A new approach for testing the Rasch model

Though calibration of an achievement test within psychological and educational context is very often carried out by the Rasch model, data sampling is hardly designed according to statistical foundations. However, Kubinger, Rasch, and Yanagida (2009) recently suggested an approach for the determination of sample size according to a given Type I and Type II risk, and a certain effect of model misfit when testing the Rasch model is supported by some new results. The approach uses a three-way analysis of variance design with mixed classification. There is a (fixed) group factor A, a (random) factor B of testees within A, and a (fixed) factor C of items cross-classified with. The simulation study in this article deals with further item parameter ranges and ability parameter distributions, and with larger sample sizes and item numbers than the original paper. The results are: The approach works given several restrictions, and its main aim, the determination of the sample size, is attained.