Individual Likelihood for Confirmatory Factor Analysis

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.

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

if (FALSE) {
#############################################################################
# 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
}