irtoys (version 0.2.2)

iif: 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 $a^{2}PQ$.

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.

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

Details

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

See Also

plot.iif, irf

Examples

# NOT RUN {
plot(iif(Scored2pl, items=1:3))

# }