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

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.

KEYWORDS:

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

Acknowledgements

The author expresses his thanks to the anonymous reviewers whose comments contributed to the improvement of this paper.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

K. J. Beath  http://orcid.org/0000-0002-4536-0603