Item Information

In Item Response Theory, Item Information quantifies the precision with which a given item measures a test-taker’s latent ability, $\theta$.

In Classical Test Theory, we assume that items are equally precise across all test-takers. In contrast, IRT measures precision as a function of ability. And item information tells you where along a continuum of ability a given item functions best (i.e. where it provides the most information).

Item Information is inversely related to standard error, i.e.

$$SE(\theta )=\frac{1}{\sqrt{I(\theta )}}$$

Item information is tied to the metric of $\theta$. This means that item information is directly comparable across items on the same scale. For instance, an item with $I(0)=1.0$ provides four times as much precision at $\theta =0$ as an item with $I(0)=0.25$.

Item information is also additive, so we can get test information by just summing all of the item information scores, i.e.:

$$I_{test}(\theta )=\sum _{i=1}^N{I}_i(\theta )$$

Because item information is additive, test information is directly comparable across tests. Test information is a function of both item quality and test length. A shorter test can outperform a longer test (i.e. provide more information) if its items have higher discrimination ($a$) parameters for a given $\theta$. One obvious corollary here is that this only applies to 2PL and 3PL items. Assuming items are equally-discriminating, longer tests will yield more test information.

Item Information Function

The Item Information Function is a curve that plots the item information across a range of values of $\theta$.