Testing the Rasch Model

Abstract

In this chapter, it is shown that the problem of evaluating model fit can be solved within the framework of the general multinomial model, and it is shown how tests for this framework can be adapted to the Rasch model. Four types of tests are considered: generalized Pearson tests, likelihood ratio tests, Wald tests, and likelihood ratio tests. The statistics presented not only support the purpose of a global overall model test, but also provide information with respect to specific model violations, such as violation of sufficiency of the sum score, strictly monotone increasing and parallel item response functions, unidimensionality, and differential item functioning.