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This contribution deals with effect measures for covariates in ordinal data models to address the interpretation of the results on the extreme categories of the scales, evaluate possible response styles, and motivate collapsing of extreme categories. It provides a simpler interpretation of the influence of the covariates on the probability of the response categories both in standard cumulative link models under the proportional odds assumption and in the recent extension of the Combination of Uncertainty and Preference of the respondents models, the mixture models introduced to account for uncertainty in rating systems. The article shows by means of marginal effect measures that the effects of the covariates are underestimated when the uncertainty component is neglected. Visualization tools for the effect of covariates are proposed, and measures of relative size and partial effect based on rates of change are evaluated by the use of real data sets.

We present a Bayesian approach for the analysis of rating data when a scaling component is taken into account, thus incorporating a specific form of heteroskedasticity. Model-based probability effect measures for comparing distributions of several groups, adjusted for explanatory variables affecting both location and scale components, are proposed. Markov Chain Monte Carlo techniques are implemented to obtain parameter estimates of the fitted model and the associated effect measures. An analysis on students' evaluation of a university curriculum counselling service is carried out to assess the performance of the method and demonstrate its valuable support for the decision-making process. [ABSTRACT FROM AUTHOR]

This paper extends the ordinary quasi-symmetry ( QS) model for square contingency tables with commensurable classification variables. The proposed generalised QS model is defined in terms of odds ratios that apply to ordinal variables. In particular, we present QS models based on global, cumulative and continuation odds ratios and discuss their properties. Finally, the conditional generalised QS model is introduced for local and global odds ratios. These models are illustrated through the analysis of two data sets. [ABSTRACT FROM AUTHOR]