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Title: Generalized mixed model with non-normal density Authors:  Yusuke Saigusa - Yokohama City University (Japan) [presenting]
Osamu Komori - Seikei University (Japan)
Shinto Eguchi - The Institute of Statistical Mathematics (Japan)
Abstract: Generalized linear mixed model (GLMM) is used frequently in the analysis of non-independent data which includes longitudinal data. In GLMM, the biased estimates and/or poor coverage rates for confidence intervals can arise from the misspecification of the distribution of random effects. We newly propose an extended GLMM with predictor formed by generalized average. The predictor of proposed model has non-normal density whereas the linear predictor of GLMM has normal density when the random effect part has a normal distribution. The relaxed constraint of proposed model would reduce the influence of misspecification on random effects when the distributional assumption is violated. We obtain a computational algorithm for estimating fixed and random effect parameters based on penalized quasi-likelihood, and variance components of random effects based on restricted maximum likelihood in the proposed model. The conditional Akaike information criterion is used for model selection. We give some simulation experiments and example of analysis of longitudinal data from randomized clinical trial for comparing treatments for epileptics.