The IRT Procedure

Item and Test information

Let $P_{jk}(\theta )$ be the probability of endorsing category k for item j for a subject whose ability score is $\theta $. Then the item information function can be defined as

\[ I_ j(\theta ) = \sum _{k=1}^{K} I_ k(\theta ) P_{jk}(\theta ) \]

where

\[ I_ k(\theta ) = -\frac{\partial ^2}{\partial \theta ^2}\log P_{jk}(\theta ) \]

The test information function is the sum of the information functions of the items in the test. The information function of a test that has J items is

\[ I(\theta ) = \sum _{j=1}^{J} I_ j(\theta ) \]