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Ordered Correlation Forest

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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.

Suggested Citation

  • Riccardo Di Francesco, 2024. "Ordered Correlation Forest," CEIS Research Paper 577, Tor Vergata University, CEIS, revised 06 May 2024.
    • Handle: RePEc:rtv:ceisrp:577
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    References listed on IDEAS

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    1. Franco Peracchi & Claudio Rossetti, 2013. "The heterogeneous thresholds ordered response model: identification and inference," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(3), pages 703-722, June.
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    3. Bruno S. Frey & Alois Stutzer, 2002. "What Can Economists Learn from Happiness Research?," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 402-435, June.
    4. Stefan Wager & Susan Athey, 2018. "Estimation and Inference of Heterogeneous Treatment Effects using Random Forests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1228-1242, July.
    5. Franco Peracchi & Claudio Rossetti, 2012. "Heterogeneity in health responses and anchoring vignettes," Empirical Economics, Springer, vol. 42(2), pages 513-538, April.
    6. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference for High-Dimensional Sparse Econometric Models," Papers 1201.0220, arXiv.org.
    7. Janitza, Silke & Tutz, Gerhard & Boulesteix, Anne-Laure, 2016. "Random forest for ordinal responses: Prediction and variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 57-73.
    8. Lechner, Michael & Okasa, Gabriel, 2019. "Random Forest Estimation of the Ordered Choice Model," Economics Working Paper Series 1908, University of St. Gallen, School of Economics and Political Science.
    9. Wright, Marvin N. & Ziegler, Andreas, 2017. "ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 77(i01).
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    More about this item

    Keywords

    Ordered non-numeric outcomes; choice probabilities; machine learning;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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