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Modeling Poisson variables with positive spatial dependence

Author

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  • Kaiser, Mark S.
  • Cressie, Noel

Abstract

The Poisson auto-model is a natural vehicle for modeling data that consist of small counts and may exhibit dependence, frequently spatial dependence. Unfortunately, it is not possible to model positive dependence with a regular Poisson auto-model. We develop a model that allows positive dependencies in multivariate count data by specifying conditional distributions as Winsorized Poisson probability mass functions. This model may be used to incorporate either positive or negative dependencies among the variables.

Suggested Citation

  • Kaiser, Mark S. & Cressie, Noel, 1997. "Modeling Poisson variables with positive spatial dependence," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 423-432, November.
    • Handle: RePEc:eee:stapro:v:35:y:1997:i:4:p:423-432
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    Citations

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    Cited by:

    1. Liesenfeld, Roman & Richard, Jean-François & Vogler, Jan, 2013. "Analysis of discrete dependent variable models with spatial correlation," Economics Working Papers 2013-01, Christian-Albrechts-University of Kiel, Department of Economics.
    2. Isabel Proença & Ludgero Glórias, 2021. "Revisiting the Spatial Autoregressive Exponential Model for Counts and Other Nonnegative Variables, with Application to the Knowledge Production Function," Sustainability, MDPI, vol. 13(5), pages 1-22, March.
    3. Haining, Robert & Law, Jane & Griffith, Daniel, 2009. "Modelling small area counts in the presence of overdispersion and spatial autocorrelation," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2923-2937, June.
    4. 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.
    5. Pushpakanthie Wijekoon & Alwell Oyet & Brajendra C. Sutradhar, 2019. "Pair-Wise Family-Based Correlation Model for Spatial Count Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 133-184, June.
    6. Angel Alañon-Pardo & Patrick J. Walsh & Rafael Myro, 2018. "Do neighboring municipalities matter in industrial location decisions? Empirical evidence from Spain," Empirical Economics, Springer, vol. 55(3), pages 1145-1179, November.
    7. Roberto Cellini & Tiziana Cuccia & Domenico Lisi, 2020. "Spatial dependence in museum services: an analysis of the Italian case," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 44(4), pages 535-562, December.
    8. Mabel Morales-Otero & Vicente Núñez-Antón, 2021. "Comparing Bayesian Spatial Conditional Overdispersion and the Besag–York–Mollié Models: Application to Infant Mortality Rates," Mathematics, MDPI, vol. 9(3), pages 1-33, January.
    9. Lee, Jaehyung & Kaiser, Mark S. & Cressie, Noel, 2001. "Multiway Dependence in Exponential Family Conditional Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 171-190, November.
    10. Angel Alañón Pardo & Josep Maria Arauzo Carod, 2009. "Accessibility and Industrial Location: evidence from Spain," Documentos de trabajo de la Facultad de Ciencias Económicas y Empresariales 09-01, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
    11. Daniel A. Griffith, 2024. "Comments on the Bernoulli Distribution and Hilbe’s Implicit Extra-Dispersion," Stats, MDPI, vol. 7(1), pages 1-15, March.
    12. David Mushinski & Stephan Weiler & Benjamin Widner, 2014. "The impact of retail establishments in hinterlands on the export role of retail establishments in rural places," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(2), pages 469-487, March.
    13. Balakrishnan, N. & Jones, M.C., 2022. "Closure of beta and Dirichlet distributions under discrete mixing," Statistics & Probability Letters, Elsevier, vol. 188(C).
    14. Ángel Alanón & Rafael Myro, "undated". "Does neighboring "industrial atmosphere" matter in industrial location?. Empirical evidence from Spanish municipalities," Studies on the Spanish Economy 199, FEDEA.
    15. Griffith, Daniel A., 2002. "A spatial filtering specification for the auto-Poisson model," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 245-251, July.

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