Robust quasi-likelihood inference in generalized linear mixed models with outliers

Abstract

It is well known that in a traditional outlier-free situation, the generalized quasi-likelihood (GQL) approach [B.C. Sutradhar, On exact quasilikelihood inference in generalized linear mixed models, Sankhya: Indian J. Statist. 66 (2004), pp. 261–289] performs very well to obtain the consistent as well as the efficient estimates for the parameters involved in the generalized linear mixed models (GLMMs). In this paper, we first examine the effect of the presence of one or more outliers on the GQL estimation for the parameters in such GLMMs, especially in two important models such as count and binary mixed models. The outliers appear to cause serious biases and hence inconsistency in the estimation. As a remedy, we then propose a robust GQL (RGQL) approach in order to obtain the consistent estimates for the parameters in the GLMMs in the presence of one or more outliers. An extensive simulation study is conducted to examine the consistency performance of the proposed RGQL approach.

Keywords:

• consistency
• count and binary mixed models
• generalized linear mixed model
• generalized quasi-likelihood
• outliers
• overdispersion
• regression effects
• robust approach

Acknowledgements

This research was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada. The authors would like to thank the Associate editor and the referee for their comments and suggestions.