Papers › Marginal Inference for Hierarchical Generalized Linear Mixed Models with Patterned...
Marginal Inference for Hierarchical Generalized Linear Mixed Models with Patterned Covariance Matrices Using the Laplace Approximation
Jay M. Ver Hoef, Eryn Blagg, Michael Dumelle, Philip M. Dixon, Dale L. Zimmerman, Paul Conn
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to marginally estimate covariance parameters while integrating out 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, for any patterned covariance matrix in the hierarchical generalized linear mixed models framework. 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. The methods are illustrated with simulations from stochastic processes with known parameters, and their efficacy in terms of bias and interval coverage is shown through simulation experiments. Examples with binary and proportional data on election results, count data for marine mammals, and positive-continuous data on heavy metal concentration in the environment are used to illustrate all six distributions with a variety of patterned covariance structures that include spatial models (e.g., geostatistical and areal models), time series models (e.g., first-order autoregressive models), and mixtures with typical random intercepts based on grouping.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections