Multinomial and Compound Multinomial Error Models for Tests With Complex Item Scoring

Abstract

This article introduces a multinomial error model, which models an examinee's test scores obtained over repeated measurements of an assessment that consists of polytomously scored items. A compound multinomial error model is also introduced for situations in which items are stratified according to content categories and/or prespecified numbers of score points. The multinomial and compound multinomial models are implemented in this article for estimating conditional standard errors of measurement and reliability. The applicability of the multinomial and compound multinomial models is illustrated with two real data examples. The first example considers test scores obtained from polytomous items only, and the second example contains test scores from a mixture of dichotomous and polytomous items. A simulation study is conducted to examine the amount and pattern of bias in the estimated conditional standard errors of measurement. Index terms: multinomial model, compound multinomial model, standard errors of measurement, reliability, scale scores