Conversion of the Parameterization of the Partial Credit Model
Converts a parameterization of the partial credit model (see Details).
pcm.conversion(b)
b |
Matrix of item-category-wise intercepts b_{ik} (see Details). |
Assume that the input matrix b containing parameters b_{ik}
is defined according to the following parametrization of the partial credit
model
P( X_{pi}=k | θ_p ) \propto exp ( k θ_p - b_{ik} )
if item i possesses K_i categories. The transformed parameterization is defined as
b_{ik}=k δ_i + ∑_{v=1}^{k} τ_{iv} \quad \mbox{with} \quad ∑_{k=1}^{K_i} τ_{ik}=0
The function pcm.conversion has the δ and τ
parameters as values. The δ parameter is simply
δ_i=b_{iK_i} / K_i.
List with the following entries
delta |
Vector of δ parameters |
tau |
Matrix of τ parameters |
## Not run:
#############################################################################
# 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
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