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

Ken J. Beath*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)2256-2268
    Number of pages13
    JournalJournal of Applied Statistics
    Issue number12
    Early online date18 Dec 2017
    Publication statusPublished - 10 Sept 2018


    • binomial regression
    • generalised linear model
    • mixture model
    • outliers
    • Poisson regression
    • robustness


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