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Bayesian Case-deletion Model Complexity and Information Criterion

1Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.
2Department of Biostatistics, Vanderbilt University, Nashville, TN, USA.
Publication Date:
Stat Interface
Volume Number:
Issue Number:
Stat Interface. 2014 Oct 1;7(4):531-42.
PubMed ID:
Bayesian, Case influence measures, Cross Validation, Information criterion, Markov chain Monte Carlo, Model complexity
Appears in Collections:
R21 HL097334/HL/NHLBI NIH HHS/United States
UL1 TR001111/TR/NCATS NIH HHS/United States
U54 EB005149/EB/NIBIB NIH HHS/United States
R01 MH086633/MH/NIMH NIH HHS/United States
R01 GM070335/GM/NIGMS NIH HHS/United States
UL1 RR025747/RR/NCRR NIH HHS/United States
UL1 RR024975/RR/NCRR NIH HHS/United States
P01 CA142538/CA/NCI NIH HHS/United States
R21 AG033387/AG/NIA NIH HHS/United States
TL1 TR001110/TR/NCATS NIH HHS/United States
R01 CA074015/CA/NCI NIH HHS/United States
R01 EB020426/EB/NIBIB NIH HHS/United States
Generated Citation:
Zhu H., Ibrahim J.G., Chen Q. Bayesian Case-deletion Model Complexity and Information Criterion. Stat Interface. 2014 Oct 1;7(4):531-42. PMID: 26180578. PMCID: PMC4500159.
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We establish a connection between Bayesian case influence measures for assessing the influence of individual observations and Bayesian predictive methods for evaluating the predictive performance of a model and comparing different models fitted to the same dataset. Based on such a connection, we formally propose a new set of Bayesian case-deletion model complexity (BCMC) measures for quantifying the effective number of parameters in a given statistical model. Its properties in linear models are explored. Adding some functions of BCMC to a conditional deviance function leads to a Bayesian case-deletion information criterion (BCIC) for comparing models. We systematically investigate some properties of BCIC and its connection with other information criteria, such as the Deviance Information Criterion (DIC). We illustrate the proposed methodology on linear mixed models with simulations and a real data example.