convP2N {lazy.irt}

R Documentation

Convert Partial Credit Item Parameters in Standard Format (step parameters) to Nominal Format

Description

Convert Partial Credit Item Parameters in Standard Format (step parameters) to Nominal Format

Usage

convP2N(param, print = 0, DinP = 1)

Arguments

param	Item Parameter Data Frame for Partial Credit Items
print	= 1 to print result
DinP	= 1 to include D=1.7 in logistic function

Details

ICRF of category k of item j at theta, namely, p_{jk}(\theta)
is defined as
p_{jk}(\theta) = Ez_{jk}(\theta) / \sum_{k=0}^{ncat[j]-1} Ez_{jk}(theta)
where

if type = "P" ,
Ez_{jk}(\theta) = exp( 1.7^{DinP} \sum_{h=0}^k a*_j \; (\theta - b*_{jh}) )
, k=0,1, ..., ncat[j]-1
where b*_{jk} is the step parameter with b*_{0j}=0.

if type = "PN" and ctype=0,
Ez_{jk}(\theta) = exp( 1.7^{DinP} a_j \; k (\theta - b_{jk}) )
, k=0,1, ..., ncat[j]-1
with b_{j0}=0.

if type = "PN" and ctype=1,
Ez_{jk}(\theta) = exp( a_j k \theta + c_{jk}) )
, k=0,1, ..., ncat[j]-1
with c_{j0}=0.

Note that if DinP=1, 1.7 will be used.

The step parameter, b*_{jk}, is the value of theta where P_{jk-1}(\theta) and P_{jk}(\theta) intersect.

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