Theoretical and Empirical Comparison of the Mokken and the Rasch Approach to IRT

摘要

The Mokken model of monotone homogeneity,the Mokken model of double monotonicity, andthe Rasch model are theoretically and empiricallycompared. These models are compared with respectto restrictiveness to empirical test data, propertiesof the scale, and accuracy of measurement. Applicationof goodness-of-fit procedures to empiricaldata largely confirmed the expected order of themodels according to restrictiveness: Almost allitems were in concordance with the model of monotonehomogeneity, and fewer items complied withthe model of double monotonicity and the Raschmodel. The model of monotone homogeneity wasfound to be a suitable alternative to more restrictivemodels for basic testing applications; moresophisticated applications, such as equating andadaptive testing, appear to require the use of parametricmodels. Index terms: goodness-of-fit, itemresponse theory, measurement properties, Mokkenmodel, Rasch model.