Likelihood Evaluation of High-Dimensional Spatial Latent Gaussian Models with Non-Gaussian Response Variables

We propose a generic algorithm for numerically accurate likelihood evaluation of a broad class of spatial models characterized by a high-dimensional latent Gaussian process and non-Gaussian response variables.The class of models under consideration includes specifications for discrete choices, event counts and limited dependent variables (truncation, censoring, and sample selection) among others.Our algorithm relies upon a novel implementation of Efficient Importance Sampling (EIS) specifically designed to exploit typical sparsity of high-dimensional spatial precision (or covariance) matrices. It is numerically very accurate and computationally feasible even for very high-dimensional latent processes. Thus Maximum Likelihood (ML) estimation of high-dimensional non-Gaussian spatial models, hitherto considered to be computationally prohibitive, becomes feasible. We illustrate our approach with ML estimation of a spatial probit for US presidential voting decisions and spatial count data models (Poisson and Negbin) for firm location choices.