On the use of splines for representing ordered factors

TL;DR

This paper discusses an enhanced method for assigning numeric scores to ordered factors in regression models, increasing flexibility in how qualitative levels are represented numerically.

Contribution

It extends a previous methodology to provide more flexible mappings from ordered factor levels to numeric scores in regression analysis.

Findings

Provides a generalized approach for score assignment

Improves model flexibility with ordered factors

Builds on Azzalini's previous methodology

Abstract

In the context of regression-type statistical models, the inclusion of some ordered factors among the explanatory variables requires the conversion of qualitative levels to numeric components of the linear predictor. The present note represent a follow-up of a methodology proposed by Azzalini (2023} for constructing numeric scores assigned to the factors levels. The aim of the present supplement it to allow additional flexibility of the mapping from ordered levels and numeric scores.