iif {irtoys}

Item information function

Description

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

I(\theta) = a^2\frac{Q(\theta)}{P(\theta)}\left[\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.

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 (\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.

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))