account for the effects of time over a long time span (23 years). We examined imputation diagnostics, including 1) comparing the descriptives and distributions of observed and imputed data, 2) overimputation (sequentially removing and imputing observed values as if they had actually been missing values), 3) using overdispersed starting values (convergence in the imputations from different starting values), and 4) examining time series to ensure the imputed data fell within the participants’ general trends. Diagnostics suggested that the imputed data were acceptable. The conditional multilevel models were run on each imputed data set separately, and then the results were combined using the mitools (Lumley, 2010) and mix (Schafer, 1997) packages in R, which use Rubin’s (1987) rules for combining results of analyses on multiply imputed data sets.
