Loglinear Multivariate and Mixture Rasch Models

Abstract

In this chapter, Rasch models (RMs) are derived from a stochastic subject model. Fixed-effects RMs are shown to be equivalent to loglinear models with raw-score variables; random-effects RMs are equivalent to loglinear models with latent class variables. Within the larger framework of loglinear models, various extensions of the RM can be formulated. We discuss loglinear RMs for polytomous items, loglinear multidimensional RMs, RMs violating measurement invariance, mixture-distribution RMs, mixture-measurement RMs, RMs in which item responses are conditionally dependent, and RMs with latent responses. We also give some software scripts to compute ML estimates and fit statistics.