A logistic mixture distribution model for polychotomous item responses

The polychotomous Rasch model is generalized to a mixture distribution model. It is assumed that the observed data are generated by two or more latent classes of individuals so that within each class the polychotomous Rasch model holds but with different parameters between the classes. Hence, the proposed model is also a generalization of latent class analysis which allows for quantitative individual differences within the classes. A parameter estimation procedure is outlined, employing conditional inference methods for the item parameters within classes and the EM‐algorithm for unmixing the data. The application of the model and control of model fit are illustrated by means of real data and simulated data.