Skalierungsverfahren nach Mokken

The Mokken Scale ist a nonparametric, probabilistic latent-trait model for scaling binary cumulative items, originally introduced by R. J. Mokken in 1971. In this doctoral thesis the elements of the scaling procedure under consideration of the existing extensions are presented and joined together. The application of the different methods to check the main item requirements of double monotony are examined by investigating simulated and empirical data. Especially problems concerning the specific attributes of the coeffizicient of homogenity (mainly the bias due to population dependence and extreme score groups) are discussed. The relevance of this bias for the resulting scale solution and further on for testing the robustness of scales respectively differtial scaling are discussed and extensions of the procedures (elimination of extreme score groups, introduction of the C-coefficient, random test) are presented. Numerous possibibilities to examine the unique itemorder (P-matices, Itemsplit, restscoresplit, comparison of restscoregoups, the coefficient H"T and the ordinal analysis of latent classes) and different procedures for the scale construction (stepwise scale-construction, full combinations, clusteralgorithms) are investigated regarding their applicability. Further developements (the generalization of the model to ordinal polytomous items and nonparametric probabilistic unfolding) are shortly presented.