Ordered Correlation Forest

TL;DR

This paper introduces the ordered correlation forest, a flexible non-parametric estimator for ordered categorical outcomes that improves prediction accuracy and provides valid confidence intervals without restrictive assumptions.

Contribution

The paper develops a novel ordered correlation forest method that handles non-linearities and does not rely on specific error distribution assumptions, enhancing analysis of ordered outcomes.

Findings

Outperforms alternative forest estimators in prediction accuracy

Provides valid confidence intervals for covariates' marginal effects

Demonstrates superior performance on synthetic data

Abstract

Empirical studies in various social sciences often involve categorical outcomes with inherent ordering, such as self-evaluations of subjective well-being and self-assessments in health domains. While ordered choice models, such as the ordered logit and ordered probit, are popular tools for analyzing these outcomes, they may impose restrictive parametric and distributional assumptions. This paper introduces a novel estimator, the ordered correlation forest, that can naturally handle non-linearities in the data and does not assume a specific error term distribution. The proposed estimator modifies a standard random forest splitting criterion to build a collection of forests, each estimating the conditional probability of a single class. Under an "honesty" condition, predictions are consistent and asymptotically normal. The weights induced by each forest are used to obtain standard errors for the predicted probabilities and the covariates' marginal effects. Evidence from synthetic data shows that the proposed estimator features a superior prediction performance than alternative forest-based estimators and demonstrates its ability to construct valid confidence intervals for the covariates' marginal effects.