A Hierarchical IRT Model for Criterion-Referenced Measurement

Abstract

A hierarchical IRT model is proposed for mastery classification in criterion-referenced measurement. In this model, items measuring the same criterion are grouped, and a difficulty and discrimination parameter of the criterion is estimated on the same scale as the person and item parameters. The level of proficiency of a student with respect to the criterion is determined by the probability of success on the criterion. Cutoff points on the probability scale can be used to classify respondents into masters and nonmasters. The hierarchical IRT model is estimated using the Gibbs sampler and tested using posterior predictive checks. The model is illustrated with a test measuring the attainment targets of reading comprehension (in Dutch) at the end of primary education.