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

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Abstract
The Mokken model of monotone homogeneity, the Mokken model of double monotonicity, and the Rasch model are theoretically and empirically compared. These models are compared with respect to restrictiveness to empirical test data, properties of the scale, and accuracy of measurement. Appli cation of goodness-of-fit procedures to empirical data largely confirmed the expected order of the models according to restrictiveness: Almost all items were in concordance with the model of mono tone homogeneity, and fewer items complied with the model of double monotonicity and the Rasch model. The model of monotone homogeneity was found to be a suitable alternative to more restric tive models for basic testing applications; more sophisticated applications, such as equating and adaptive testing, appear to require the use of para metric models.