Tree-Structured Scale Effects in Binary and Ordinal Regression

TL;DR

This paper introduces a recursive partitioning method that constructs two trees to separately model location and scaling effects in binary and ordinal regression, improving interpretability and accounting for variance heterogeneity.

Contribution

The paper presents a novel recursive partitioning approach that creates separate trees for location and scaling, addressing limitations of existing methods in modeling heterogeneity.

Findings

The method effectively identifies variables influencing response location.

It accounts for variance heterogeneity in ordinal and binary data.

Applications demonstrate improved interpretability and model performance.

Abstract

In binary and ordinal regression one can distinguish between a location component and a scaling component. While the former determines the location within the range of the response categories, the scaling indicates variance heterogeneity. In particular since it has been demonstrated that misleading effects can occur if one ignores the presence of a scaling component it is important to account for potential scaling effects in the regression model, which is not possible in available recursive partitioning methods. The proposed recursive partitioning method yields two trees, one for the location and one for the scaling. They show in a simple interpretable way how variables interact to determine the binary or ordinal response. The developed algorithm controls for the global significance level and automatically selects the variables that have an impact on the response. The modelling approach is illustrated by several real-world applications.