Derivations of the Rasch Model

Chapters 1 and 3 through 6 describe a number of especially attractive features of the Rasch model (RM). These assets - in particular, sufficiency of the unweighted raw score, existence of conditional maximum likelihood estimators of the model parameters and of conditional likelihood ratio tests for hypothesis testing - suggest the question as to whether they are shared by a larger class of IRT models, or whether they are, within a certain framework, unique properties of the RM. In the latter case, we would have to conclude that the RM plays a rather singular role within IRT. As we shall see, this is actually so. The derivations in this chapter lay a foundation both for the RM and for the metric scale properties of Rasch measurement.