Goodness of Fit Test and Latent Distribution Estimation in the Mixed Rasch Model

The Cramér-von Mises test methodology is applied to build a goodness-of fit test for the mixed Rasch model. The Mixed Rasch Model is a probability model of a multivariate discrete random variable driven by an unknown latent continuous variable. The problem of estimation of the unknown fixed difficulty parameters and the latent density function is also considered. The theoretical results are illustrated through simulations and an application to real Quality of Life data.