Rasch models in latent classes: An integration of two approaches to item analysis

Abstract

A model is proposed that combines the theoretical strength of the Rasch model with the heuristic power of latent class analysis. It assumes that the Rasch model holds for all persons within a latent class, but it allows for different sets of item parameters between the latent classes. An estimation algorithm is outlined that gives conditional maximum likelihood estimates of item parameters for each class. No a priori assumption about the item order in the latent classes or the class sizes is required. Application of the model is illustrated, both for simulated data and for real data. Index terms: conditional likelihood, EM algorithm, latent class analysis, Rasch model.