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Adjusted quantile residual for generalized linear models

Author

Listed:
  • Juliana Scudilio

    (University of São Paulo
    Federal University of São Carlos)

  • Gustavo H. A. Pereira

    (Federal University of São Carlos)

Abstract

Generalized linear models are widely used in many areas of knowledge. As in other classes of regression models, it is desirable to perform diagnostic analysis in generalized linear models using residuals that are approximately standard normally distributed. Diagnostic analysis in this class of models are usually performed using the standardized Pearson residual or the standardized deviance residual. The former has skewed distribution and the latter has negative mean, specially when the variance of the response variable is high. In this work, we introduce the adjusted quantile residual for generalized linear models. Using Monte Carlo simulation techniques and two applications, we compare this residual with the standardized Pearson residual, the standardized deviance residual and two other residuals. Overall, the results suggest that the adjusted quantile residual is a better tool for diagnostic analysis in generalized linear models.

Suggested Citation

  • Juliana Scudilio & Gustavo H. A. Pereira, 2020. "Adjusted quantile residual for generalized linear models," Computational Statistics, Springer, vol. 35(1), pages 399-421, March.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:1:d:10.1007_s00180-019-00896-w
    DOI: 10.1007/s00180-019-00896-w
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    References listed on IDEAS

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    1. Bernhard Klar & Simos Meintanis, 2012. "Specification tests for the response distribution in generalized linear models," Computational Statistics, Springer, vol. 27(2), pages 251-267, June.
    2. D. A. Williams, 1987. "Generalized Linear Model Diagnostics Using the Deviance and Single Case Deletions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(2), pages 181-191, June.
    3. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    4. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
    5. Cordeiro, Gauss M., 2004. "On Pearson's residuals in generalized linear models," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 213-219, February.
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    Cited by:

    1. Vadim Elenev & Tim Landvoigt & Stijn Van Nieuwerburgh, 2021. "A Macroeconomic Model With Financially Constrained Producers and Intermediaries," Econometrica, Econometric Society, vol. 89(3), pages 1361-1418, May.
    2. Andrade, Ana C.C. & Pereira, Gustavo H.A. & Artes, Rinaldo, 2023. "The circular quantile residual," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).

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