Nonparametric tests for the Rasch model: explanation, development, and application of quasi-exact tests for small samples

by Ingrid Koller and Reinhold Hatzinger.

Abstract: Psychological test validation by means of item response models is commonly carried out with large samples. However, in practice, the use of large samples is not always feasible, e.g., it is not possible to get large samples because of not enough people showing the construct of interest, and collecting new data would incur high costs. Therefore, it would be preferable to a priori analyze newly-developed items using small samples. Ponocny (2001) introduced quasi-exact tests for the Rasch model based on Monte-Carlo simulations in order to sample random matrices with identical margins compared to the observed matrix. These tests allow the investigation of the model fit even in small samples. In this paper we describe some tests of Ponocny and two newly-developed tests based on the simulation algorithm of Verhelst (2008). Theoretical foundations, practical recommendations and an empirical example are given. The present study underlines the usefulness of these nonparametric tests and demonstrates how new tailored methods for small samples applied to an examination of item quality can easily be developed.

Key Words: Rasch model, nonparametric test, quasi-exact test, model test, small samples

Authors:
Ingrid Koller, ingrid.koller@unvie.ac.at
Reinhold Hatzinger,

Editor: Richard G. Graf, rgraf@sunstroke.sdsu.edu

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