Advanced SearchSearch Tips
Effects on Regression Estimates under Misspecified Generalized Linear Mixed Models for Counts Data
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Effects on Regression Estimates under Misspecified Generalized Linear Mixed Models for Counts Data
Jeong, Kwang Mo;
  PDF(new window)
The generalized linear mixed model(GLMM) is widely used in fitting categorical responses of clustered data. In the numerical approximation of likelihood function the normality is assumed for the random effects distribution; subsequently, the commercial statistical packages also routinely fit GLMM under this normality assumption. We may also encounter departures from the distributional assumption on the response variable. It would be interesting to investigate the impact on the estimates of parameters under misspecification of distributions; however, there has been limited researche on these topics. We study the sensitivity or robustness of the maximum likelihood estimators(MLEs) of GLMM for counts data when the true underlying distribution is normal, gamma, exponential, and a mixture of two normal distributions. We also consider the effects on the MLEs when we fit Poisson-normal GLMM whereas the outcomes are generated from the negative binomial distribution with overdispersion. Through a small scale Monte Carlo study we check the empirical coverage probabilities of parameters and biases of MLEs of GLMM.
Generalized linear mixed model;random effects distribution;overdispersion;negative binomial responses;Kullback-Leibler information;coverage probability;bias;
 Cited by
Agresti, A. (2002). Categorical Data Analysis, Second Ed., Wiley, New York.

Alonso, A., Litiere, S. and Molenberghs, G. (2010). Testing for misspecification in generalized linear mixed models, Biostatistics, 11, 771-786. crossref(new window)

Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models, Journal of the American Statistical Association, 88, 9-25.

McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, Second Ed., London, Chapman and Halls.

Heagerty, P. J. and Kurland, B. F. (2001). Misspecified maximum likelihood estimates and generalized linear mixed models, Biometrika, 88, 9-25.

Litiere, S., Alonso, A. and Molenberghs, G. (2007). Type I and Type II error under random-effects misspecification in generalized linear mixed models, Biometrics, 63, 1038-1044. crossref(new window)

Litiere, S., Alonso, A. and Molenberghs, G. (2008). The impact of a misspecified random-effects distribution on the estimation and the performance of inferential procedures in generalized linear mixed models, Statistics in Medicine, 27, 3125-3144.

Molenberghs, G., Declerck, L. and Aerts, M. (1998). Misspecifying the likelihood for clustered binary data, Computational Statistics and Data Analysis, 26, 327-349. crossref(new window)

Neuhaus, J. M., Hauck, W. W. and Kalbfleisch, J. D. (1992). The effects of mixture distribution misspecification when fitting mixed-effects logistic models, Biometrika, 79, 755-762. crossref(new window)

Whites, H. (1982). Maximum likelihood estimation of misspecified models, Econometrica, 50, 1-26. crossref(new window)