IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/ws085820.html
   My bibliography  Save this paper

Smooth-car mixed models for spatial count data

Author

Listed:
  • Lee, Dae-Jin
  • Durbán, María

Abstract

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.

Suggested Citation

  • Lee, Dae-Jin & Durbán, María, 2008. "Smooth-car mixed models for spatial count data," DES - Working Papers. Statistics and Econometrics. WS ws085820, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws085820
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/869b0d07-9507-4311-84e3-8447f76bb5de/content
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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, April.
    2. Thomas Kneib & Ludwig Fahrmeir, 2006. "Structured Additive Regression for Categorical Space–Time Data: A Mixed Model Approach," Biometrics, The International Biometric Society, vol. 62(1), pages 109-118, March.
    3. Simon N. Wood, 2006. "Low-Rank Scale-Invariant Tensor Product Smooths for Generalized Additive Mixed Models," Biometrics, The International Biometric Society, vol. 62(4), pages 1025-1036, December.
    4. 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, March.
    5. Eilers, Paul H.C. & Currie, Iain D. & Durban, Maria, 2006. "Fast and compact smoothing on large multidimensional grids," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 61-76, January.
    6. Marx, Brian D. & Eilers, Paul H. C., 1998. "Direct generalized additive modeling with penalized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 193-209, August.
    7. 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.
    8. 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.
    9. 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.
    10. Hinde, John & Demetrio, Clarice G. B., 1998. "Overdispersion: Models and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 27(2), pages 151-170, April.
    11. 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.
    12. 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, March.
    13. Congdon, Peter, 2006. "A model for non-parametric spatially varying regression effects," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 422-445, January.
    14. 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, January.
    15. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
    16. 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, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lee, Dae-Jin & Durbán, María, 2009. "Smooth-CAR mixed models for spatial count data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2968-2979, June.
    2. Lee, Dae-Jin & Durbán, María, 2009. "P-spline anova-type interaction models for spatio-temporal smoothing," DES - Working Papers. Statistics and Econometrics. WS ws093312, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
    4. Lee, Dae-Jin & Ayma Anza, Diego Armando & Durbán, María & Eilers, Paul, 2015. "Penalized composite link mixed models for two-dimensional count data," DES - Working Papers. Statistics and Econometrics. WS ws1509, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Nicole H. Augustin & Stefan Lang & Monica Musio & Klaus Von Wilpert, 2007. "A spatial model for the needle losses of pine‐trees in the forests of Baden‐Württemberg: an application of Bayesian structured additive regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(1), pages 29-50, January.
    6. Rodríguez-Álvarez, María Xosé & Lee, Dae-Jin & Kneib, Thomas & Durbán, María & Eilers, Paul, 2013. "Fast algorithm for smoothing parameter selection in multidimensional generalized P-splines," DES - Working Papers. Statistics and Econometrics. WS ws133026, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. María Xosé Rodríguez‐Álvarez & María Durbán & Paul H.C. Eilers & Dae‐Jin Lee & Francisco Gonzalez, 2023. "Multidimensional adaptive P‐splines with application to neurons' activity studies," Biometrics, The International Biometric Society, vol. 79(3), pages 1972-1985, September.
    8. Simon N. Wood & Zheyuan Li & Gavin Shaddick & Nicole H. Augustin, 2017. "Generalized Additive Models for Gigadata: Modeling the U.K. Black Smoke Network Daily Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1199-1210, July.
    9. Lee, Dae-Jin & Durbán, María & Eilers, Paul, 2013. "Efficient two-dimensional smoothing with P-spline ANOVA mixed models and nested bases," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 22-37.
    10. Lee, Dae-Jin, 2019. "Out-of-sample prediction in multidimensional P-spline models," DES - Working Papers. Statistics and Econometrics. WS 28630, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Militino, A.F. & Goicoa, T. & Ugarte, M.D., 2012. "Estimating the percentage of food expenditure in small areas using bias-corrected P-spline based estimators," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2934-2948.
    12. Ayma Anza, Diego Armando & Durbán, María & Lee, Dae-Jin & Van de Kassteele, Jan, 2016. "Modelling latent trends from spatio-temporally grouped data using composite link mixed models," DES - Working Papers. Statistics and Econometrics. WS 23448, Universidad Carlos III de Madrid. Departamento de Estadística.
    13. Belitz, Christiane & Lang, Stefan, 2008. "Simultaneous selection of variables and smoothing parameters in structured additive regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 61-81, September.
    14. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.
    15. Lee, Wang-Sheng & McKinnish, Terra, 2019. "Locus of control and marital satisfaction: Couple perspectives using Australian data," Journal of Economic Psychology, Elsevier, vol. 74(C).
    16. Mariola Sánchez-González & María Durbán & Dae-Jin Lee & Isabel Cañellas & Hortensia Sixto, 2017. "Smooth additive mixed models for predicting aboveground biomass," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(1), pages 23-41, March.
    17. Lihui Zhao & Tom Chen & Vladimir Novitsky & Rui Wang, 2021. "Joint penalized spline modeling of multivariate longitudinal data, with application to HIV‐1 RNA load levels and CD4 cell counts," Biometrics, The International Biometric Society, vol. 77(3), pages 1061-1074, September.
    18. Román Mínguez & Roberto Basile & María Durbán, 2020. "An alternative semiparametric model for spatial panel data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 669-708, December.
    19. Arūnas P. Verbyla & Joanne Faveri & John D. Wilkie & Tom Lewis, 2018. "Tensor Cubic Smoothing Splines in Designed Experiments Requiring Residual Modelling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(4), pages 478-508, December.
    20. Alba Carballo & María Durbán & Dae-Jin Lee, 2021. "Out-of-Sample Prediction in Multidimensional P-Spline Models," Mathematics, MDPI, vol. 9(15), pages 1-23, July.

    More about this item

    Keywords

    Mixed models;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cte:wsrepe:ws085820. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.