Comparing of four IRT models when analyzing two tests for inductive reasoning

This article discusses the use of the nonparametric IRT Mokken models of monotone homogeneity and double monotonicity and the parametric Rasch and Verhelst models for the analysis of binary test data. First, the four IRT models are discussed and compared at the theoretical level, and for each model, methods are discussed for evaluating the fit of the model to test data. Second, each of the four IRT models is used for analyzing the data collected by means of two versions of a test for inductive reasoning. Finally, the results are discussed and recommendations are given about the practical use of each of the IRT models. It is concluded that the simultaneous use of several IRT models for practical data analysis provides more insight into the structure of tests than the rigid use of only one model.