icrfP {lazy.irt}

R Documentation

Calculation of Item Response Function of Partial Credit Items

Description

Calculation of Item Response Function of Partial Credit Items

Usage

icrfP(paramP, theta, DinP = 1, smallP = 0, print = 0, plot = 0, debug = 0)

Arguments

paramP	Item Parameter Data Frame of Partial Credit Items
theta	Discrete theta values
DinP	= 1 to include D=1.7 in logistic function
smallP	Minimum value of probability
print	= 1 to print result
plot	= 1 to plot result
debug	= 1 to print intemediate result

Details

An Example of Item Parameter datastet: maxncat = 5
Note that the subscript of the b-parameter ranges between
1 and ncat-1 (= maxscore) (We set c0=0.)

ncat A b1 b2 b3 b4

Item3 3 1.5 -1.0 0.0 . .
Item4 4 1.5 -1.0 0.0 1.0 .
Item5 5 1.5 -1.0 0.0 1.0 2.0

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
Ez_{jk}(theta) = exp( 1.7^DinP a*_j k (theta - sum_{h=0}^k b*_{jh}) )
= exp( 1.7^DinP a*_j k (theta - sum_{h=1}^k b*_{jh}) )
, k=0,1, ..., ncat[j]-1
with b*_{j0}=0.

This b*_{jk} is the original step parameter and it is
the value of theta where P_{jk-1} and P_{jk} intersect.

Value

A list of:
P length(theta) x sum(ncat) icrf matrix
PP length(theta) x sum(ncat) icbf matrix
Pt length(theta) x nitems item response function

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