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.
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