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A mixture-based approach to robust analysis of generalised linear models

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  • Ken J. Beath

Abstract

A method for robustness in linear models is to assume that there is a mixture of standard and outlier observations with a different error variance for each class. For generalised linear models (GLMs) the mixture model approach is more difficult as the error variance for many distributions has a fixed relationship to the mean. This model is extended to GLMs by changing the classes to one where the standard class is a standard GLM and the outlier class which is an overdispersed GLM achieved by including a random effect term in the linear predictor. The advantages of this method are it can be extended to any model with a linear predictor, and outlier observations can be easily identified. Using simulation the model is compared to an M-estimator, and found to have improved bias and coverage. The method is demonstrated on three examples.

Suggested Citation

  • Ken J. Beath, 2018. "A mixture-based approach to robust analysis of generalised linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(12), pages 2256-2268, September.
    • Handle: RePEc:taf:japsta:v:45:y:2018:i:12:p:2256-2268
    DOI: 10.1080/02664763.2017.1414164
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    Cited by:

    1. Bernhard, Marco & Leuch, Corina & Kordi, Maryam & Gruebner, Oliver & Matthes, Katarina L. & Floris, Joël & Staub, Kaspar, 2023. "From pandemic to endemic: Spatial-temporal patterns of influenza-like illness incidence in a Swiss canton, 1918–1924," Economics & Human Biology, Elsevier, vol. 50(C).
    2. Gagnon, Philippe & Wang, Yuxi, 2024. "Robust heavy-tailed versions of generalized linear models with applications in actuarial science," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).

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