Ordinal Trees and Random Forests: Score-Free Recursive Partitioning and Improved Ensembles

TL;DR

This paper introduces new ordinal trees and random forests that respect the ordinal scale without artificial scores, combining binary models for improved, score-free recursive partitioning and ensemble methods.

Contribution

It proposes ordinal trees based on binary models that avoid artificial scoring, and ensembles combining parametric models for better performance across settings.

Findings

Score-free ordinal trees effectively model ordinal data.

Ensembles with parametric models improve predictive accuracy.

Empirical evaluation shows competitive performance.

Abstract

Existing ordinal trees and random forests typically use scores that are assigned to the ordered categories, which implies that a higher scale level is used. Versions of ordinal trees are proposed that take the scale level seriously and avoid the assignment of artificial scores. The basic construction principle is based on an investigation of the binary models that are implicitly used in parametric ordinal regression. These building blocks can be fitted by trees and combined in a similar way as in parametric models. The obtained trees use the ordinal scale level only. Since binary trees and random forests are constituent elements of the trees one can exploit the wide range of binary trees that have already been developed. A further topic is the potentially poor performance of random forests, which seems to have ignored in the literature. Ensembles that include parametric models are proposed to obtain prediction methods that tend to perform well in a wide range of settings. The performance of the methods is evaluated empirically by using several data sets.