Perturbation Selection and Local Influence Analysis for Generalized Linear Mixed Models

Identification of influential cases is an important step in data analysis. However, arbitrarily perturbing a model may result in misleading inference about the influential cases. Hence, an important issue of local influence analysis is to select an appropriate perturbation vector. In this article, we develop a perturbation selection method and a second-order local influence measure to address this issue and conduct local influence analysis in generalized linear mixed models. Four perturbation schemes are considered. The proposed approach is illustrated by a simulation study and two real examples. Some technical details are given in three appendices contained in a supplemental material which is available online.

[1]  J. Ibrahim,et al.  Perturbation selection and influence measures in local influence analysis , 2007, 0803.2986.

[2]  Sik-Yum Lee,et al.  Maximum Likelihood Analysis of a General Latent Variable Model with Hierarchically Mixed Data , 2004, Biometrics.

[3]  Sik-Yum Lee,et al.  Local Influence Analysis for Mixture of Structural Equation Models , 2004, J. Classif..

[4]  R. Platt,et al.  A generalized linear mixed models approach for detecting incident clusters of disease in small areas, with an application to biological terrorism. , 2004, American journal of epidemiology.

[5]  Sik-Yum Lee,et al.  Local influence for generalized linear mixed models , 2003 .

[6]  Sik-Yum Lee,et al.  Analysis of generalized linear mixed models via a stochastic approximation algorithm with Markov chain Monte-Carlo method , 2002, Stat. Comput..

[7]  Wai-Yin Poon,et al.  Influence analysis of structural equation models with polytomous variables , 1999 .

[8]  E Lesaffre,et al.  Local influence in linear mixed models. , 1998, Biometrics.

[9]  J A Stein,et al.  The effects of establishment practices, knowledge and attitudes on condom use among Filipina sex workers. , 1998, AIDS care.

[10]  N. Breslow,et al.  Bias Correction in Generalized Linear Mixed Models with Multiple Components of Dispersion , 1996 .

[11]  Kai-Tai Fang,et al.  Bayesian Local Influence for the Growth Curve Model with Rao's Simple Covariance Structure , 1996 .

[12]  R. Wolfinger,et al.  Generalized linear mixed models a pseudo-likelihood approach , 1993 .

[13]  N. Breslow,et al.  Approximate inference in generalized linear mixed models , 1993 .

[14]  J. H. Schuenemeyer,et al.  Generalized Linear Models (2nd ed.) , 1992 .

[15]  R. Dennis Cook,et al.  Assessing influence on regression coefficients in generalized linear models , 1989 .

[16]  M. Woodbury,et al.  Empirical Bayes procedures for stabilizing maps of U.S. cancer mortality rates. , 1989, Journal of the American Statistical Association.

[17]  Christopher J. Nachtsheim,et al.  Diagnostics for mixed-model analysis of variance , 1987 .

[18]  N. Breslow.  Extra‐Poisson Variation in Log‐Linear Models , 1984 .

[19]  D. A. Williams,et al.  Extra‐Binomial Variation in Logistic Linear Models , 1982 .

[20]  Martin Crowder,et al.  Beta-binomial Anova for Proportions , 1978 .

[21]  Xin-Yuan Song,et al.  LOCAL INFLUENCE ANALYSIS OF TWO-LEVEL LATENT VARIABLE MODELS WITH CONTINUOUS AND POLYTOMOUS DATA , 2004 .

[22]  Sik-Yum Lee,et al.  Local influence for incomplete data models , 2001 .

[23]  J. Booth,et al.  Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm , 1999 .

[24]  R. Cook.  Assessment of Local Influence , 1986 .