ABSTRACT
This chapter focuses on selected methods for estimating parameters used with the polytomous Rasch model. It shows that estimation is an area of active research by many psychometricians using advanced statistical methodologies. The chapter focuses on the most popular methods: maximum likelihood, weighted maximum likelihood, maxiumum a posteriori, and expected a posteriori estimators. Jr. George Engelhard described a variety of estimation methods for the dichotomous Rasch model. These methods can also be applied to the polytomous Rasch model for ratings. G. Rasch took the logs of the ratios of successes to failures on each test item, and then fit a linear model with no interactions to the item and score groups logits. Conditional maximum likelihood estimation takes full advantage of the invariance properties of Rasch Measurement Theory. The pairwise algorithm provides an elegant and effective approach for teaching the basic principles of Rasch Measurement Theory.
