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Empirical Bayes estimates for correlated hierarchical data with overdispersion
Author(s) -
Iddi Samuel,
Molenberghs Geert,
Aregay Mehreteab,
Kalema George
Publication year - 2014
Publication title -
pharmaceutical statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 38
eISSN - 1539-1612
pISSN - 1539-1604
DOI - 10.1002/pst.1635
Subject(s) - overdispersion , bayes' theorem , statistics , econometrics , mathematics , bayes factor , computer science , bayesian probability , count data , poisson distribution
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. Copyright © 2014 John Wiley & Sons, Ltd.