iif: Item information function

In irtoys: A Collection of Functions Related to Item Response Theory (IRT)

Item information function

Description

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

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

where θ 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.

Usage

iif(ip, items = NULL, x = NULL)

Arguments

ip	Item parameters: the output of est, or a 3-column matrix corresponding to its first element, est.
items	The item(s) for which the information function is computed. If NULL (the default), irf for all items will be returned
x	The values of the latent variable (θ 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.

Details

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

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

plot(iif(Scored2pl, items=1:3))

irtoys documentation built on May 12, 2022, 5:06 p.m.