A Computationally Efficient Projection-Based Approach for Spatial Generalized Linear Mixed Models

TL;DR

This paper introduces a computationally efficient projection-based method for spatial generalized linear mixed models that reduces dimensionality, improves inference speed, and mitigates spatial confounding, demonstrated through simulations and real data applications.

Contribution

The paper proposes a novel reduced-dimensional approach using random projections for SGLMMs, enhancing computational efficiency and inference accuracy over existing methods.

Findings

Method speeds up Bayesian inference for high-dimensional SGLMMs.

Reduced-dimensional approach compares favorably to existing reduced-rank methods.

Successful applications to bird count and rock type classification data.

Abstract

Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain Monte Carlo (MCMC) algorithms for these models tend to be slow mixing. Moreover, spatial confounding inflates the variance of fixed effect (regression coefficient) estimates. Our approach addresses both the computational and confounding issues by replacing the high-dimensional spatial random effects with a reduced-dimensional representation based on random projections. Standard MCMC algorithms mix well and the reduced-dimensional setting speeds up computations per iteration. We show, via simulated examples, that Bayesian inference for this reduced-dimensional approach works well both in terms of inference as well as prediction, our methods also compare favorably to existing "reduced-rank" approaches. We also apply our methods to two real world data examples, one on bird count data and the other classifying rock types.