Applying the Rasch sampler to identify aberrant responding through person fit statistics under fixed nominal α-level

Testing hypotheses on a respondent's individual fit under the Rasch model requires knowledge of the distributional properties of a person fit statistic. We argue that the Rasch Sampler (Verhelst, 2008), a Markov chain Monte Carlo algorithm for sampling binary data matrices from a uniform distribution, can be applied for simulating the distribution of person fit statistics with the Rasch model in the same way as it used to test for other forms of misfit. Results from two simulation studies are presented which compare the approach to the original person fit statistics based on normalization formulas. Simulation 1 shows the new approach to hold the expected Type I error rates while the normalized statistics deviate from the nominal alpha-level. In Simulation 2 the power of the new approach was found to be approximately the same or higher than for the normalized statistics under most conditions.