After identifying all of the risk factors that were individually associated with the intercepts or slopes of externalizing trajectories, we combined the risk factors in one model. To avoid systematic bias in model parameter estimates and inferences, we used multiple imputation, which is preferable in developmental studies when there is missingness (Jeličić, Phelps, & Lerner, 2009). We multiply imputed 20 data sets using Amelia II version 1.6.3 (Honaker, King, & Blackwell, 2011) in R to have adequate power (i.e., power falloff of about 1% with respect to full information maximum likelihood estimates) when missingness is between 10–50% (most of the variables in the present study) (Graham, Olchowski, & Gilreath, 2007). Amelia uses an expectation-maximization with bootstrapping algorithm, and is well suited for longitudinal data (Honaker & King, 2010). For accurate imputations, we imputed the data with a cubic polynomial to 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
