title: Empirical Bayes estimates for correlated hierarchical data with overdispersion.
abstract: An extension of the generalized linear mixed model was constructed to simultaneously accommodate overdispersion and hierarchies present in longitudinal or clustered data. This so-called combined model includes conjugate random effects at observation level for overdispersion and normal random effects at subject level to handle correlation, respectively. A variety of data types can be handled in this way, using different members of the exponential family. Both maximum likelihood and Bayesian estimation for covariate effects and variance components were proposed. The focus of this paper is the development of an estimation procedure for the two sets of random effects. These are necessary when making predictions for future responses or their associated probabilities. Such (empirical) Bayes estimates will also be helpful in model diagnosis, both when checking the fit of the model as well as when investigating outlying observations. The proposed procedure is applied to three datasets of different outcome types.
authors.affiliation: Department of Statistics, University of Ghana, Legon-Accra, Ghana; I-BioStat, KU Leuven - University of Leuven.
authors.forename: Samuel
authors.initials: S
authors.lastname: Iddi
authors.forename: Geert
authors.initials: G
authors.lastname: Molenberghs
authors.forename: Mehreteab
authors.initials: M
authors.lastname: Aregay
authors.forename: George
authors.initials: G
authors.lastname: Kalema
mesh_terms: D001499:Bayes Theorem; D036262:Empirical Research; D006801:Humans; D008137:Longitudinal Studies; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data*; D013223:Statistics as Topic / Q000379:methods*
keywords: beta-binomial; combined model; conjugacy; empirical bayes; generalized linear mixed model; logistic-normal model; maximum likelihood; negative-binomial; partial marginalization; posterior; prediction; random effects; strong conjugacy