Analysis of grouped data using conjugate generalized linear mixed models

Summary This article concerns a class of generalized linear mixed models for two-level grouped data, where the random effects are uniquely indexed by groups and are independent. We derive necessary and sufficient conditions for the marginal likelihood to be expressed in explicit form. These models a...

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Bibliographic Details
Published in:Biometrika 2020-03, Vol.107 (1), p.231-237
Main Authors: Lee, Jarod Y L, Green, Peter J, Ryan, Louise M
Format: Article
Language:English
Subjects:
Bayesian analysis
Binomial distribution
Computer applications
Computer simulation
Computing time
Conjugates
Mathematical models
Robustness (mathematics)
Statistical models
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Summary:Summary This article concerns a class of generalized linear mixed models for two-level grouped data, where the random effects are uniquely indexed by groups and are independent. We derive necessary and sufficient conditions for the marginal likelihood to be expressed in explicit form. These models are unified under the conjugate generalized linear mixed models framework, where conjugate refers to the fact that the marginal likelihood can be expressed in closed form, rather than implying inference via the Bayesian paradigm. The proposed framework allows simultaneous conjugacy for Gaussian, Poisson and gamma responses, and thus can accommodate both unit- and group-level covariates. Only group-level covariates can be incorporated for the binomial distribution. In a simulation of Poisson data, our framework outperformed its competitors in terms of computational time, and was competitive in terms of robustness against misspecification of the random effects distributions.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asz053