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

See all articles by Roman Liesenfeld

Roman Liesenfeld

University of Cologne, Department of Economics

Jean-Francois Richard

University of Pittsburgh - Department of Economics

Jan Vogler

University of Cologne, Department of Economics

Date Written: February 25, 2015

Abstract

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

Suggested Citation

Liesenfeld, Roman and Richard, Jean-Francois and Vogler, Jan, Likelihood Evaluation of High-Dimensional Spatial Latent Gaussian Models with Non-Gaussian Response Variables (February 25, 2015). Available at SSRN: https://ssrn.com/abstract=2196041 or http://dx.doi.org/10.2139/ssrn.2196041

Roman Liesenfeld (Contact Author)

University of Cologne, Department of Economics ( email )

Albertus-Magnus-Platz
D-50931 Köln
Germany

Jean-Francois Richard

University of Pittsburgh - Department of Economics ( email )

4901 Wesley Posvar Hall
230 South Bouquet Street
Pittsburgh, PA 15260
United States
412-648-1750 (Phone)

Jan Vogler

University of Cologne, Department of Economics ( email )

Albertus-Magnus-Platz
Cologne, 50923
Germany

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