Effect Structures in Ordinal Regression: The Adjacent Categories Approach

The potential of the adjacent categories approach for capturing the influence of explanatory variables on ordinal responses is investigated. Several models with increasing complexity in their linear predictors are considered, and their relationships are discussed, including the basic adjacent categories model, the stereotype model, models with category-specific effects, and dispersion models. For the adjacent categories framework, regularization methods for effect selection are introduced with the aim of distinguishing between no effect, global effects, and category-specific effects. Particular attention is given to the adjacent dispersion model, which provides a parsimonious parameterization while substantially improving model fit compared to the basic model. Effect selection for both the location and dispersion effects in the adjacent dispersion model is introduced. The proposed approaches are illustrated using several real data sets.