We employed a two-stage modeling approach. In the first stage, we tested the three models described above, and selected a structure based on agreement between Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC), where a lower AIC/BIC optimizes the balance between explanatory power and parsimony. We began testing with the structure of C, leaving A and E in a hypothesis-free state (i.e., a Cholesky decomposition). Once the structure for C was selected, it was fixed and the three possible A structures were compared; once the A structure was selected, it too was fixed and the three possible E structures were compared. After the higher-order structures were fixed for A, C, and E, we conducted the second stage of model fitting. This involved testing hypothesis-based models nested within the previously identified ACE structure, again selecting submodels based on AIC/BIC as well as the p-value of the χ2 test resulting from a comparison of −2 times the log likelihoods (−2LL) of the full and nested models. Our selection of the factor structure within each source of variance was based on agreement
