Model-based random forests for ordinal regression

Abstract

We study and compare several variants of random forests tailored to prognostic models for ordinal outcomes. Models of the conditional odds function are employed to understand the various random forest flavours. Existing random forest variants for ordinal outcomes, such as Ordinal Forests and Conditional Inference Forests, are evaluated in the presence of a non-proportional odds impact of prognostic variables. We propose two novel random forest variants in the model-based transformation forest family, only one of which explicitly assumes proportional odds. These two novel transformation forests differ in the specification of the split procedures for the underlying ordinal trees. One of these split criteria is able to detect changes in non-proportional odds situations and the other one focuses on finding proportional-odds signals. We empirically evaluate the performance of the existing and proposed methods using a simulation study and illustrate the practical aspects of the procedures by a re-analysis of the respiratory sub-item in functional rating scales of patients suffering from Amyotrophic Lateral Sclerosis (ALS).

Keywords: amyotrophic lateral sclerosis; conditional distribution function; conditional odds function; ordinal outcome; random forest; transformation model.