IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v109y2012icp88-102.html
   My bibliography  Save this article

Bayesian spatial models with a mixture neighborhood structure

Author

Listed:
  • Rodrigues, E.C.
  • Assunção, R.

Abstract

In Bayesian disease mapping, one needs to specify a neighborhood structure to make inference about the underlying geographical relative risks. We propose a model in which the neighborhood structure is part of the parameter space. We retain the Markov property of the typical Bayesian spatial models: given the neighborhood graph, disease rates follow a conditional autoregressive model. However, the neighborhood graph itself is a parameter that also needs to be estimated. We investigate the theoretical properties of our model. In particular, we investigate carefully the prior and posterior covariance matrix induced by this random neighborhood structure, providing interpretation for each element of these matrices.

Suggested Citation

  • Rodrigues, E.C. & Assunção, R., 2012. "Bayesian spatial models with a mixture neighborhood structure," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 88-102.
    • Handle: RePEc:eee:jmvana:v:109:y:2012:i:c:p:88-102
    DOI: 10.1016/j.jmva.2012.02.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12000589
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.02.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Leonhard Knorr‐Held & Nicola G. Best, 2001. "A shared component model for detecting joint and selective clustering of two diseases," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(1), pages 73-85.
    2. Gelfand A.E. & Kim H-J. & Sirmans C.F. & Banerjee S., 2003. "Spatial Modeling With Spatially Varying Coefficient Processes," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 387-396, January.
    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. White, Gentry & Ghosh, Sujit K., 2009. "A stochastic neighborhood conditional autoregressive model for spatial data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3033-3046, June.
    5. 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.
    6. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Earl W Duncan & Kerrie L Mengersen, 2020. "Comparing Bayesian spatial models: Goodness-of-smoothing criteria for assessing under- and over-smoothing," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-28, May.
    2. Osafu Augustine Egbon & Omodolapo Somo-Aina & Ezra Gayawan, 2021. "Spatial Weighted Analysis of Malnutrition Among Children in Nigeria: A Bayesian Approach," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(3), pages 495-523, December.
    3. I. Gede Nyoman Mindra Jaya & Henk Folmer, 2020. "Bayesian spatiotemporal mapping of relative dengue disease risk in Bandung, Indonesia," Journal of Geographical Systems, Springer, vol. 22(1), pages 105-142, January.
    4. Douglas R. M. Azevedo & Marcos O. Prates & Dipankar Bandyopadhyay, 2021. "MSPOCK: Alleviating Spatial Confounding in Multivariate Disease Mapping Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 464-491, September.
    5. Gehong Zhang & Junming Li & Sijin Li & Yang Wang, 2018. "Exploring Spatial Trends and Influencing Factors for Gastric Cancer Based on Bayesian Statistics: A Case Study of Shanxi, China," IJERPH, MDPI, vol. 15(9), pages 1-17, August.

    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. Douglas R. M. Azevedo & Marcos O. Prates & Dipankar Bandyopadhyay, 2021. "MSPOCK: Alleviating Spatial Confounding in Multivariate Disease Mapping Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 464-491, September.
    2. Li Xu & Qingshan Jiang & David R. Lairson, 2019. "Spatio-Temporal Variation of Gender-Specific Hypertension Risk: Evidence from China," IJERPH, MDPI, vol. 16(22), pages 1-26, November.
    3. Congdon, Peter, 2006. "A model for non-parametric spatially varying regression effects," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 422-445, January.
    4. Keunseo Kim & Hyojoong Kim & Vinnam Kim & Heeyoung Kim, 2020. "A Multiscale Spatially Varying Coefficient Model for Regional Analysis of Topsoil Geochemistry," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 74-89, March.
    5. Ropo E. Ogunsakin & Themba G. Ginindza, 2022. "Bayesian Spatial Modeling of Diabetes and Hypertension: Results from the South Africa General Household Survey," IJERPH, MDPI, vol. 19(15), pages 1-17, July.
    6. Chen, Yewen & Chang, Xiaohui & Luo, Fangzhi & Huang, Hui, 2023. "Additive dynamic models for correcting numerical model outputs," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    7. Cindy Xin Feng, 2015. "Bayesian joint modeling of correlated counts data with application to adverse birth outcomes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(6), pages 1206-1222, June.
    8. Quick, Matthew & Li, Guangquan & Brunton-Smith, Ian, 2018. "Crime-general and crime-specific spatial patterns: A multivariate spatial analysis of four crime types at the small-area scale," Journal of Criminal Justice, Elsevier, vol. 58(C), pages 22-32.
    9. Kassahun Abere Ayalew & Samuel Manda & Bo Cai, 2021. "A Comparison of Bayesian Spatial Models for HIV Mapping in South Africa," IJERPH, MDPI, vol. 18(21), pages 1-10, October.
    10. Alexander Razen & Stefan Lang & Judith Santer, 2016. "Estimation of Spatially Correlated Random Scaling Factors based on Markov Random Field Priors," Working Papers 2016-33, Faculty of Economics and Statistics, Universität Innsbruck.
    11. Ying C. MacNab, 2018. "Some recent work on multivariate Gaussian Markov random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 497-541, September.
    12. Jane Law & Christopher Perlman, 2018. "Exploring Geographic Variation of Mental Health Risk and Service Utilization of Doctors and Hospitals in Toronto: A Shared Component Spatial Modeling Approach," IJERPH, MDPI, vol. 15(4), pages 1-13, March.
    13. Qingyun Du & Mingxiao Zhang & Yayan Li & Hui Luan & Shi Liang & Fu Ren, 2016. "Spatial Patterns of Ischemic Heart Disease in Shenzhen, China: A Bayesian Multi-Disease Modelling Approach to Inform Health Planning Policies," IJERPH, MDPI, vol. 13(4), pages 1-14, April.
    14. Ping Yin & Lan Mu & Marguerite Madden & John Vena, 2014. "Hierarchical Bayesian modeling of spatio-temporal patterns of lung cancer incidence risk in Georgia, USA: 2000–2007," Journal of Geographical Systems, Springer, vol. 16(4), pages 387-407, October.
    15. Xiaoping Jin & Sudipto Banerjee & Bradley P. Carlin, 2007. "Order‐free co‐regionalized areal data models with application to multiple‐disease mapping," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 817-838, November.
    16. Wheeler, David C. & Hickson, DeMarc A. & Waller, Lance A., 2010. "Assessing local model adequacy in Bayesian hierarchical models using the partitioned deviance information criterion," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1657-1671, June.
    17. Gamerman, Dani & Moreira, Ajax R. B., 2004. "Multivariate spatial regression models," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 262-281, November.
    18. G. Vicente & T. Goicoa & P. Fernandez‐Rasines & M. D. Ugarte, 2020. "Crime against women in India: unveiling spatial patterns and temporal trends of dowry deaths in the districts of Uttar Pradesh," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 655-679, February.
    19. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    20. Eibich, Peter & Ziebarth, Nicolas, 2014. "Examining the Structure of Spatial Health Effects in Germany Using Hierarchical Bayes Models," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 49, pages 305-320.

    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:eee:jmvana:v:109:y:2012:i:c:p:88-102. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.