iif {irtoys}R Documentation

Item information function

Description

The item information function (IIF) for the 3PL model can be computed as

I(theta) = a^2frac{Q(theta)}{P(theta)}<=ft[frac{P(theta)-c}{1-c}right]^2,

where theta is the value of the latent variable for a person, a is the discrimination parameter for the item, P is the IRF for the person and item, and Q=1-P. For the 1PL and 2PL models, the expression reduces to a^2PQ.

A common use of this function would be to obtain a plot of the IIF.

Usage

iif(ip, x = NULL)

Arguments

ip Item parameters: a matrix with one row per item, and three columns: [,1] item discrimination a, [,2] item difficulty b, and [,3] asymptote c.
x The values of the latent variable (theta in the equation above), at which the IIF will be evaluated. If not given, 99 values spaced evenly between -4 and +4 will be used, handy for plotting.

Value

A list of:

x A copy of the argument x
f A matrix containing the IIF values: persons (values of (x) as rows and items as columns

Author(s)

Ivailo Partchev

See Also

plot.iif, irf

Examples

data(Scored)
p.2pl  <- est(Scored, model="2PL", engine="ltm")
plot(iif(p.2pl[1:3,]))

[Package irtoys version 0.1.1 Index]