Regularization and Predictor Selection for Ordinal and Categorical Data

Categorical data are quite common in applied statistics, and various regularized fitting procedures have been proposed for appropriate handling of such variables in regression. This chapter gives an overview of some of those techniques. Special emphasis is put on model selection with ordinal explanatory variables if the number of categories and/or the number of predictors is relatively large. In this context, regularized fitting is compared to more classical procedures like forward selection. Structuring of ordinal predictors is considered within the framework of generalized additive models (GAMs), and tools provided within this framework are employed for statistical inference.