In the CPM approach, a latent variable representing the shared variance across all symptoms was decomposed into genetic and error variance in two steps. First, an exploratory factor model (EFA) was fitted to a random selected half of the sample to determine the phenotypic factor structure of AUD; this model was then confirmed using confirmatory factor analysis (CFA) of the remaining half of the sample. AUD factor scores were extracted from the full sample and used in the analyses described above. In the EGFA approach, which represents a multivariate extension of GREML, a factor analysis was conducted on the 11×11 variance/covariance matrix of inter-criterion bivariate SNP heritabilities through a series of steps. First, GREML was used to estimate bivariate SNP genetic covariance estimates across each pair of criteria. Next, these estimates were used to construct an 11×11 genetic variance/covariance matrix. Because covariance matrices constructed from bivariate estimates may not be positive definite, we determined the nearest positive definite variance/covariance matrix using the Higham algorithm (Higham, 2002) within the nearPD package in R, version 3.4.0 (Team, 2017). Finally, we conducted factor
