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Likelihood based inference and prediction in spatio-temporal panel count models for urban crimes

Author

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  • Vogler, Jan
  • Liesenfeld, Roman
  • Richard, Jean-Francois
Abstract
PRELIMINARY DRAFT We discuss maximum likelihood (ML) analysis for panel count data models, in which the observed counts are linked via a measurement density to a latent Gaussian process with spatial as well as temporal dynamics and random effects. For likelihood evaluation requiring high-dimensional integration we rely upon Efficient Importance Sampling (EIS). The algorithm we develop extends existing EIS implementations by constructing importance sampling densities, which closely approximate the nontrivial spatio-temporal correlation structure under dynamic spatial panel models. In order to make this high-dimensional approximation computationally feasible, our EIS implementation exploits the typical sparsity of spatial precision matrices in such a way that all the high-dimensional matrix operations it requires can be performed using computationally fast sparse matrix functions. We use the proposed sparse EIS-ML approach for an extensive empirical study analyzing the socio-demographic determinants and the space-time dynamics of urban crime in Pittsburgh, USA, between 2008 and 2013 for a panel of monthly crime rates at census-tract level.

Suggested Citation

  • Vogler, Jan & Liesenfeld, Roman & Richard, Jean-Francois, 2015. "Likelihood based inference and prediction in spatio-temporal panel count models for urban crimes," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113131, Verein für Socialpolitik / German Economic Association.
    • Handle: RePEc:zbw:vfsc15:113131
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    1. Alok Bhargava & J. D. Sargan, 2006. "Estimating Dynamic Random Effects Models From Panel Data Covering Short Time Periods," World Scientific Book Chapters, in: Econometrics, Statistics And Computational Approaches In Food And Health Sciences, chapter 1, pages 3-27, World Scientific Publishing Co. Pte. Ltd..
    2. Gorr, Wilpen & Harries, Richard, 2003. "Introduction to crime forecasting," International Journal of Forecasting, Elsevier, vol. 19(4), pages 551-555.
    3. Gourieroux,Christian & Monfort,Alain, 1997. "Time Series and Dynamic Models," Cambridge Books, Cambridge University Press, number 9780521423083.
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    5. Badi H. Baltagi & Bernard Fingleton & Alain Pirotte, 2014. "Estimating and Forecasting with a Dynamic Spatial Panel Data Model," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(1), pages 112-138, February.
    6. 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.
    7. J. Paul Elhorst, 2014. "Dynamic Spatial Panels: Models, Methods and Inferences," SpringerBriefs in Regional Science, in: Spatial Econometrics, edition 127, chapter 0, pages 95-119, Springer.
    8. Jung, Robert C. & Kukuk, Martin & Liesenfeld, Roman, 2006. "Time series of count data: modeling, estimation and diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2350-2364, December.
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    11. Gorr, Wilpen & Olligschlaeger, Andreas & Thompson, Yvonne, 2003. "Short-term forecasting of crime," International Journal of Forecasting, Elsevier, vol. 19(4), pages 579-594.
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    Cited by:

    1. Golosnoy, Vasyl & Gribisch, Bastian & Seifert, Miriam Isabel, 2019. "Exponential smoothing of realized portfolio weights," Journal of Empirical Finance, Elsevier, vol. 53(C), pages 222-237.
    2. Lim, Krisha & Wichmann, Bruno & Luckert, Martin, 2021. "Adaptation, spatial effects, and targeting: Evidence from Africa and Asia," World Development, Elsevier, vol. 139(C).
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    4. Karsten Schweikert & Manuel Huth & Mark Gius, 2021. "Detecting a copycat effect in school shootings using spatio‐temporal panel count models," Contemporary Economic Policy, Western Economic Association International, vol. 39(4), pages 719-736, October.
    5. Pablo Cadena-Urzúa & Álvaro Briz-Redón & Francisco Montes, 2022. "Crime Analysis of the Metropolitan Region of Santiago de Chile: A Spatial Panel Data Approach," Social Sciences, MDPI, vol. 11(10), pages 1-12, September.

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    More about this item

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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