irtoys (version 0.1.2)

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 $a^2PQ$. 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

See Also

plot.iif, irf

Examples

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