TAM: IRTLikelihood.cfa – R documentation

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IRTLikelihood.cfa

Individual Likelihood for Confirmatory Factor Analysis

Description

This function computes the individual likelihood evaluated at a theta grid for confirmatory factor analysis under the normality assumption of residuals. Either the item parameters (item loadings L, item intercepts nu and residual covariances psi) or a fitted cfa object from the lavaan package can be provided. The individual likelihood can be used for drawing plausible values.

Usage

IRTLikelihood.cfa(data, cfaobj=NULL, theta=NULL, L=NULL, nu=NULL,
    psi=NULL, snodes=NULL, snodes.adj=2, version=1)

Arguments

`data`	Dataset with item responses
`cfaobj`	Fitted `lavaan::cfa` (lavaan) object
`theta`	Optional matrix containing the `theta` values used for evaluating the individual likelihood
`L`	Matrix of item loadings (if `cfaobj` is not provided)
`nu`	Vector of item intercepts (if `cfaobj` is not provided)
`psi`	Matrix with residual covariances (if `cfaobj` is not provided)
`snodes`	Number of `theta` values used for the approximation of the distribution of latent variables.
`snodes.adj`	Adjustment factor for quasi monte carlo nodes for more than two latent variables.
`version`	Function version. `version=1` is based on a Rcpp implementation while `version=0` is a pure R implementation.

Value

Individual likelihood evaluated at theta

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Two-dimensional CFA data.Students
#############################################################################

library(lavaan)
library(CDM)

data(data.Students, package="CDM")
dat <- data.Students

dat2 <- dat[, c(paste0("mj",1:4), paste0("sc",1:4)) ]
# lavaan model with DO operator
lavmodel <- "
DO(1,4,1)
   mj=~ mj%
   sc=~ sc%
DOEND
   mj ~~ sc
   mj ~~ 1*mj
   sc ~~ 1*sc
     "
lavmodel <- TAM::lavaanify.IRT( lavmodel, data=dat2 )$lavaan.syntax
cat(lavmodel)

mod4 <- lavaan::cfa( lavmodel, data=dat2, std.lv=TRUE )
summary(mod4, standardized=TRUE, rsquare=TRUE )
# extract item parameters
res4 <- TAM::cfa.extract.itempars( mod4 )
# create theta grid
theta0 <- seq( -6, 6, len=15)
theta <- expand.grid( theta0, theta0 )
L <- res4$L
nu <- res4$nu
psi <- res4$psi
data <- dat2
# evaluate likelihood using item parameters
like2 <- TAM::IRTLikelihood.cfa( data=dat2, theta=theta, L=L, nu=nu, psi=psi )
# The likelihood can also be obtained by direct evaluation
# of the fitted cfa object "mod4"
like4 <- TAM::IRTLikelihood.cfa( data=dat2, cfaobj=mod4 )
attr( like4, "theta")
# the theta grid is automatically created if theta is not
# supplied as an argument

## End(Not run)

TAM

Test Analysis Modules

v3.6-45

GPL (>= 2)

Authors

Alexander Robitzsch [aut,cre] (<https://orcid.org/0000-0002-8226-3132>), Thomas Kiefer [aut], Margaret Wu [aut]

Initial release

2021-04-22 14:35:52