In this article, we develop spatial-temporal generalized linear mixed models for spatial-temporal binary data observed on a spatial lattice and repeatedly over discrete time points. To account for spatial and temporal dependence, we introduce a spatial-temporal random effect in the link function and model by a diffusion-convection dynamic model. We propose a Bayesian hierarchical model for statistical inference and devise Markov chain Monte Carlo algorithms for computation. We illustrate the methodology by an example of outbreaks of mountain pine beetle on the Chilcotin Plateau of British Columbia, Canada. We examine the effect of environmental factors while accounting for the potential spatial and temporal dependence.
- Dendroctonus ponderosae
- Generalized linear mixed model
- Mountain pine beetle
- Partial differential equation
- Spatial-temporal process