A Connection between Rasch's Item Analysis Model and a Multiplicative Poisson Model

Abstract

Introduction of random row in Rasch's item analysis model (or the two-way logit-additive model for binary data), followed by a (not very controversial) extension of this model leads to a model which is shown to be equivalent to a conditional multiplicative Poisson model. This result gives some new insight in the structure of Rasch's model and suggests some goodness of fit tests which are applicable also to the original fixed effects Rasch model.