Ordinal Mixed-Effects Random Forest

TL;DR

The paper introduces OMERF, a novel random forest extension for hierarchical and ordinal data, enabling flexible modeling and inference at multiple data levels, validated through simulations and a PISA case study.

Contribution

OMERF is the first random forest method to explicitly model hierarchical structures with ordinal responses, combining flexibility with statistical inference capabilities.

Findings

OMERF outperforms existing models in simulation studies.

It effectively identifies key predictors of student performance.

The case study demonstrates its practical utility in educational data analysis.

Abstract

We propose an innovative statistical method, called Ordinal Mixed-Effect Random Forest (OMERF), that extends the use of random forest to the analysis of hierarchical data and ordinal responses. The model preserves the flexibility and ability of modeling complex patterns of both categorical and continuous variables, typical of tree-based ensemble methods, and, at the same time, takes into account the structure of hierarchical data, modeling the dependence structure induced by the grouping and allowing statistical inference at all data levels. A simulation study is conducted to validate the performance of the proposed method and to compare it to the one of other state-of-the art models. The application of OMERF is exemplified in a case study focusing on predicting students performances using data from the Programme for International Student Assessment (PISA) 2022. The model identifies discriminating student characteristics and estimates the school-effect.