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Tutz, Gerhard; Moritz, Berger (22. February 2016): Separating Location and Dispersion in Ordinal Regression Models. Department of Statistics: Technical Reports, No.190
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In ordinal regression the focus is typically on location effects, potential variation in the distribution of the probability mass over response categories referring to stronger or weaker concentration in the middle is mostly ignored. If dispersion effects are present but ignored goodness-of-fit suffers and, more severely, biased estimates of location effects are to be expected since ordinal regression models are non-linear. A model is proposed that explicitly links varying dispersion to explanatory variables. The embedding into the framework of multivariate generalized linear models allows to use computational tools and asymptotic results that have been developed for this class of models. The model is compared to alternative approaches in applications and simulations. In addition, a visualization tool for the combination of location and dispersion effects is proposed and used in applications.