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A Reproducing Kernel-Based Spatial Model in Poisson Regressions

Author

Listed:
  • Zhang Hongmei

    (University of South Carolina - Columbia)

  • Gan Jianjun

    (GlaxoSmithKline)

Abstract

A semi-parametric spatial model for spatial dependence is proposed in Poisson regressions to study the effects of risk factors on incidence outcomes. The spatial model is constructed through an application of reproducing kernels. A Bayesian framework is proposed to infer the unknown parameters. Simulations are performed to compare the reproducing kernel-based method with several commonly used approaches in spatial modeling, including independent Gaussian and CAR models. Compared with these models, the reproducing kernel-based method is easy to implement and more flexible in terms of the ability to model various spatial dependence patterns. To further demonstrate the proposed method, two real data applications are discussed: Scottish lip cancer data and Florida smoke-related cancer data.

Suggested Citation

  • Zhang Hongmei & Gan Jianjun, 2012. "A Reproducing Kernel-Based Spatial Model in Poisson Regressions," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-26, October.
    • Handle: RePEc:bpj:ijbist:v:8:y:2012:i:1:n:28
    DOI: 10.1515/1557-4679.1360
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    References listed on IDEAS

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    1. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    2. Dawei Liu & Xihong Lin & Debashis Ghosh, 2007. "Semiparametric Regression of Multidimensional Genetic Pathway Data: Least-Squares Kernel Machines and Linear Mixed Models," Biometrics, The International Biometric Society, vol. 63(4), pages 1079-1088, December.
    3. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    4. Kate E. Jones & Nikkita G. Patel & Marc A. Levy & Adam Storeygard & Deborah Balk & John L. Gittleman & Peter Daszak, 2008. "Global trends in emerging infectious diseases," Nature, Nature, vol. 451(7181), pages 990-993, February.
    5. Kelsall J. & Eld J.W., 2002. "Modeling Spatial Variation in Disease Risk: A Geostatistical Approach," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 692-701, September.
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