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Smooth-car mixed models for spatial count data

Listed author(s):
  • Durbán, María
  • Lee, Dae-Jin
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    Penalized splines (P-splines) and individual random effects are used for the analysis of spatial count data. P-splines are represented as mixed models to give a unified approach to the model estimation procedure. First, a model where the spatial variation is modelled by a two-dimensional P-spline at the centroids of the areas or regions is considered. In addition, individual area-effects are incorporated as random effects to account for individual variation among regions. Finally, the model is extended by considering a conditional autoregressive (CAR) structure for the random effects, these are the so called “Smooth-CAR” models, with the aim of separating the large-scale geographical trend, and local spatial correlation. The methodology proposed is applied to the analysis of lip cancer incidence rates in Scotland.

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    Paper provided by Universidad Carlos III de Madrid. Departamento de Estadística in its series DES - Working Papers. Statistics and Econometrics. WS with number ws085820.

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    Date of creation: Nov 2008
    Handle: RePEc:cte:wsrepe:ws085820
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    1. I. D. Currie & M. Durban & P. H. C. Eilers, 2006. "Generalized linear array models with applications to multidimensional smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 259-280.
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    3. Arũnas P. Verbyla & Brian R. Cullis & Michael G. Kenward & Sue J. Welham, 1999. "The Analysis of Designed Experiments and Longitudinal Data by Using Smoothing Splines," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 269-311.
    4. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400.
    5. Sally W. Thurston & M. P. Wand & John K. Wiencke, 2000. "Negative Binomial Additive Models," Biometrics, The International Biometric Society, vol. 56(1), pages 139-144, 03.
    6. Congdon, Peter, 2007. "Mixtures of spatial and unstructured effects for spatially discontinuous health outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3197-3212, March.
    7. Hinde, John & Demetrio, Clarice G. B., 1998. "Overdispersion: Models and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 27(2), pages 151-170, April.
    8. C. B. Dean & M. D. Ugarte & A. F. Militino, 2001. "Detecting Interaction Between Random Region and Fixed Age Effects in Disease Mapping," Biometrics, The International Biometric Society, vol. 57(1), pages 197-202, 03.
    9. Congdon, Peter, 2006. "A model for non-parametric spatially varying regression effects," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 422-445, January.
    10. E. E. Kammann & M. P. Wand, 2003. "Geoadditive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 1-18.
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