Journal article
Marginal inference for hierarchical generalized linear mixed models with patterned covariance matrices using the Laplace approximation
Environmetrics (London, Ont.), Vol.35(7), e2872
11/2024
DOI: 10.1002/env.2872
PMCID: PMC11684526
PMID: 39737161
Abstract
Abstract We develop hierarchical models and methods in a fully parametric approach to generalized linear mixed models for any patterned covariance matrix. The Laplace approximation is used to marginally estimate covariance parameters by integrating over all fixed and latent random effects. The Laplace approximation relies on Newton–Raphson updates, which also leads to predictions for the latent random effects. We develop methodology for complete marginal inference, from estimating covariance parameters and fixed effects to making predictions for unobserved data. The marginal likelihood is developed for six distributions that are often used for binary, count, and positive continuous data, and our framework is easily extended to other distributions. We compare our methods to fully Bayesian methods, automatic differentiation, and integrated nested Laplace approximations (INLA) for bias, mean‐squared (prediction) error, and interval coverage, and all methods yield very similar results. However, our methods are much faster than Bayesian methods, and more general than INLA. Examples with binary and proportional data, count data, and positive‐continuous data are used to illustrate all six distributions with a variety of patterned covariance structures that include spatial models (both geostatistical and areal models), time series models, and mixtures with typical random intercepts based on grouping.
Details
- Title: Subtitle
- Marginal inference for hierarchical generalized linear mixed models with patterned covariance matrices using the Laplace approximation
- Creators
- Jay M. Ver Hoef - NOAA National Marine Fisheries Service Alaska Fisheries Science CenterEryn Blagg - Iowa State UniversityMichael Dumelle - Environmental Protection AgencyPhilip M. Dixon - Iowa State UniversityDale L. Zimmerman - University of IowaPaul B. Conn - NOAA National Marine Fisheries Service Alaska Fisheries Science Center
- Resource Type
- Journal article
- Publication Details
- Environmetrics (London, Ont.), Vol.35(7), e2872
- DOI
- 10.1002/env.2872
- PMID
- 39737161
- PMCID
- PMC11684526
- NLM abbreviation
- Environmetrics
- ISSN
- 1180-4009
- eISSN
- 1099-095X
- Language
- English
- Electronic publication date
- 07/22/2024
- Date published
- 11/2024
- Academic Unit
- Statistics and Actuarial Science; Biostatistics
- Record Identifier
- 9984688446002771
Metrics
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