iif function

Item information function

The item information function (IIF) for the 3PL model can be computed as [REMOVE_ME]$I(\theta) =a^2\frac{Q(\theta)}{P(\theta)}\left[\frac{P(\theta)-c}{1-c}\right]^2, [REMOVE_ME_2]$ 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 $a^2PQ$.

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.

Returns

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

Description

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

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 $a^2PQ$.

Details

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

Examples

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

See Also

plot.iif, irf

Author(s)

Ivailo Partchev