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Hierarchical Poisson models for spatial count data

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  • De Oliveira, Victor

Abstract

This work proposes a class of hierarchical models for geostatistical count data that includes the model proposed by Diggle et al. (1998) [13] as a particular case. For this class of models the main second-order properties of the count variables are derived, and three models within this class are studied in some detail. It is shown that for this class of models there is a close connection between the correlation structure of the counts and their overdispersions, and this property can be used to explore the flexibility of the correlation structures of these models. It is suggested that the models in this class may not be adequate to represent data consisting mostly of small counts with substantial spatial correlation. Three geostatistical count datasets are used to illustrate these issues and suggest how the results might be used to guide the selection of a model within this class.

Suggested Citation

  • De Oliveira, Victor, 2013. "Hierarchical Poisson models for spatial count data," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 393-408.
  • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:393-408
    DOI: 10.1016/j.jmva.2013.08.015
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    References listed on IDEAS

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    1. Jo Eidsvik & Sara Martino & Håvard Rue, 2009. "Approximate Bayesian Inference in Spatial Generalized Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 1-22, March.
    2. Virginia Recta & Murali Haran & James L. Rosenberger, 2012. "A two‐stage model for incidence and prevalence in point‐level spatial count data," Environmetrics, John Wiley & Sons, Ltd., vol. 23(2), pages 162-174, March.
    3. Robin Henderson, 2003. "A serially correlated gamma frailty model for longitudinal count data," Biometrika, Biometrika Trust, vol. 90(2), pages 355-366, June.
    4. Ipek Sener & Chandra Bhat, 2012. "Flexible spatial dependence structures for unordered multinomial choice models: formulation and application to teenagers’ activity participation," Transportation, Springer, vol. 39(3), pages 657-683, May.
    5. Chib, Siddhartha & Winkelmann, Rainer, 2001. "Markov Chain Monte Carlo Analysis of Correlated Count Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 428-435, October.
    6. Gilles Guillot & Niklas Lorén & Mats Rudemo, 2009. "Spatial prediction of weed intensities from exact count data and image‐based estimates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 525-542, September.
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