Case-Deletion Diagnostics for Linear Mixed Models

Abstract

Based on the Q-function, the conditional expectation of the logarithm of the joint-likelihood between responses and random effects, we propose a case-deletion approach to identify influential subjects and influential observations in linear mixed models. The models considered here are very broad in the sense that any covariance structures can be specified in the covariance matrices of the random effects and random errors. Analytically explicit forms of diagnostic measures for the fixed effects and variance components are provided. Comparisons with existing methods, including likelihood-based case-deletion and local influence methods, are made. Numerical results, including real data analysis and simulation studies, are presented for both illustration and comparison. This article has supplementary material online.

• Covariance structures
• Generalized Cook distance
• Influence analysis
• Q-function

ACKNOWLEDGMENTS

Pan’s research was supported by a grant from the Royal Society of the UK (International Joint Project; 2010/R112497), and Fei’s research was supported by The National Natural Science Foundation of China (11061036). We gratefully acknowledge very helpful and constructive comments and suggestions made by the editor, associate editor, and two anonymous referees, which lead to significant improvements to the article.