  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.
