Mixed-Effects Frequency-Adjusted Borders Ordinal Forest: A Tree Ensemble Method for Ordinal Prediction with Hierarchical Data

Predicting ordinal responses such as school grades or rating scale data is a common task in the social and life sciences. Currently, two major streams of methodology exist for ordinal prediction: parametric models such as the proportional odds model and machine learning (ML) methods such as random forest (RF) adapted to ordinal prediction. While methods from the latter stream have displayed high predictive performance, particularly for data characterized by non-linear effects, most of these methods do not support hierarchical data. As such data structures frequently occur in the social and life sciences, e.g., students nested in classes or individual measurements nested within the same person, accounting for hierarchical data is of importance for prediction in these fields. A recently proposed ML method for ordinal prediction displaying promising results for non-hierarchical data is Frequency-Adjusted Borders Ordinal Forest (fabOF). Building on an iterative expectation-maximization-type estimation procedure, I extend fabOF to hierarchical data settings in this work by proposing Mixed-Effects Frequency-Adjusted Borders Ordinal Forest (mixfabOF). Through simulation and a real data example on math achievement, I demonstrate that mixfabOF can improve upon fabOF and other RF-based ordinal prediction methods for (non-)hierarchical data in the presence of random effects.