Influence diagnostics for generalized linear mixed models: applications to clustered data

Authors:
Liming Xiang;Siu-Keung Tse;Andy H. Lee
Affiliations:
Department of Management Sciences, City University of Hong Kong, 83 Tat Chee Ave, Kowloon, Hong Kong;Department of Management Sciences, City University of Hong Kong, 83 Tat Chee Ave, Kowloon, Hong Kong;Department of Epidemiology & Biostatistics, School of Public Health, Curtin University of Technology, Perth, Australia
Venue:
Computational Statistics & Data Analysis
Year:
2002

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Abstract

The Cook's distance for generalized linear mixed models is investigated, with applications to clustered data. In particular, first-order approximations are derived for the best linear unbiased predictor of the parameters due to cluster deletion. A small-scale simulation study shows that the method provides an efficient way to identify influential clusters. The notion of joint and conditional influence is also considered to address the masking effects of cluster-wise deletion. A data set on maternity length of hospital stay illustrates the usefullness of the proposed diagnostics.