sirt (version 1.5-0)

pcm.conversion: Conversion of the Parameterization of the Partial Credit Model

Description

Converts a parameterization of the partial credit model (see Details).

Usage

pcm.conversion(b)

Arguments

b

Matrix of item-category-wise intercepts $b_{ik}$ (see Details).

Value

• List with the following entries
• delta
  Vector of $\delta$ parameters
• tau
  Matrix of $\tau$ parameters

Details

Assume that the input matrix b containing parameters $b_{ik}$ is defined according to the following paramerization of the partial credit model $$P( X_{pi} = k | \theta_p ) \propto exp ( k \theta_p - b_{ik} )$$ if item $i$ possesses $K_i$ categories. The transformed parameterization is defined as $$b_{ik} = k \delta_i + \sum_{v=1}^{k} \tau_{iv} \quad \mbox{with} \quad \sum_{k=1}^{K_i} \tau_{ik} = 0$$ The function pcm.conversion has the $\delta$ and $\tau$ parameters as values. The $\delta$ parameter is simply $\delta_i = b_{iK_i} / K_i$.

Examples

#############################################################################
# EXAMPLE 1: Transformation PCM for data.mg
#############################################################################

library(CDM)
data(data.mg,package="CDM")
dat <- data.mg[ 1:1000 , paste0("I",1:11) ]

#*** Model 1: estimate partial credit model in parameterization "PCM"
mod1a <- TAM::tam.mml( dat , irtmodel="PCM")
# use parameterization "PCM2"
mod1b <- TAM::tam.mml( dat , irtmodel="PCM2")
summary(mod1a)
summary(mod1b)

# convert parameterization of Model 1a into parameterization of Model 1b
b <- mod1a$item[ , c("AXsi_.Cat1","AXsi_.Cat2","AXsi_.Cat3") ]
# compare results
pcm.conversion(b)
mod1b$xsi