Statistical Modelling 12(6) (2012), 487–502

Modelling random effect variance with double hierarchical generalized linear models

Youngjo Lee
Department of Statistics
Seoul National University
Seoul 151-742
South Korea
email: youngjo@snu.ac.kr

Maengseok Noh
Department of Statistics
Pukyong National University
Busan 608-737
South Korea
email: msnoh@pknu.ac.kr

Abstract:

Random-effect models are becoming increasingly popular in the analysis of data. Lee and Nelder (2006) introduced double hierarchical generalized linear models (DHGLMs) in which not only the mean but also the residual variance (overdispersion) can be further modeled as random-effect models. In this paper, we introduce DHGLMs that allow random-effect models for both the variances of random effects and the residual variance. We show how to use this general model class for the analysis of data and discuss how to select the best fitting model using the likelihood and various model-checking plots.

Keywords:

double hierarchical generalized linear models; hierarchical generalized linear models; hierarchical likelihood; random effects

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