Testing the unidimensionality assumption of the Rasch model

Statistical tests especially designed to test the unidimensionality axiom of the Rasch model are scarce. For two of them, the Martin-Löf test (ML-test) and the splitter-item- technique, an extensive power analysis has been carried out, showing clearly the superiority of the ML-test. The disadvantage of the ML-test, however, is that its null distribution deviates strongly from the asymptotic chi-square distribution unless one has huge samples. A new test with one degree of freedom is proposed. Its power is superior to that of the ML-test, and its null distribution converges rapidly to the chi-square.