A Mixture Item Response Model for Multiple-Choice Data

Abstract

A mixture item response model is proposed for investigating individual differences in the selection of response categories in multiple-choice items. The model accounts for local dependence among response categories by assuming that examinees belong to discrete latent classes that have different propensities towards those responses. Varying response category propensities are captured by allowing the category intercept parameters in a nominal response model ( Bock, 1972 ) to assume different values across classes. A Markov Chain Monte Carlo algorithm for the estimation of model parameters and classification of examinees is described. A real-data example illustrates how the model can be used to distinguish examinees that are disproportionately attracted to different types of distractors in a test of English usage. A simulation study evaluates item parameter recovery and classification accuracy in a hypothetical multiple-choice test designed to be diagnostic. Implications for test construction and the use of multiple-choice tests to perform cognitive diagnoses of item response patterns are discussed.