We employed robust weighted least squares analysis based on tetrachoric correlations for the exploratory factor analyses (EFAs) with GEOMIN oblique rotation. These factor structures were established using both 12-month and lifetime diagnoses and were established as reliable using random split half replications. Next, we fit structural models relating the latent factors identified in the EFAs to alcohol dependence while treating sex and age as covariates. Finally, we introduced the residual (relative to the latent factor) of each internalizing diagnosis into the model (i.e., a path from the residual to alcohol dependence) using the MODINDICIES option under the OUTPUT command in Mplus. The statistical significance of the addition of each residual path was determined by examining the Chi-square value with one degree of freedom representing the improvement in the fit of the model when the residual path was (vs. was not) included in the model. (Note that one-tailed tests are used since the hypothesis of an improvement in fit is being evaluated.) Finally, note that all SEM results shown are standardized and thus do not depend on how the original latent
