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

TL;DR

This paper extends generalized additive models to include ordinal predictors by incorporating quadratic penalties, enabling statistical inference such as confidence intervals and significance testing for these predictors, with an application to neonatal medicine.

Contribution

It introduces a novel framework integrating quadratic penalties for ordinal predictors into generalized additive models, facilitating inference procedures for such predictors.

Findings

Quadratic penalties can be effectively incorporated into GAMs for ordinal predictors.

Confidence intervals and significance tests are applicable to penalized ordinal predictors.

Application demonstrates practical utility in neonatal medicine research.

Abstract

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.