Tests of Fit for Polytomous Rasch Models

Abstract

In this chapter, a number of the tests of model fit for the Rasch model for dichotomous items presented in Chapter 5 are generalized to a class of IRT models for polytomous items. Again, the problem of evaluating model fit is solved in the framework of the general multinomial model, and it is shown that the four types of tests considered in Chapter 5 — generalized Pearson tests, likelihood ratio tests, Wald tests, and Lagrange multiplier tests can — all be adapted to the framework of polytomous items. Apart from providing global measures of overall model fit, test statistics must also provide information with respect to specific model violations. The last section of this chapter gives an example of a testing procedure focussing on the model violation of item bias or differential item functioning.