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

Roman Liesenfeld ^a

Jean-François Richard ^b

Jan Vogler ^a

^aInstitut für Ökonometrie und Statistik, Universität Köln, Cologne, Germany

^bDepartment of Economics, University of Pittsburgh, PA, USA

Spatial Econometrics: Qualitative and Limited Dependent Variables

ISBN: 978-1-78560-986-2, eISBN: 978-1-78560-985-5

Publication date: 1 December 2016

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.

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Acknowledgements

Acknowledgments

The authors thank the anonymous referee for its helpful and constructive comments. They also thank Jason Brown for providing the firm location choice data set used in this paper and Albrecht Mengel for providing access to the grid computing facilities of the Institute of Statistics and Econometrics at University of Kiel. R. Liesenfeld and J. Vogler acknowledge support by the Deutsche Forschungsgemeinschaft (grant LI 901/3-1). For the helpful comments and suggestions they provided on earlier versions of the paper, we thank seminar and conference participants at the University of Kiel, University of Cologne, University of Université catholique de Louvain (CORE), Erasmus University of Rotterdam, 2013 Spatial Statistics conference (Ohio), the 2013 Econometric Society European Meeting (Gothenburg), the 2013 International Conference on Computational and Financial Econometrics (London), the 2014 World Conference of the Spatial Econometrics Association (Zürich), the 2014 International Conference on Computational Statistics (Geneva), the 2014 ERSA Congress (Saint Petersburg), the Statistische Woche 2014 (Hannover) and the 2015 Advances in Econometrics Conference (Louisiana State University). A former version of this paper circulated under the title “Analysis of discrete-dependent variable models with spatial correlation.”

Citation

Liesenfeld, R., Richard, J.-F. and Vogler, J. (2016), "Likelihood Evaluation of High-Dimensional Spatial Latent Gaussian Models with Non-Gaussian Response Variables", Spatial Econometrics: Qualitative and Limited Dependent Variables (Advances in Econometrics, Vol. 37), Emerald Group Publishing Limited, Leeds, pp. 35-77. https://doi.org/10.1108/S0731-905320160000037009

Publisher

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Emerald Group Publishing Limited