# IRTLikelihood.ctt: Computes Individual Likelihood from Classical Test Theory... In TAM: Test Analysis Modules

 IRTLikelihood.ctt R Documentation

## Computes Individual Likelihood from Classical Test Theory Estimates

### Description

Computes individual likelihood from classical test theory estimates under a unidimensional normal distribution of measurement errors.

### Usage

IRTLikelihood.ctt(y, errvar, theta=NULL)


### Arguments

 y Vector of observed scores errvar Vector of error variances theta Optional vector for \theta grid.

### Value

Object of class IRT.likelihood

### Examples

#############################################################################
# EXAMPLE 1: Individual likelihood and latent regression in CTT
#############################################################################

set.seed(75)

#--- simulate data
N <- 2000
x1 <- stats::rnorm(N)
x2 <- .7 * x1 + stats::runif(N)
# simulate true score
theta <- 1.2 + .6*x1 + .3 *x2 + stats::rnorm(N, sd=sqrt(.50) )
var(theta)
# simulate measurement error variances
errvar <- stats::runif( N, min=.6, max=.9 )
# simulate observed scores
y <- theta + stats::rnorm( N, sd=sqrt( errvar) )

#--- create likelihood object
like1 <- TAM::IRTLikelihood.ctt( y=y, errvar=errvar, theta=NULL )

#--- estimate latent regression
X <- data.frame(x1,x2)
mod1 <- TAM::tam.latreg( like=like1, Y=X )

## Not run:
#--- draw plausible values
pv1 <- TAM::tam.pv( mod1, normal.approx=TRUE )

#--- create datalist
datlist1 <- TAM::tampv2datalist( pv1, pvnames="thetaPV", Y=X )

#--- statistical inference on plausible values using mitools package
library(mitools)
datlist1a <- mitools::imputationList(datlist1)

# fit linear regression and apply Rubin formulas
mod2 <- with( datlist1a, stats::lm( thetaPV ~ x1 + x2 ) )
summary( mitools::MIcombine(mod2) )

## End(Not run)


TAM documentation built on May 29, 2024, 2:20 a.m.