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

Computational Statistics and Data Analysis

Volumn 54, Issue 6, 2010, Pages 1657-1671

  Wheeler, David C ^a   Hickson, DeMarc A ^b   Waller, Lance A ^c  

^a NATIONAL CANCER INSTITUTE   (United States)

^b UNIVERSITY OF MISSISSIPPI SCHOOL OF MEDICINE   (United States)

^c EMORY UNIVERSITY   (United States)

Author keywords

Bayesian statistics; DIC; Hierarchical models; HIV; Linear models; Rwanda; Spatial statistics

Indexed keywords

AKAIKE INFORMATION CRITERION; ASSESSING MODEL; BAYESIAN; BAYESIAN FRAMEWORKS; BAYESIAN HIERARCHICAL MODEL; BAYESIAN STATISTICS; COVARIATES; DIAGNOSTIC TOOLS; GLOBAL EFFECTS; GOODNESS OF FIT; GOODNESS-OF-FIT MEASURE; HIERARCHICAL MODEL; INFORMATION CRITERION; LINEAR MODEL; LINEAR REGRESSION MODELS; LOCAL IMPACTS; LOCAL MODEL; MODEL PARAMETERS; MODEL SELECTION; PREGNANT WOMAN; REFINED MODEL; SPATIAL STATISTICS; VARYING COEFFICIENT MODEL;

BAYESIAN NETWORKS; HIERARCHICAL SYSTEMS; MATHEMATICAL MODELS; REGRESSION ANALYSIS; VIRUSES; VISUALIZATION;

DATA VISUALIZATION;

EID: 77249093462     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2010.01.025     Document Type: Article

References (44)

1. Akaike H. Information theory and an extension of the maximum likelihood principle. In: Petrov B.N., and Csaki F. (Eds). 2nd International Symposium on Information Theory (1973), Akademiai Kiado, Budapest 267-281
2. Allen S., Van de Perre P., Serufiliram A., Lepage P., Carael M., DeClercq A., Tice J., Black D., Nsengumuremyi F., Ziegler J., Levy L., and Hulley S. Human immunodeficiency virus and malaria in a representative sample of childbearing women in Kigali, Rwanda. Journal of Infectious Diseases 164 (1991) 67-71
3. Anselin L. GeoDa 0.9 User's Guide (2003)
4. Banerjee S., Carlin B., and Gelfand A. Hierarchical Modeling and Analysis for Spatial Data (2004), Chapman & Hall/CRC, Boca Raton, FL
5. Besag J., York J., and Mollie A. Bayesian image restoration, with two applications in spatial statistics (with discussion). Annals of the Institute of Statistical Mathematics 43 (1991) 1-59
6. Best N.G., Arnold R.A., Thomas A., Waller L.A., and Conlon E.M. Bayesian models for spatially correlated disease and exposure data. In: Bernardo J.M., Berger J.O., Dawid A.P., and Smith A.F.M. (Eds). Bayesian Statistics, vol. 6 (1999), Oxford University Press, Oxford, UK 131-156
7. Boerma J.T., Urassa M., Senkoro K., Klokke A., and Ngweshemi J.Z. Spread of HIV infection in a rural area of Tanzania. AIDS 13 (1999) 1233-1240
8. Bucyendore A., Van de Perre P., Karita E., Nziyumvia A., Sow I., and Fox E. Estimating the seroincidence of HIV-1 in the general adult population in Kigali, Rwanda. AIDS 7 (1993) 275-277
9. Bulterys M., Chao A., Habimana P., Dushimimana A., Nawrocki P., and Saah A. Incident HIV-1 infection in a cohort of young women in Butare, Rwanda. AIDS 8 (1994) 1585-1591
10. Burnham K.P., and Anderson D.R. Model Selection and Multimodel Inference: A Practical Information-theoretic Approach. 2nd ed (2002), Springer-Verlag, New York
11. Carlin B.P., and Louis T.A. Bayesian Methods for Data Analysis. 3rd ed (2009), Chapman & Hall/CRC, Boca Raton, FL
12. Chambers J.M., Cleveland W.S., Kleiner B., and Tukey P.A. Graphical Methods for Data Analysis (1983), Wadsworth & Brooks/Cole, Pacific Grove, CA
13. Chao A., Bulterys M., Musanganire F., Habimana P., Nawrocki P., Taylor E., Dushimimana A., and Saah A. Risk factors associated with prevalent HIV-1 infection among pregnant women in Rwanda. International Journal of Epidemiology 23 (1994) 371-380
14. Cleveland W.S., and McGill M.E. Dynamic Graphics for Statistics (1988), Wadsworth, Monterey, CA
15. Congdon P. Bayesian predictive model comparison via parallel sampling. Computational Statistics & Data Analysis 48 (2005) 735-753
16. Congdon P. Mixtures of spatial and unstructured effects for spatially discontinuous health outcomes. Computational Statistics & Data Analysis 51 (2007) 3197-3212
17. Cook R.D., and Weisberg S. An Introduction to Regression Graphics (1994), Wiley, New York
18. Cook R.D., and Weisberg S. Applied Regression Including Computing and Graphics (1999), Wiley, New York
19. Dixon D.O., and Simon R. Bayesian subset analysis. Biometrics 47 (1991) 871-881
20. ESRI. ArcGIS 9.1 Users Guide (2005)
21. Fotheringham A.S., Brunsdon C., and Charlton M. Geographically Weighted Regression: The Analysis of Spatially Varying Relationships (2002), Wiley, West Sussex
22. Gelfand A.E., Kim H., Sirmans C.F., and Banerjee S. Spatial modeling with spatially varying coefficient processes. Journal of the American Statistical Association 98 (2003) 387-396
23. Gelfand A., and Vounatsou P. Proper multivariate conditional autoregressive models for spatial data analysis. Biostatistics 4 (2003) 11-25
24. Gelman A., and Pardoe I. Bayesian measure of explained variation and pooling in multilevel (hierarchical) models. Technometrics 48 (2006) 241-251
25. Guenther-Grey C.A., Varnell S., Weiser J.I., Mathy R.M., O'Donnell L.O., Stueve A., Remafedi G., and The Community Intervention Trial for Youth (CITY) study team. Journal of the National Medical Association 97 (2005) 38S-43S
26. Hastie T., and Tibshirani R. Generalized Additive Models (1990), Chapman & Hall, London
27. Haw S., and Higgins K. A comparison of the prevalence of HIV infection and injecting risk behaviour in urban and rural samples in Scotland. Addiction 93 (1998) 855-863
28. Hickson, D.A., 2005. Multilevel (hierarchical) analysis of the human immunodeficiency virus and high risk sexual behavior: Assessing model fit with the deviance information criterion and generalized coefficient of determination. Dissertation. Emory University, Department of Biostatistics. Atlanta, GA.
29. Kass R.E., and Raftery A.E. Bayes factors. Journal of the American Statistical Association 90 (1995) 773-795
30. Leone P., Hightow L., Owen-O'Dowd J., Phillip S., Gray P., Jones B., Fitzpatrick L., Millet G., Jones K., Stall R., Holmberg S., and Greenberg A. HIV transmission among black college student and non-student men who have sex with men-North Carolina, 2003. MMWR 53 (2004) 731-734
31. Mardia K.V. Multi-dimensional multivariate Gaussian Markov random fields with application to image processing. Journal of Multivariate Analysis 24 (1988) 265-284
32. Mathei C., Robaeys G., Van Damme P., Buntinx F., and Verrando R. Prevalence of hepatitis C in drug users in Flanders: Determinants and geographic differences. Epidemiology Infections 133 (2004) 127-136
33. McFarland W., Katz M.H., Stoyanoff S.R., Shehan D.A., LaLota M., Celentano D.D., Koblin B.A., Torian L.V., and Thiede H. MMWR 50 (2001) 440-444
34. Neter, J., Kutner, M.H., Nachtsheim, C.J., Wasserman, W., 1996. Applied Linear Regression Models. Irwin, Chicago.
35. Schwarz G. Estimating the dimension of a model. The Annals of Statistics 6 (1978) 461-466
36. Shafer G., and Olkin G. Adjusting p values to account for selection over dichotomies. Journal of the American Statistical Association 78 (1983) 674-678
37. Spiegelhalter D.J., Best N.G., Carlin B.P., and van der Linde A. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64 (2002) 583-639 With discussion
38. Spiegelhalter, D.J., Thomas, A., Best, N.G., Lunn, D., 2003. WinBUGS user manual, version 1.4. MRC Biostatistics Unit. Cambridge.
39. Thomas, A., Best, N., Lunn, D., Arnold, R., Spiegelhalter, D., 2004. GeoBUGS user manual, version 1.2. MRC Biostatistics Unit. Cambridge.
40. Tierney L. LISP-STAT: An Object Oriented Environment for Statistical Computing and Dynamic Graphics (1990), Wiley, Chichester
41. Tukey J.W. Explanatory Data Analysis (1977), Addison-Wesley, Reading, MA
42. Van de Perre P., Clumeck N., Carael M., Nzabihimana E., Robert-Guroff M., De Mol P., Freyens P., Butzler J.P., Gallo R.C., and Kanyamupira J.B. Female prostitutes: A risk group for infection with human T-cell lymphotropic virus type III. Lancet ii (1985) 524-526
43. Wahba G. Spline Models for Observational Data (1990), Society for Industrial and Applied Mathematics, Philadelphia
44. Zhu L., and Carlin B.P. Comparing hierarchical models for spatio-temporally misaligned data using the deviance information criterion. Statistics in Medicine 19 (2000) 2265-2278