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

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  • Jean-François Richard

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.

Suggested Citation

  • Jean-François Richard, 2015. "Likelihood Evaluation of High-Dimensional Spatial Latent Gaussian Models with Non-Gaussian Response Variables," Working Paper 5778, Department of Economics, University of Pittsburgh.
  • Handle: RePEc:pit:wpaper:5778
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    File URL: https://www.econ.pitt.edu/sites/default/files/working_papers/WP15-006.pdf
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    References listed on IDEAS

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    1. Jung, Robert C. & Liesenfeld, Roman & Richard, Jean-François, 2011. "Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 73-85.
    2. Roman Liesenfeld & Jean-François Richard, 2006. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 335-360.
    3. Robert C. Jung & Roman Liesenfeld & Jean-François Richard, 2011. "Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 73-85, January.
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    5. Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
    6. Heijnen, P. & Samarina, A.. & Jacobs, J.P.A.M. & Elhorst, J.P., 2013. "State transfers at different moments in time," Research Report 13006-EEF, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    7. Buczkowska, Sabina & de Lapparent, Matthieu, 2014. "Location choices of newly created establishments: Spatial patterns at the aggregate level," Regional Science and Urban Economics, Elsevier, vol. 48(C), pages 68-81.
    8. Wang, Honglin & Iglesias, Emma M. & Wooldridge, Jeffrey M., 2013. "Partial maximum likelihood estimation of spatial probit models," Journal of Econometrics, Elsevier, vol. 172(1), pages 77-89.
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    11. Xiaokun Wang & Kara M. Kockelman, 2009. "Baysian Inference For Ordered Response Data With A Dynamic Spatial-Ordered Probit Model," Journal of Regional Science, Wiley Blackwell, vol. 49(5), pages 877-913.
    12. Lambert, Dayton M. & Brown, Jason P. & Florax, Raymond J.G.M., 2010. "A two-step estimator for a spatial lag model of counts: Theory, small sample performance and an application," Regional Science and Urban Economics, Elsevier, vol. 40(4), pages 241-252, July.
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    14. Kleppe, Tore Selland & Skaug, Hans Julius, 2012. "Fitting general stochastic volatility models using Laplace accelerated sequential importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3105-3119.
    15. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
    16. James P. LeSage & Manfred M. Fischer & Thomas Scherngell, 2007. "Knowledge spillovers across Europe: Evidence from a Poisson spatial interaction model with spatial effects," Papers in Regional Science, Wiley Blackwell, vol. 86(3), pages 393-421, August.
    17. Roman Liesenfeld & Guilherme V. Moura & Jean-François Richard & Hariharan Dharmarajan, 2013. "Efficient Likelihood Evaluation of State-Space Representations," Review of Economic Studies, Oxford University Press, vol. 80(2), pages 538-567.
    18. Christian M. Hafner & Hans Manner, 2012. "Dynamic stochastic copula models: estimation, inference and applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(2), pages 269-295, March.
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    22. Roman Liesenfeld & Guilherme Valle Moura & Jean-François Richard, 2010. "Determinants and Dynamics of Current Account Reversals: An Empirical Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(4), pages 486-517, August.
    23. Vijverberg, Wim P. M., 1997. "Monte Carlo evaluation of multivariate normal probabilities," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 281-307.
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    Cited by:

    1. Jean-François Richard, 2015. "Likelihood Based Inference and Prediction in Spatio-temporal Panel Count Models for Urban Crimes," Working Paper 5657, Department of Economics, University of Pittsburgh.
    2. repec:wly:japmet:v:32:y:2017:i:3:p:600-620 is not listed on IDEAS
    3. Roman Liesenfeld & Jean‐François Richard & Jan Vogler, 2017. "Likelihood‐Based Inference and Prediction in Spatio‐Temporal Panel Count Models for Urban Crimes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(3), pages 600-620, April.

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