| Gelman et al. (2003) state that, "Checking the model is crucial to statistical analysis". Residuals have long been used to perform model assessment. However, properties of residuals for normal linear models of correlated observations have not been assessed. In this study, various studentized residuals are examined in terms of their ability to produce approximate standard normal distributions under correct model specification. This assessment includes both frequentist and Bayesian modeling approaches. Not only is there interest in assessing the properties of such residuals, but there is also interest in obtaining suitable diagnostic plots and tests to check violations of model assumptions when a fitted model is misspecified. This includes the ability of the residuals to identify misspecification of the covariance structure. Residuals that have been recommended in the literature are considered as well as new residuals based upon replicated observations. Particular emphasis is given to models with patterned covariance matrices in order to examine the effects of covariance matrix complexity and the number of subjects on the properties of the proposed residuals and diagnostics. |
