Maximum Likelihood Estimation in Generalized Rasch Models

We review various models and techniques that have been proposed for item analysis according to the ideas of Rasch. A general model is proposed that unifies them, and maximum likelihood procedures are discussed for this general model. We show that unconditional maximum likelihood estimation in the functional Rasch model, as proposed by Wright and Haberman, is an important special case. Conditional maximum likelihood estimation, as proposed by Rasch and Andersen, is another important special case. Both procedures are related to marginal maximum likelihood estimation in the structural Rasch model, which has been studied by Sanathanan, Andersen, Tjur, Thissen, and others. Our theoretical results lead to suggestions for alternative computational algorithms.