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

[Package lazy.irt version 0.1.3 Index]