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

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  • Gerhard Tutz

    (Ludwig-Maximilians-Universität München)

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 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 proposed 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 been neglected 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.

Suggested Citation

  • Gerhard Tutz, 2022. "Ordinal Trees and Random Forests: Score-Free Recursive Partitioning and Improved Ensembles," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 241-263, July.
  • Handle: RePEc:spr:jclass:v:39:y:2022:i:2:d:10.1007_s00357-021-09406-4
    DOI: 10.1007/s00357-021-09406-4
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    1. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    2. J. A. Anderson & P. R. Philips, 1981. "Regression, Discrimination and Measurement Models for Ordered Categorical Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(1), pages 22-31, March.
    3. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    4. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    5. Archer, Kellie J., 2010. "rpartOrdinal: An R Package for Deriving a Classification Tree for Predicting an Ordinal Response," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i07).
    6. Zardad Khan & Asma Gul & Aris Perperoglou & Miftahuddin Miftahuddin & Osama Mahmoud & Werner Adler & Berthold Lausen, 2020. "Ensemble of optimal trees, random forest and random projection ensemble classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(1), pages 97-116, March.
    7. Mariangela Sciandra & Antonella Plaia & Vincenza Capursi, 2017. "Classification trees for multivariate ordinal response: an application to Student Evaluation Teaching," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 641-655, March.
    8. Geofferey Masters & Benjamin Wright, 1984. "The essential process in a family of measurement models," Psychometrika, Springer;The Psychometric Society, vol. 49(4), pages 529-544, December.
    9. Deb, Partha & Trivedi, Pravin K, 1997. "Demand for Medical Care by the Elderly: A Finite Mixture Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 313-336, May-June.
    10. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    11. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    12. Galimberti, Giuliano & Soffritti, Gabriele & Maso, Matteo Di, 2012. "Classification Trees for Ordinal Responses in R: The rpartScore Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(i10).
    13. Bercedis Peterson & Frank E. Harrell, 1990. "Partial Proportional Odds Models for Ordinal Response Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(2), pages 205-217, June.
    14. 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.
    15. Domenico Piccolo & Rosaria Simone, 2019. "Rejoinder to the discussion of “The class of cub models: statistical foundations, inferential issues and empirical evidence”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 477-493, September.
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