convP2PN {lazy.irt}

R Documentation

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

Description

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

Usage

convP2PN(param, print = 0, DinP = 1, ctype = 0)

Arguments

param	Item Parameter Data Frame
print	= 1 to print result
DinP	= 1 to include D=1.7 in logistic function
ctype	= 1 to convert to type PN with c-parameters

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.

Value

Partial Credit Item Parameter Data Frame in Nominal Format

Examples

temp <- irf( paramS1[4,], plot=1 )
temp <- irf( convP2PN(paramS1[4,]), plot=1 )

temp1 <- convP2PN(paramS1[4,])
temp2 <- convPN2P(temp1)
Print(paramS1[4,],temp1,temp2)

temp1 <- convP2PN(paramS1[4,], ctype=1)
temp2 <- convPN2P(temp1, ctype=1)
Print(paramS1[4,],temp1,temp2)

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