Loglinear Rasch model tests

Abstract

Existing statistical tests for the fit of the Rasch model have been criticized, because they are only sensitive to specific violations of its assumptions. Contingency table methods using loglinear models have been used to test various psychometric models. In this paper, the assumptions of the Rasch model are discussed and the Rasch model is reformulated as a quasi-independence model. The model is a quasi-loglinear model for the incomplete subgroup × score × item 1 × item 2 × ... × item k contingency table. Using ordinary contingency table methods the Rasch model can be tested generally or against less restrictive quasi-loglinear models to investigate specific violations of its assumptions. © 1984 The Psychometric Society.