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Abstract We propose a Bayesian model selection approach for generalized linear mixed models (GLMMs). We consider covariance structures for the random effects that are widely used in areas such as longitudinal studies, genome-wide association studies, and spatial statistics. Since the random effects cannot be integrated out of GLMMs analytically, we approximate the integrated likelihood function using a pseudo-likelihood approach. Our Bayesian approach assumes a flat prior for the fixed effects and includes both approximate reference prior and half-Cauchy prior choices for the variances of random effects. Since the flat prior on the fixed effects is improper, we develop a fractional Bayes factor approach to obtain posterior probabilities of the several competing models. Simulation studies with Poisson GLMMs with spatial random effects and overdispersion random effects show that our approach performs favorably when compared to widely used competing Bayesian methods including deviance information criterion and Watanabe–Akaike information criterion. We illustrate the usefulness and flexibility of our approach with three case studies including a Poisson longitudinal model, a Poisson spatial model, and a logistic mixed model. Our proposed approach is implemented in the R package GLMMselect that is available on CRAN.
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Multivariate nearest‐neighbors Gaussian processes with random covariance matrices
Abstract We propose a non‐stationary spatial model based on a normal‐inverse‐Wishart framework, conditioning on a set of nearest‐neighbors. The model, called nearest‐neighbor Gaussian process with random covariance matrices is developed for both univariate and multivariate spatial settings and allows for fully flexible covariance structures that impose no stationarity or isotropic restrictions. In addition, the model can handle duplicate observations and missing data. We consider an approach based on integrating out the spatial random effects that allows fast inference for the model parameters. We also consider a full hierarchical approach that leverages the sparse structures induced by the model to perform fast Monte Carlo computations. Strong computational efficiency is achieved by leveraging the adaptive localized structure of the model that allows for a high level of parallelization. We illustrate the performance of the model with univariate and bivariate simulations, as well as with observations from two stationary satellites consisting of albedo measurements.
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- Award ID(s):
- 1953168
- PAR ID:
- 10523586
- Publisher / Repository:
- Environmetrics - Wiley
- Date Published:
- Journal Name:
- Environmetrics
- Volume:
- 35
- Issue:
- 3
- ISSN:
- 1180-4009
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1002/env.2839
