Effects on Regression Estimates under Misspecified Generalized Linear Mixed Models for Counts Data

- Journal title : Korean Journal of Applied Statistics
- Volume 25, Issue 6, 2012, pp.1037-1047
- Publisher : The Korean Statistical Society
- DOI : 10.5351/KJAS.2012.25.6.1037

Title & Authors

Effects on Regression Estimates under Misspecified Generalized Linear Mixed Models for Counts Data

Jeong, Kwang Mo;

Jeong, Kwang Mo;

Abstract

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.

Keywords

Generalized linear mixed model;random effects distribution;overdispersion;negative binomial responses;Kullback-Leibler information;coverage probability;bias;

Language

English

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