Comparison of the Nonparametric Mokken Model and Parametric IRT Models Using Latent Class Analysis

Abstract

A nonparametric Mokken analysis of test data generally results in the rejection of different items as misfitting than an analysis with a parametric item response theory model. This is due to differences between the methods of analysis employed. Croon (1991) demonstrated that the assumption of "double monotony" of the nonparametric Mokken model can be tested with a latent class analysis using the EM procedure. This allows a comparison of the Mokken model of double monotony and parametric item response models within the same framework. The Mokken model was compared with parametric models using simulated data. It was demonstrated that latent class analysis provides a consistent comparison of item response models. Index terms: EM algorithm, item fit, item response theory, latent class analysis, model comparisons, Mokken model, Rasch model.