Although differential item functioning (DIF) theory traditionally focuses on the behavior of individual items in two (or a few) specific groups, in educational measurement contexts, it is often plausible to regard the set of items as a random sample from a broader category. This article presents logistic mixed models that can be used to model…

In IRT models, responses are explained on the basis of person and item effects. Person effects are usually defined as a random sample from a population distribution. Regular IRT models therefore can be formulated as multilevel models, including a within-person part and a between-person part. In a similar way, the effects of the items can be…

Presents a fully Bayesian analysis for the Probability Matrix Decomposition (PMD) model using the Gibbs sampler. Identifies the advantages of this approach and illustrates the approach by applying the PMD model to opinions of respondents from different countries concerning the possibility of contracting AIDS in a specific situation. (SLD)

Proposes a hierarchical item response theory (IRT) model for mastery classification in criterion-referenced measurement. In this model, items measuring the same criterion are grouped, and a difficulty and discrimination parameter for the criterion is estimated on the same scale as the person and item parameters. Illustrates the model with a test…