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A new residual for ordinal outcomes

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  • Chun Li
  • Bryan E. Shepherd

Abstract

We propose a new residual for regression models of ordinal outcomes, defined as E{sign(y,Y)}, where y is the observed outcome and Y is a random variable from the fitted distribution. This new residual is a single value per subject irrespective of the number of categories of the ordinal outcome, contains directional information between the observed value and the fitted distribution, and does not require the assignment of arbitrary numbers to categories. We study its properties, describe its connections with other residuals, ranks and ridits, and demonstrate its use in model diagnostics. Copyright 2012, Oxford University Press.

Suggested Citation

  • Chun Li & Bryan E. Shepherd, 2012. "A new residual for ordinal outcomes," Biometrika, Biometrika Trust, vol. 99(2), pages 473-480.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:2:p:473-480
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    File URL: http://hdl.handle.net/10.1093/biomet/asr073
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    Cited by:

    1. 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.
    2. Svetlana K. Eden & Chun Li & Bryan E. Shepherd, 2022. "Nonparametric estimation of Spearman's rank correlation with bivariate survival data," Biometrics, The International Biometric Society, vol. 78(2), pages 421-434, June.
    3. Qi Liu & Chun Li & Valentine Wanga & Bryan E. Shepherd, 2018. "Covariate†adjusted Spearman's rank correlation with probability†scale residuals," Biometrics, The International Biometric Society, vol. 74(2), pages 595-605, June.
    4. Daniel Fernández & Louise McMillan & Richard Arnold & Martin Spiess & Ivy Liu, 2022. "Goodness-of-Fit and Generalized Estimating Equation Methods for Ordinal Responses Based on the Stereotype Model," Stats, MDPI, vol. 5(2), pages 1-14, June.
    5. Victor Chernozhukov & Iv'an Fern'andez-Val & Jonas Meier & Aico van Vuuren & Francis Vella, 2024. "Conditional Rank-Rank Regression," Papers 2407.06387, arXiv.org.

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