Multiple Imputation for Model Checking: Completed-Data Plots with Missing and Latent Data

• Published in: Biometrics Vol. 61; no. 1; pp. 74 - 85
• Main Authors: Gelman, Andrew, Van Mechelen, Iven, Verbeke, Geert, Heitjan, Daniel F., Meulders, Michel
• Format: Journal Article
• Language: English
• Published: 350 Main Street , Malden , MA 02148 , U.S.A , and P.O. Box 1354, 9600 Garsington Road , Oxford OX4 2DQ , U.K Blackwell Publishing 01.03.2005; International Biometric Society; Blackwell Publishing Ltd
• Subjects: Animals; Bayes Theorem; Bayesian model checking; Clinical Trials as Topic - statistics & numerical data; Data Collection; Data imputation; Data Interpretation, Statistical; Data models; Datasets; Dosage; Exploratory data analysis; Histograms; Humans; Missing data; Modeling; Models, Statistical; Multiple imputation; Nonresponse; Patient Dropouts - statistics & numerical data; Posterior predictive checks; Predictive modeling; Rats; Realized discrepancies; Residuals; School dropouts; Symptoms
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/j.0006-341X.2005.031010.x

In problems with missing or latent data, a standard approach is to first impute the unobserved data, then perform all statistical analyses on the completed dataset-corresponding to the observed data and imputed unobserved data-using standard procedures for complete-data inference. Here, we extend this approach to model checking by demonstrating the advantages of the use of completed-data model diagnostics on imputed completed datasets. The approach is set in the theoretical framework of Bayesian posterior predictive checks (but, as with missing-data imputation, our methods of missing-data model checking can also be interpreted as "predictive inference" in a non-Bayesian context). We consider the graphical diagnostics within this framework. Advantages of the completed-data approach include: (1) One can often check model fit in terms of quantities that are of key substantive interest in a natural way, which is not always possible using observed data alone. (2) In problems with missing data, checks may be devised that do not require to model the missingness or inclusion mechanism; the latter is useful for the analysis of ignorable but unknown data collection mechanisms, such as are often assumed in the analysis of sample surveys and observational studies. (3) In many problems with latent data, it is possible to check qualitative features of the model (for example, independence of two variables) that can be naturally formalized with the help of the latent data. We illustrate with several applied examples.