Statistical Inference for Ordinal Predictors in Generalized Linear and Additive Models with Application to Bronchopulmonary Dysplasia

Discrete but ordered covariates are quite common in applied statistics, and some regularized fitting procedures have been proposed for proper handling of ordinal predictors in statistical modeling. In this study, we show how quadratic penalties on adjacent dummy coefficients of ordinal predictors proposed in the literature can be incorporated in the framework of generalized additive models, making tools for statistical inference developed there available for ordinal predictors as well. Motivated by an application from neonatal medicine, we discuss whether results obtained when constructing confidence intervals and testing significance of smooth terms in generalized additive models are useful with ordinal predictors/penalties as well.