AMonte Carlo Approach to Unidimensionality Testing in Polytomous RaschModels

Many statistical tests are designed to test the different assumptions of the Rasch model, but only few are directed at detecting multidimensionality. The Martin-Löf test is an attractive approach, the disadvantage being that its null distribution deviates strongly from the asymptotic chi-square distribution for most realistic sample sizes. A Monte Carlo test approach to p value computation is proposed and is shown to yield a powerful test. Repeated and sequential Monte Carlo tests that can greatly reduce computing time are discussed. Index terms: Rasch models, unidimensionality, Martin-Löf test, Monte Carlo tests, sequential tests