Likelihood Evaluation of High-Dimensional Spatial Latent Gaussian Models with Non-Gaussian Response Variables
42 Pages Posted: 4 Jan 2013 Last revised: 16 Apr 2015
Date Written: February 25, 2015
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.
Keywords: count data models, discrete choice models, firm location choice, importance sampling, Monte Carlo integration, spatial econometrics
JEL Classification: C15, C21, C25, D22, R12
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