Sparser Ordinal Regression Models Based on Parametric and Additive Location-Shift Approaches

Abstract

The potential of location-shift models to find adequate models between the proportional odds model and the non-proportional odds model is investigated. It is demonstrated that these models are very useful in ordinal modelling. While proportional odds models are often too simple, non-proportional odds models are typically unnecessary complicated and seem widely dispensable. In addition, the class of location-shift models is extended to allow for smooth effects. The additive location-shift model contains two functions for each explanatory variable, one for the location and one for dispersion. It is much sparser than hard-to-handle additive models with category-specific covariate functions but more flexible than common vector generalised additive models. An R package is provided that is able to fit parametric and additive location-shift models.