ABSTRACT
FIGURE 6.7: Scatterplots of observed residuals versus tted values for the longitudinal process for the PBC dataset.
We again observe that the tted loess curve in the plot of the standardized marginal residuals versus the tted values shows a systematic trend. Note, however, that high levels of serum bilirubin indicate a worsening of a patient's condition resulting in higher death rates (i.e., dropout). Similar to Figure 6.2, we cannot denitely conclude from this gure that the lack-of-t is attributed to a misspecication of X. Thus, both the AIDS and PBC data examples illustrate that residual plots based on the observed data alone can be proven
To overcome the problems caused by the nonrandom dropout and produce residuals for the longitudinal process that can be readily used in diagnostic plots, Rizopoulos et al. (2010) proposed to augment the observed data with randomly imputed longitudinal responses under the complete data model, corresponding to the longitudinal outcomes that would have been observed had the patients not dropped out. Using these augmented longitudinal responses, residuals are then calculated for the complete data, and a multiple imputation approach is used to properly account for the uncertainty in the imputed values due to missingness (Gelman et al., 2005).
