IRT.linearCFA: Linear Approximation of a Confirmatory Factor Analysis

Description

This function approximates a fitted item response model by a linear confirmatory factor analysis. I.e., given item response functions, the expectation $E(X_i | \theta_1 , \ldots , \theta_D)$ is linearly approximated by $a_{i1} \theta _1 + \ldots + a_{iD} \theta_D$. See Vermunt and Magidson (2005) for details.

Usage

IRT.linearCFA( object , group=1)
	
"summary"(object,  ...)

Arguments

object

Fitted item response model for which the IRT.expectedCounts method is defined.

group

Group identifier which defines the selected group.

...

Further arguments to be passed.

Value

loadings: Data frame with factor loadings. Mlat and SDlat denote the model-implied item mean and standard deviation. The values ResidVar and h2 denote residual variances and item communality.
stand.loadings: Data frame with standardized factor loadings.
M.trait: Mean of factors
SD.trait: Standard deviations of factors

References

Vermunt, J. K., & Magidson, J. (2005). Factor Analysis with categorical indicators: A comparison between traditional and latent class approaches. In A. Van der Ark, M.A. Croon & K. Sijtsma (Eds.), New Developments in Categorical Data Analysis for the Social and Behavioral Sciences (pp. 41-62). Mahwah: Erlbaum

Examples

Run this code

## Not run: 
# library(lavaan)	
# 	
# #############################################################################
# # EXAMPLE 1: Two-dimensional confirmatory factor analysis data.Students
# #############################################################################
# 
# data(data.Students, package="CDM")
# # select variables
# vars <- scan(nlines=1 , what="character")
#     sc1 sc2 sc3 sc4 mj1 mj2 mj3 mj4
# dat <- data.Students[ , vars]
# 
# # define Q-matrix
# Q <- matrix( 0 , nrow=8 , ncol=2 )
# Q[1:4,1] <- Q[5:8,2] <- 1
# 
# #*** Model 1: Two-dimensional 2PL model
# mod1 <- tam.mml.2pl( dat , Q=Q  , control=list( nodes=seq(-4,4,len=12) ) )
# summary(mod1)
# 
# # linear approximation CFA
# cfa1 <- IRT.linearCFA(mod1)
# summary(cfa1)
# 
# # linear CFA in lavaan package
# lavmodel <- "
#     sc =~ sc1+sc2+sc3+sc4
#     mj =~ mj1+mj2+mj3+mj4
#     sc1 ~ 1
#     sc ~~ mj
#     "
# mod1b <- lavaan::sem( lavmodel , data = dat , missing="fiml" , std.lv=TRUE)    
# summary(mod1b , standardized=TRUE , fit.measures=TRUE )
# 
# #############################################################################
# # EXAMPLE 2: Unidimensional confirmatory factor analysis data.Students
# #############################################################################
# 
# data(data.Students, package="CDM")
# # select variables
# vars <- scan(nlines=1 , what="character")
#     sc1 sc2 sc3 sc4
# dat <- data.Students[ , vars]
# 
# #*** Model 1: 2PL model
# mod1 <- tam.mml.2pl( dat )
# summary(mod1)
# 
# # linear approximation CFA
# cfa1 <- IRT.linearCFA(mod1)
# summary(cfa1)
# 
# # linear CFA
# lavmodel <- "
#     sc =~ sc1+sc2+sc3+sc4
#     "
# mod1b <- lavaan::sem( lavmodel , data = dat , missing="fiml" , std.lv=TRUE)    
# summary(mod1b , standardized=TRUE , fit.measures=TRUE )
# ## End(Not run)