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Order‐free co‐regionalized areal data models with application to multiple‐disease mapping

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  • Xiaoping Jin
  • Sudipto Banerjee
  • Bradley P. Carlin

Abstract

Summary. With the ready availability of spatial databases and geographical information system software, statisticians are increasingly encountering multivariate modelling settings featuring associations of more than one type: spatial associations between data locations and associations between the variables within the locations. Although flexible modelling of multivariate point‐referenced data has recently been addressed by using a linear model of co‐regionalization, existing methods for multivariate areal data typically suffer from unnecessary restrictions on the covariance structure or undesirable dependence on the conditioning order of the variables. We propose a class of Bayesian hierarchical models for multivariate areal data that avoids these restrictions, permitting flexible and order‐free modelling of correlations both between variables and across areal units. Our framework encompasses a rich class of multivariate conditionally autoregressive models that are computationally feasible via modern Markov chain Monte Carlo methods. We illustrate the strengths of our approach over existing models by using simulation studies and also offer a real data application involving annual lung, larynx and oesophageal cancer death‐rates in Minnesota counties between 1990 and 2000.

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  • 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.
    • Handle: RePEc:bla:jorssb:v:69:y:2007:i:5:p:817-838
    DOI: 10.1111/j.1467-9868.2007.00612.x
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    References listed on IDEAS

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    1. Mardia, K. V., 1988. "Multi-dimensional multivariate Gaussian Markov random fields with application to image processing," Journal of Multivariate Analysis, Elsevier, vol. 24(2), pages 265-284, February.
    2. Xiaoping Jin & Bradley P. Carlin & Sudipto Banerjee, 2005. "Generalized Hierarchical Multivariate CAR Models for Areal Data," Biometrics, The International Biometric Society, vol. 61(4), pages 950-961, 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. 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.
    5. 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.
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    Citations

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    Cited by:

    1. Mahmoud Torabi, 2014. "Hierarchical Bayesian bivariate disease mapping: analysis of children and adults asthma visits to hospital," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(3), pages 612-621, March.
    2. Marco Gramatica & Peter Congdon & Silvia Liverani, 2021. "Bayesian modelling for spatially misaligned health areal data: A multiple membership approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 645-666, June.
    3. Qian Ren & Sudipto Banerjee, 2013. "Hierarchical Factor Models for Large Spatially Misaligned Data: A Low-Rank Predictive Process Approach," Biometrics, The International Biometric Society, vol. 69(1), pages 19-30, March.
    4. 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.
    5. Ippoliti, L. & Martin, R.J. & Romagnoli, L., 2018. "Efficient likelihood computations for some multivariate Gaussian Markov random fields," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 185-200.
    6. 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.
    7. Esra Kürüm & Danh V. Nguyen & Qi Qian & Sudipto Banerjee & Connie M. Rhee & Damla Şentürk, 2024. "Spatiotemporal multilevel joint modeling of longitudinal and survival outcomes in end-stage kidney disease," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(4), pages 827-852, October.
    8. Ying C. MacNab, 2023. "On coregionalized multivariate Gaussian Markov random fields: construction, parameterization, and Bayesian estimation and inference," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 263-293, March.
    9. Fedele Greco & Carlo Trivisano, 2018. "Comments on: 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 549-553, September.
    10. Moraga, Paula & Lawson, Andrew B., 2012. "Gaussian component mixtures and CAR models in Bayesian disease mapping," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1417-1433.

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