Statistical inference for ordinal predictors in generalized additive models with application to Bronchopulmonary Dysplasia

Abstract

Objective: 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 models. Motivated by a study from neonatal medicine on Bronchopulmonary Dysplasia (BPD), we show how quadratic penalties on adjacent dummy coefficients of ordinal factors 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.

Results: The approach presented allows to exploit the scale level of ordinally scaled factors in a sound statistical framework. Furthermore, several ordinal factors can be considered jointly without the need to collapse levels even if the number of observations per level is small. By doing so, results obtained earlier on the BPD data analyzed could be confirmed.

Keywords: Chronic lung disease; Logit model; Ordinal data; Regularization; Smoothing penalty.

Fig. 1

QQ-plots of p-values for frst- and second-order penalty (red/blue)

Fig. 2

Fitted coefficients of ordinal predictors together with pointwise 95% confidence intervals in the full model with second-order penalties