to compute polychoric, polyserial and/or Pearson correlations.
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")
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 |
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.
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.
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.
# 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)
Export a fitted lavaan object to an external program.
lavExport(object, target = "lavaan", prefix = "sem", dir.name = "lavExport", export = TRUE)lavExport(object, target = "lavaan", prefix = "sem", dir.name = "lavExport", export = TRUE)
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 |
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.
If export = TRUE, a directory (called lavExport 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.
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)
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.
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", ...)
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. |
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() and vcov().
"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 if we ignore any equality
constraints. They correspond with 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 have the
same standard error for both parameters.
Aliases: "std.err" and "standard.errors".
"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".
"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.)
Information about the data:
"data":A matrix containing the observed variables
that have been used to fit the model. No column/row names are provided.
Column names correspond to the output of lavNames(object),
while the rows correspond to the output of
lavInspect(object, "case.idx".
"ordered":A character vector. The ordered variables.
"nobs":Integer vector. The number of observations in each group that were used in the analysis.
"norig":Integer vector. The original number of observations in each group.
"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.
"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.
"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
TRUE and FALSE if lavTech() 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 where each element contains the proportion of observed datapoints 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 variables are
continuous, and missing = "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 is
not present (perhaps, because the model was fitted with
h1 = FALSE), we return the sample statistics from the
SampleStats slot. Here, 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.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. TRUE if a meanstructure
was included in the model.
"categorical":Logical. TRUE if categorical endogenous
variables were part of the model.
"fixed.x":Logical. TRUE if 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".
"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".
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.fs":The Mahalanobis distances for the (Bartlett-based) casewise residuals.
Optimizer information:
"converged":Logical. TRUE if the optimizer has
converged; FALSE otherwise.
"iteratons":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.
"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 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 for each bootstrap sample. Only relevant when bootstrapping was used.
"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".
"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 by fitMeasures().
"mi":The modification indices. Alias: "modindices",
"modification.indices". The same output as given
by modindices().
"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") or
lavInspect(fit, "theta") return a non-positive definite matrix.
"zero.cell.tables":List. List of bivariate frequency tables where at least one cell is empty.
"version":The lavaan version number that was used to construct the fitted lavaan object.
# 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")
The lavListInspect() and lavListTech() functions can be used to
inspect/extract information that is stored inside (or can be computed from) a
lavaanList object.
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)
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 |
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() and vcov().
"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 if we ignore any equality
constraints. They correspond with 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. TRUE if a meanstructure
was included in the model.
"categorical":Logical. TRUE if categorical endogenous
variables were part of the model.
"fixed.x":Logical. TRUE if 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.
# fit model HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' # a data generating function generateData <- function() simulateData(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() simulateData(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")
Extend the parameter table with a matrix representation.
lavMatrixRepresentation(partable, representation = "LISREL", add.attributes = FALSE, as.data.frame. = TRUE)lavMatrixRepresentation(partable, representation = "LISREL", add.attributes = FALSE, as.data.frame. = TRUE)
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. |
add.attributes |
Logical. If |
as.data.frame. |
Logical. If |
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.
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")]
Extract variables names from a fitted lavaan object.
lavNames(object, type = "ov", ...)lavNames(object, type = "ov", ...)
object |
An object of class |
type |
Character. The type of variables whose names should be extracted. See details for a complete list. |
... |
Additional selection variables. For example |
The order of the variable names, as returned by lavNames
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": modelled 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": lonely observed variables (only intercepts/variancesappear in the model syntax)
"ov.interaction": interaction terms (defined by the colon operator)
"th": threshold names ordinal variables only
"th.mean": threshold names ordinal + numeric variables (if any)
"lv": latent variables
"lv.regular": latent variables (defined by =~ only)
"lv.formative": latent variables (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
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")
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 will be added to the '...'
argument.
lavOptions(x = NULL, default = NULL, mimic = "lavaan")lavOptions(x = NULL, default = NULL, mimic = "lavaan")
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. |
This is the full list of options that are accepted by the lavaan()
function, organized in several sections:
Model features (always available):
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. If FALSE, the
exogenous ‘x’ variables are modeled jointly with the other variables, and
the model-implied statistics refect 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. If FALSE, 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. If
FALSE, 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 = TRUE and "loadings" is included in
the group.equal argument, 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 implies
effect.coding = c("loadings", "intercepts"). If logical and
FALSE, 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 with std.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 will be freely estimated and usually
equal 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 with op = "==").
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 to 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. Always assuming
fixed.x = FALSE and conditional.x = FALSE (for now).
Model features (only available for the lavaan() function):
auto.fix.first:If TRUE, the factor loading of the
first indicator is set to 1.0 for every latent variable.
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.
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, unless fixed.x = FALSE.
Use this option with caution; it can be used to test if (for example)
nonconvergence was due to scaling issues. But this is still a covariance
based analysis, in the sense that no constraints are involved (to
ensure the model-implied (co)variance matrix has unit variances), and the
standard errors still assume that the input was unstandardized. See
also the correlation option.
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, and
fixed.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 if fixed.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 (eg. mice) to
generate imputed datasets, which can then be analyzed using
the semList function. 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.
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 may change from pair to pair.
By default, in the categorical case we use conditional.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 "total".
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 is TRUE.
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 to TRUE if
maximum likelihood estimation is used and likelihood="normal",
and FALSE otherwise.
ridge:Logical. If TRUE a small constant value will
be added the diagonal elements of the covariance (or correlation)
matrix before analysis. The value can be set using the
ridge.constant option.
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.loadings",
"intercepts", "means",
"thresholds", "regressions", "residuals",
"residual.covariances", "lv.variances" or
"lv.covariances", specifying the pattern of equality
constraints across multiple groups.
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. If
FALSE (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.
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: if mimic="lavaan" or mimic="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 lavTest function 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 the
lavTest function to extract (alternative)
test statistics from a fitted lavaan object.
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.oneLogical. If TRUE, we divide the
Gamma matrix by N-1 (instead of the default N).
gamma.unbiasedLogical. If TRUE, we compute an
unbiased version for the Gamma matrix. Only available for single-level
complete data and when conditional.x = FALSE and
fixed.x = FALSE (for now).
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 of nlminb for 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 when
estimator = "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.tolNumeric. 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 are smaller than this tolerance value. Default is
1e-05 for DLS estimation and 1e-07 otherwise.
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: FALSE implies no bounds are imposed on the parameters.
If TRUE, this implies bounds = "wide". If character,
possible options are "none" (the default), "standard",
"wide", "pos.var", "pos.ov.var", and
"pos.lv.var".
If bounds = "pos.ov.var", the observed variances are forced to be
nonnegative. If bounds = "pos.lv.var", the latent variances are
forced to be nonnegative. If bounds = "pos.var", both observed
and latent variances are forced to be nonnegative. If
bounds = "standard", lower and upper bounds are computed for
observed and latent variances, and factor loadings. If
bounds = "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
bounds argument to allow more control. Possible elements of the
list are lower, upper, lower.factor and
upper.factor. All of these accept a vector. The lower and
upper elements indicate for which type of parameters bounds
should be computed. Possible choice are "ov.var", "lv.var",
"loadings" and "covariances". The lower.factor and
upper.factor elements should have the same length as the
lower and upper elements 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 are
min.reliability.marker which sets the lower bound for the
reliability of the marker indicator (if any) of each factor
(default is 0.1). Finally, the min.var.lv.endo element indicates
the lower bound of the variance of any endogenous latent variance
(default is 0.0).
Parallelization options (currently only used for bootstrapping):
The type of parallel operation to be used (if any). If
missing, the default is "no".
Integer: number of processes to be used in parallel operation:
typically one would chose this to the number of available CPUs. By
By default this is the number of cores (as detected by
parallel::detectCores()) minus one.
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 the bootstrapLavaan
or bootstrapLRT call.
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" if parallel = "multicore". If
parallel = "snow" (under windows),
parallel::clusterSetRNGStream() is called which automatically
switches to "L'Ecuyer-CMRG". When iseed is 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 uses zero.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". The default is TRUE.
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.
Starting values options:
start:If it is a character string, the two options are
currently "simple" and "Mplus". In the first case, all
parameter values are set to zero, except the factor loadings and
(residual) variances, which are set to one.
When start is "Mplus", the factor loadings are
estimated using the fabin3 estimator (tsls) per factor. The
residual variances of observed variables are set tot half the
observed variance, and all other (residual) variances are set to 0.05.
The remaining parameters (regression coefficients, covariances) are
set to zero.
If start is a fitted object of class lavaan,
the estimated values of the corresponding parameters will be extracted.
If it is a parameter table, for example the output of the
paramaterEstimates() function, the values of the est or
start or ustart column (whichever is found first) will be
extracted.
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.gradient:Logical. If TRUE, and the model
converged, a warning
is given if the optimizer decided that a (local) solution has
been found, 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
acitive 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 to
"lavaan", which is very close to "Mplus".
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,
and conditional.x = TRUE, the (default) baseline model will
allow the slopestructure to be unrestricted.
store.vcovLogical. If TRUE, and se= is not
set to "none", store the full variance-covariance matrix of
the model parameters in the vcov slot of the fitted lavaan object.
parserCharacter. 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.
lavOptions() lavOptions("std.lv") lavOptions(c("std.lv", "orthogonal"))lavOptions() lavOptions("std.lv") lavOptions(c("std.lv", "orthogonal"))
The main purpose of the lavPredict() function is to compute (or
‘predict’) estimated values 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.)
lavPredict(object, newdata = NULL, type = "lv", method = "EBM", transform = FALSE, se = "none", acov = "none", label = TRUE, fsm = FALSE, mdist = FALSE, append.data = FALSE, assemble = FALSE, level = 1L, optim.method = "bfgs", ETA = 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, append.data = FALSE, assemble = FALSE, level = 1L, optim.method = "bfgs", ETA = NULL, drop.list.single.group = TRUE)
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 |
append.data |
Logical. Only used when |
assemble |
Logical. If TRUE, the separate multiple groups are reassembled again to form a single data.frame with a group column, having the same dimensions are 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 |
drop.list.single.group |
Logical. If |
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 values (in the regression sense). In other words,
the structural component is completely ignored (for now).
lavPredictY to predict y-variables given x-variables.
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")) ## ------------------------------------------ ## 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 susequent 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")) ## ------------------------------------------ ## 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 susequent models ## ------------------------------------- ## see Examples in semTools package: ?plausibleValues
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.
lavPredictY(object, newdata = NULL, ynames = lavNames(object, "ov.y"), xnames = lavNames(object, "ov.x"), method = "conditional.mean", label = TRUE, assemble = TRUE, force.zero.mean = FALSE, lambda = 0)lavPredictY(object, newdata = NULL, ynames = lavNames(object, "ov.y"), xnames = lavNames(object, "ov.x"), method = "conditional.mean", label = TRUE, assemble = TRUE, force.zero.mean = FALSE, lambda = 0)
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 of the separate multiple groups in the output are reassembled again to form 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. |
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.
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
lavPredict to compute scores for latent variables.
lavPredictY_cv to determine an optimal lambda to increase
prediction accuracy.
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"))
This function can be used to determine an optimal lambda value for the
lavPredictY function. based on cross-validation.
lavPredictY_cv(object, data = NULL, xnames = lavNames(object, "ov.x"), ynames = lavNames(object, "ov.y"), n.folds = 10L, lambda.seq = seq(0, 1, 0.1))lavPredictY_cv(object, data = NULL, xnames = lavNames(object, "ov.x"), ynames = lavNames(object, "ov.y"), n.folds = 10L, lambda.seq = seq(0, 1, 0.1))
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 |
This function is used to generate an optimal lambda value for
lavPredictY predictions to improve prediction accuracy.
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
lavPredictY to predict the values of (observed) y-variables given
the values of (observed) x-variables in a structural equation model.
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)
‘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.
lavResiduals(object, type = "cor.bentler", custom.rmr = NULL, se = FALSE, zstat = TRUE, summary = TRUE, h1.acov = "unstructured", add.type = TRUE, add.labels = TRUE, add.class = TRUE, drop.list.single.group = TRUE, maximum.number = length(res.vech), output = "list")lavResiduals(object, type = "cor.bentler", custom.rmr = NULL, se = FALSE, zstat = TRUE, summary = TRUE, h1.acov = "unstructured", add.type = TRUE, add.labels = TRUE, add.class = TRUE, drop.list.single.group = TRUE, maximum.number = length(res.vech), output = "list")
object |
An object of class |
type |
Character.
If |
custom.rmr |
|
se |
Logical. If |
zstat |
Logical. If |
summary |
Logical. If |
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 |
output |
Character. By default, |
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.
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
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)
Frequency tables for categorical variables and related statistics.
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)
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, we can change the information
per row: 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 |
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),
a list of tables (if type = "cells") where each list element
corresponds to a pairwise table, or if type = "table", a single table
(per group). In both cases, the table entries are determined by the
(single) statistic argument.
Joreskog, K.G. & Moustaki, I. (2001). Factor analysis of ordinal variables: A comparison of three approaches. Multivariate Behavioral Research, 36, 347-387.
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")
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.
lavTablesFitCf(object) lavTablesFitCp(object, alpha = 0.05) lavTablesFitCm(object)lavTablesFitCf(object) lavTablesFitCp(object, alpha = 0.05) lavTablesFitCm(object)
object |
An object of class |
alpha |
The nominal level of signifiance of global fit. |
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 cancels 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 hypothesis can not be tested.
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.
# 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)
Compute a variety of test statistics evaluating the global fit of the model.
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)
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 |
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.
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")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")
LRT test for comparing (nested) lavaan models.
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, ...)
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. |
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 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 calculated when fitting your model(s), use
lavInspect(fit, "options")$test.
If type = "Chisq" and the test statistics are scaled, a
special scaled difference test statistic is computed. If method is
"satorra.bentler.2001", a simple approximation is used
described in Satorra & Bentler (2001). In some settings,
this can lead to a negative test statistic. To ensure a positive
test statistic, we can use the method proposed by
Satorra & Bentler (2010). Alternatively, when method="satorra.2000",
the original formulas of Satorra (2000) are used. The latter is used for
model comparison, when ... contain additional (nested) models.
Even when test statistics are scaled in object or ...,
users may request the method="standard" test statistic,
without a robust adjustment.
An object of class anova. When given a single argument, it simply returns the test statistic of this model. When given a sequence of objects, this function tests the models against one another, after reordering the models according to their degrees of freedom.
If there is a lavaan model stored in
object@external$h1.model, it will be added to ...
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 postiveness of the scaled difference chi-square test statistic. Psychometrika, 75(2), 243-248. doi:10.1007/s11336-009-9135-y
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"))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"))
Score test (or Lagrange Multiplier test) for releasing one or more fixed or constrained parameters in model.
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")
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 of the equality constraints as they 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 |
|
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 can not
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.
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 the distribution (p.value).
$uni: Optional (if univariate=TRUE).
Each 1-df score test, equivalent to modification indices.
If epc=TRUE when adding parameters (not when releasing
constraints), an unstandardized EPC is provided for each added parameter,
as would be returned by modificationIndices.
$cumulative: Optional (if cumulative=TRUE).
Cumulative score tests.
$epc: Optional (if epc=TRUE). Parameter estimates,
expected parameter changes, and expected parameter values if all
the tested constraints were freed.
Bentler, P. M., & Chou, C. P. (1993). Some new covariance structure model improvement statistics. Sage Focus Editions, 154, 235-255.
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 for testing a linear hypothesis about the parameters of fitted lavaan object.
lavTestWald(object, constraints = NULL, verbose = FALSE)lavTestWald(object, constraints = NULL, verbose = FALSE)
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 |
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.
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).
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 lavaan model syntax describes a latent variable model. The
function lavaanify turns it into a table that represents the full
model as specified by the user. We refer to this table as the parameter table.
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, effect.coding = "", conditional.x = FALSE, fixed.x = FALSE, parameterization = "delta", constraints = NULL, ceq.simple = FALSE, auto = FALSE, model.type = "sem", auto.fix.first = FALSE, 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, varTable = 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, effect.coding = "", conditional.x = FALSE, fixed.x = FALSE, parameterization = "delta", constraints = NULL, ceq.simple = FALSE, auto = FALSE, model.type = "sem", auto.fix.first = FALSE, 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, varTable = 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 = "new", 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, effect.coding = "", conditional.x = FALSE, fixed.x = FALSE, parameterization = "delta", constraints = NULL, ceq.simple = FALSE, auto = FALSE, model.type = "sem", auto.fix.first = FALSE, 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, varTable = 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, effect.coding = "", conditional.x = FALSE, fixed.x = FALSE, parameterization = "delta", constraints = NULL, ceq.simple = FALSE, auto = FALSE, model.type = "sem", auto.fix.first = FALSE, 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, varTable = 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 = "new", warn = TRUE, debug = FALSE)
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 |
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 |
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 |
varTable |
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 |
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. formative factors
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. 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. On the right is
only the number "1" representing the intercept. Including an intercept
formula in the model automatically implies meanstructure = 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 sided, separated by the "+" operator,
are named "t1", "t2", etcetera.
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.
Formative factors: The "<~" operator can be used to define
a formative factor (on the right hand side of the operator), in a
similar way to how a reflexive factor is defined (using the "=~"
operator). This is just syntax sugar to define a phantom latent
variable (equivalent to using "f =~ 0"). And in addition, the
(residual) variance of the formative factor is fixed to zero.
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 are 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.
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 constaint. 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.
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.
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 its 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 "~").
To constrain a parameter
to be equal to another target parameter, there are two ways. 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
'
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.
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
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 much the same way, using the < or >
operator indicate which estimated parameter is hypothesized to be greater/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
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
'
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
Given a fitted lavaan object, compute the modification indices (= univariate score tests) for a selected set of fixed-to-zero parameters.
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), 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), 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), 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), free.remove = TRUE, na.remove = TRUE, op = NULL)
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 using the values of the modification index values. Higher values appear first. |
minimum.value |
Numeric. Filter output and only show rows with a modification index value equal or higher than this minimum value. |
maximum.number |
Integer. Filter output and only show the first
maximum number rows. Most useful when combined with the |
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 |
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 would refit the model but allow this parameter to
be 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.
A data.frame containing modification indices and EPC's.
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)
Read in an Mplus input file, convert it to lavaan syntax, and fit the model.
mplus2lavaan(inpfile, run = TRUE)mplus2lavaan(inpfile, run = TRUE)
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 ( |
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.
Michael Hallquist
## Not run: out <- mplus2lavaan("ex5.1.inp") summary(out) ## End(Not run)## Not run: out <- mplus2lavaan("ex5.1.inp") summary(out) ## End(Not run)
Converts Mplus model syntax into lavaan model syntax.
mplus2lavaan.modelSyntax(syntax)mplus2lavaan.modelSyntax(syntax)
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 |
A character string of converted lavaan model syntax.
Michael Hallquist
## Not run: syntax <- ' f1 BY x1*1 x2 x3; x1 WITH x2; x3 (1); x2 (1); ' lavSyntax <- mplus2lavaan.modelSyntax(syntax) cat(lavSyntax) ## End(Not run)## Not run: syntax <- ' f1 BY x1*1 x2 x3; x1 WITH x2; x3 (1); x2 (1); ' lavSyntax <- mplus2lavaan.modelSyntax(syntax) cat(lavSyntax) ## End(Not run)
Parameter estimates of a latent variable model.
parameterEstimates(object, se = TRUE, zstat = TRUE, pvalue = TRUE, ci = TRUE, standardized = FALSE, fmi = 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, add.attributes = FALSE, output = "data.frame", header = FALSE)parameterEstimates(object, se = TRUE, zstat = TRUE, pvalue = TRUE, ci = TRUE, standardized = FALSE, fmi = 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, add.attributes = FALSE, output = "data.frame", header = FALSE)
object |
An object of class |
se |
Logical. If |
zstat |
Logical. If |
pvalue |
Logical. If |
ci |
If |
level |
The confidence level required. |
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 |
rsquare |
Logical. If |
add.attributes |
Deprecated argument. Please use output= instead. |
output |
Character. If |
header |
Logical. Only used if |
A data.frame containing the estimated parameters, 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.
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.
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) parameterEstimates(fit) parameterEstimates(fit, output = "text")HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data=HolzingerSwineford1939) parameterEstimates(fit) parameterEstimates(fit, output = "text")
Show the parameter table of a fitted model.
parameterTable(object) parTable(object)parameterTable(object) parTable(object)
object |
An object of class |
A data.frame containing the model parameters. This is
simply the output of the lavaanify function
coerced to a data.frame (with stringsAsFactors = FALSE).
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)
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.
data(PoliticalDemocracy)data(PoliticalDemocracy)
A data frame of 75 observations of 11 variables.
y1Expert ratings of the freedom of the press in 1960
y2The freedom of political opposition in 1960
y3The fairness of elections in 1960
y4The effectiveness of the elected legislature in 1960
y5Expert ratings of the freedom of the press in 1965
y6The freedom of political opposition in 1965
y7The fairness of elections in 1965
y8The effectiveness of the elected legislature in 1965
x1The gross national product (GNP) per capita in 1960
x2The inanimate energy consumption per capita in 1960
x3The percentage of the labor force in industry in 1960
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.
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.
head(PoliticalDemocracy)head(PoliticalDemocracy)
Fit a Structural Equation Model (SEM) using the Structural After Measurement (SAM) approach.
sam(model = NULL, data = 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(), output = "lavaan")sam(model = NULL, data = 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(), output = "lavaan")
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. |
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 additional options can be defined, 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). |
output |
Character. If |
The sam function tries to automate the SAM approach, by first
estimating the measurement part of the model,
and then the structural part of the model. See reference for more
details.
Note that in the current implementation, all indicators of latent variables have to be observed. This implies: no support for second-order factor structures (for now).
If output = "lavaan", an object of class
lavaan, for which several methods
are available, including a summary method. If output = "list",
a list.
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
## 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 a Structural Equation Model (SEM).
sem(model = NULL, data = NULL, ordered = 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, 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", ...)
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.) |
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 additional options can be defined, using 'name = value'.
See |
The sem function is a wrapper for the more general
lavaan function, but setting the following default options:
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.
An object of class lavaan, for which several methods
are available, including a summary method.
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
## 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)
Simulate data starting from a lavaan model syntax.
simulateData(model = NULL, model.type = "sem", meanstructure = FALSE, int.ov.free = TRUE, int.lv.free = FALSE, marker.int.zero = FALSE, conditional.x = FALSE, 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 = paste("G", 1:ngroups, sep = ""), skewness = NULL, kurtosis = NULL, seed = NULL, empirical = FALSE, 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, 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 = paste("G", 1:ngroups, sep = ""), skewness = NULL, kurtosis = NULL, seed = NULL, empirical = FALSE, return.type = "data.frame", return.fit = FALSE, debug = FALSE, standardized = FALSE)
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 |
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. |
seed |
Set random seed. |
empirical |
Logical. If |
return.type |
If |
return.fit |
If |
debug |
If |
standardized |
If |
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 unity by default. 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.
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").
# 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 <- simulateData(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 <- simulateData(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)
Standardized solution of a latent variable model.
standardizedSolution(object, type = "std.all", se = TRUE, zstat = TRUE, pvalue = TRUE, ci = TRUE, level = 0.95, cov.std = TRUE, remove.eq = TRUE, remove.ineq = TRUE, remove.def = FALSE, 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, cov.std = TRUE, remove.eq = TRUE, remove.ineq = TRUE, remove.def = FALSE, partable = NULL, GLIST = NULL, est = NULL, output = "data.frame")
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. |
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 ouitput by removing all rows containing parameter definitions, if any. |
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 extract from object. Only works if the |
partable |
A custom |
output |
Character. If |
A data.frame containing standardized model parameters.
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.
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)
S3 summary and print methods for class efaList.
## S3 method for class '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, ...) ## S3 method for class 'efaList.summary' print(x, nd = 3L, cutoff = 0.3, dot.cutoff = 0.1, alpha.level = 0.01, ...)## S3 method for class '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, ...) ## S3 method for class 'efaList.summary' print(x, nd = 3L, cutoff = 0.3, dot.cutoff = 0.1, alpha.level = 0.01, ...)
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 that 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 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. |
The function summary.efaList computes and returns a list of
summary statistics for the list of EFA models in object.
## The famous Holzinger and Swineford (1939) example fit <- efa(data = HolzingerSwineford1939, ov.names = paste("x", 1:9, sep = ""), nfactors = 1:3, rotation = "geomin", rotation.args = list(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 = "geomin", rotation.args = list(geomin.epsilon = 0.01, rstarts = 1)) summary(fit, nd = 3L, cutoff = 0.2, dot.cutoff = 0.05, lambda.structure = TRUE, pvalue = TRUE)
Summary information about the variables included in either a data.frame, or a fitted lavaan object.
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)
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. |
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.
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)