IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i6p1657-1671.html
   My bibliography  Save this article

Assessing local model adequacy in Bayesian hierarchical models using the partitioned deviance information criterion

Author

Listed:
  • Wheeler, David C.
  • Hickson, DeMarc A.
  • Waller, Lance A.

Abstract

Many diagnostic tools and goodness-of-fit measures, such as the Akaike information criterion (AIC) and the Bayesian deviance information criterion (DIC), are available to evaluate the overall adequacy of linear regression models. In addition, visually assessing adequacy in models has become an essential part of any regression analysis. In this paper, we focus on a spatial consideration of the local DIC measure for model selection and goodness-of-fit evaluation. We use a partitioning of the DIC into the local DIC, leverage, and deviance residuals to assess the local model fit and influence for both individual observations and groups of observations in a Bayesian framework. We use visualization of the local DIC and differences in local DIC between models to assist in model selection and to visualize the global and local impacts of adding covariates or model parameters. We demonstrate the utility of the local DIC in assessing model adequacy using HIV prevalence data from pregnant women in the Butare province of Rwanda during the period 1989-1993 using a range of linear model specifications, from global effects only to spatially varying coefficient models, and a set of covariates related to sexual behavior. Results of applying the diagnostic visualization approach include more refined model selection and greater understanding of the models as applied to the data.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:6:p:1657-1671
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00040-X
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. 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. 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.
    3. 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.
    4. Congdon, P., 2005. "Bayesian predictive model comparison via parallel sampling," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 735-753, April.
    5. 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.
    6. 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.
    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. Cantoni, Eva & Jacot, Nadège & Ghisletta, Paolo, 2024. "Review and comparison of measures of explained variation and model selection in linear mixed-effects models," Econometrics and Statistics, Elsevier, vol. 29(C), pages 150-168.

    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. Gamerman, Dani & Moreira, Ajax R. B., 2004. "Multivariate spatial regression models," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 262-281, November.
    2. Congdon, Peter, 2006. "A model for non-parametric spatially varying regression effects," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 422-445, January.
    3. 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.
    4. Areti Boulieri & Silvia Liverani & Kees Hoogh & Marta Blangiardo, 2017. "A space–time multivariate Bayesian model to analyse road traffic accidents by severity," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(1), pages 119-139, January.
    5. 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.
    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. 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. 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.
    9. 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.
    10. 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.
    11. Mayer Alvo & Jingrui Mu, 2023. "COVID-19 Data Analysis Using Bayesian Models and Nonparametric Geostatistical Models," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    12. Massimo Bilancia & Giacomo Demarinis, 2014. "Bayesian scanning of spatial disease rates with integrated nested Laplace approximation (INLA)," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 71-94, March.
    13. 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.
    14. Francisca Corpas-Burgos & Miguel A. Martinez-Beneito, 2021. "An Autoregressive Disease Mapping Model for Spatio-Temporal Forecasting," Mathematics, MDPI, vol. 9(4), pages 1-17, February.
    15. 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.
    16. Isabel Martínez-Pérez & Verónica González-Iglesias & Valentín Rodríguez Suárez & Ana Fernández-Somoano, 2021. "Spatial Distribution of Hospitalizations for Ischemic Heart Diseases in the Central Region of Asturias, Spain," IJERPH, MDPI, vol. 18(23), pages 1-10, November.
    17. F. Corpas-Burgos & P. Botella-Rocamora & M. A. Martinez-Beneito, 2019. "On the convenience of heteroscedasticity in highly multivariate disease mapping," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1229-1250, December.
    18. Alexandra Schmidt & Ajax Moreira & Steven Helfand & Thais Fonseca, 2009. "Spatial stochastic frontier models: accounting for unobserved local determinants of inefficiency," Journal of Productivity Analysis, Springer, vol. 31(2), pages 101-112, April.
    19. Maike Tahden & Juliane Manitz & Klaus Baumgardt & Gerhard Fell & Thomas Kneib & Guido Hegasy, 2016. "Epidemiological and Ecological Characterization of the EHEC O104:H4 Outbreak in Hamburg, Germany, 2011," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-19, October.
    20. Marc Marí-Dell’Olmo & Miguel Ángel Martínez-Beneito, 2015. "A Multilevel Regression Model for Geographical Studies in Sets of Non-Adjacent Cities," PLOS ONE, Public Library of Science, vol. 10(8), pages 1-12, August.

    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:csdana:v:54:y:2010:i:6:p:1657-1671. 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/locate/csda .

    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.