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Adjusted quantile residual for generalized linear models

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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.

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Acknowledgements

The authors thank “Coordenação de Aperfeiçoamento de Pessoal de Nível Superior” (CAPES) for the financial support received for this project. The authors also thank two anonymous referees for their helpful comments.

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Authors and Affiliations

  1. Institute of Mathematical and Computer Sciences, University of São Paulo, São Carlos, SP, Brazil

    Juliana Scudilio

  2. Department of Statistics, Federal University of São Carlos, São Carlos, SP, Brazil

    Juliana Scudilio & Gustavo H. A. Pereira

Authors
  1. Juliana Scudilio
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  2. Gustavo H. A. Pereira
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Correspondence to Juliana Scudilio.

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Appendix

Appendix

See Tables 7, 8, 9 and 10.

Table 7 Distributional measures for the residual in Gamma regression model
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Table 8 Distributional measures for the residuals in inverse Gaussian regression model
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Table 9 Comparison of the Anderson–Darling statistic for n \(=\) 15 and n \(=\) 50—gamma regression model
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Table 10 Comparison of the Anderson–Darling statistic for n \(=\) 15 and n \(=\) 50—inverse Gaussian regression model
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Scudilio, J., Pereira, G.H.A. Adjusted quantile residual for generalized linear models. Comput Stat 35, 399–421 (2020). https://doi.org/10.1007/s00180-019-00896-w

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  • DOI: https://doi.org/10.1007/s00180-019-00896-w

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