Residuals and Outliers in Random Effects Models

Residuals and Outliers in Bayesian Random Effects Models Robert E. Weiss* Department of Biostatistics UCLA School of Public Health Los Angeles CA 90024-1772 U.S.A. rob@sunlab.ph.ucla.edu August 11, 1994 Abstract Common repeated measures random effects models contain two ran- dom components, a random person effect and time-varying errors. An observation can be an outlier due to either an extreme person effect or an extreme time varying error. Outlier statistics are presented that can distinguish between these types of outliers. For each person there is one statistic per observation, plus one statistic per random effect. Method- ology is developed to reduce the explosion of statistics to two summary outlier statistics per person; one for the random effects and one for the time varying errors. If either of these screening statistics are large, then in- dividual statistics for each observation or random effect can be inspected. Multivariate, targeted outlier statistics and goodness-of-fit tests are also developed. Distribution theory is given, along with some geometric intu- ition. Key Words: Bayesian Data Analysis, Goodness-of-Fit, Hierarchical Models, Observed Errors, Repeated Measures. Introduction. Residual analysis in various forms is perhaps the only method for internally checking a particular model-data combination for lack of fit. Residual analysis can provide clues to useful and needed model elaboration but is only beginning *This work was supported by grant #GM50011-01 from NIGM. The author thanks Kathryn Chaloner and Sandy Weisberg for helpful feedback.