Bayesian inference of generalized linear blockNNGP model of coregionalization through INLA

In the last decade, the population of bird species has decreased in North America. Understanding the spatial patterns of bird species is important for preserving them. In particular, the abundance of K species can exhibit dependence among them, while the abundance of each kth species can be spatially autocorrelated. Standard multivariate geostatistical models for these data are computationally demanding and limited to Gaussian data. In this article, we develop the generalized linear block nearest neighbour Gaussian process model of coregionalization, which combines a generalized linear model of coregionalization (GLMC) with the block nearest neighbour Gaussian process (blockNNGP). The GLMC handles K Gaussian or non-Gaussian response variables and relies on sharing common weighted spatial random effects across the response variables. In our approach, for each kth response variable, its spatial random effects are defined via a blockNNGP, which effectively leverages conditional independence across blocks of observations to handle large spatial data. Fast Bayesian inference is implemented through R-INLA. We illustrate the performance of the proposal through simulation studies. Finally, we estimate and predict the abundance of the American Robin, Chipping Sparrow, and European Starling, among the most abundant species in North America, providing insights into their spatial distribution.