The IRT Procedure

Item and Test information

Let upper P Subscript j k Baseline left-parenthesis theta right-parenthesis 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

upper I Subscript j Baseline left-parenthesis theta right-parenthesis equals sigma-summation Underscript k equals 1 Overscript upper K Endscripts upper I Subscript k Baseline left-parenthesis theta right-parenthesis upper P Subscript j k Baseline left-parenthesis theta right-parenthesis

where

upper I Subscript k Baseline left-parenthesis theta right-parenthesis equals minus StartFraction partial-differential squared Over partial-differential theta squared EndFraction log upper P Subscript j k Baseline left-parenthesis theta right-parenthesis

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

upper I left-parenthesis theta right-parenthesis equals sigma-summation Underscript j equals 1 Overscript upper J Endscripts upper I Subscript j Baseline left-parenthesis theta right-parenthesis
Last updated: December 09, 2022