No abstract

Descriptions are presented of two related probabilistic models that can be used for making classification decisions with respect to mastery of specific concepts or skills. Included are the development of procedures for: (a) assessing the adequacy of “fit” provided by the models; (b) identifying optimal decision rules for mastery classification; and (c) identifying minimally sufficient numbers of items necessary to obtain acceptable levels of misclassification.

Loglinear latent class models are used to detect differential item functioning (DIF). These models are formulated in such a manner that the attribute to be assessed may be continuous, as in a Rasch model, or categorical, as in Latent Class Mastery models. Further, an item may exhibit DIF with respect to a manifest grouping variable, a latent grouping variable, or both. Likelihood‐ratio tests for assessing the presence of various types of DIF are described, and these methods are illustrated through the analysis of a “real world” data set.