Item information and discrimination functions for trinary pcm items

Abstract

For trinary partial credit items the shape of the item information and the item discrimination function is examined in relation to the item parameters. In particular, it is shown that these functions are unimodal if δ2 – δ1 < 4 ln 2 and bimodal otherwise. The locations and values of the maxima are derived. Furthermore, it is demonstrated that the value of the maximum is decreasing in δ2 – δ1. Consequently, the maximum of a unimodal item information function is always larger than the maximum of a bimodal one, and similarly for the item discrimination function.