Old but Gold or New and Shiny? Comparing Tree Ensembles for Ordinal Prediction with a Classic Parametric Approach

Ordinal data are frequently encountered, e.g., in the life and social sciences. Predicting ordinal outcomes can inform important decisions, e.g., in medicine or education. Two methodological streams tackle prediction of ordinal outcomes: Traditional parametric models, e.g., the proportional odds model (POM), and machine learning-based tree ensemble (TE) methods. A promising TE approach involves selecting the best performing from sets of randomly generated numeric scores assigned to ordinal response categories (ordinal forest; Hornung, 2019). We propose a new method, the ordinal score optimization algorithm, that takes a similar approach but selects scores through non-linear optimization. We compare these and other TE methods with the computationally much less expensive POM. Despite selective efforts, the literature lacks an encompassing simulation-based comparison. Aiming to fill this gap, we find that while TE approaches outperform the POM for strong non-linear effects, the latter is competitive for small sample sizes even under medium non-linear effects.