Assessing Local Model Adequacy in Bayesian Hierarchical Models Using the Partitioned Deviance Information Criterion.
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 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 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.
National Cancer Institute, 6120 Executive Boulevard, Bethesda, MD 20892.
David C
DC
Wheeler
Demarc A
DA
Hickson
Lance A
LA
Waller
Epidemiol Infect. 2005 Feb;133(1):127-36
15724720
Lancet. 1985 Sep 7;2(8454):524-7
2863544
Stat Methods Med Res. 1995 Sep;4(3):187-96
8548102
AIDS. 1999 Jul 9;13(10):1233-40
10416528
Addiction. 1998 Jun;93(6):855-63
9744121
J Am Stat Assoc. 2003;98(462):387-396
39421645
MMWR Morb Mortal Wkly Rep. 2004 Aug 20;53(32):731-4
15318156
Stat Med. 2000 Sep 15-30;19(17-18):2265-78
10960852
J Infect Dis. 1991 Jul;164(1):67-71
2056219
Biometrics. 1991 Sep;47(3):871-81
1742443
AIDS. 1994 Nov;8(11):1585-91
7848595
AIDS. 1993 Feb;7(2):275-7
8466692
Int J Epidemiol. 1994 Apr;23(2):371-80
8082965
J Natl Med Assoc. 2005 Jul;97(7 Suppl):38S-43S
16080456
Biostatistics. 2003 Jan;4(1):11-25
12925327