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 analysis of the variance/covariance matrix to determine the factor structure of the multivariate genetic relationship between AUD symptoms. To determine the number of genetic factors, we employed Parallel Analysis implemented in R with the nFactors package. This approach has been shown to outperform other methods under a variety of conditions (Ledesma and Valero-Mora, 2007). A factor was retained if the eigenvalue of the genetic variance/covariance matrix was greater than the 95th percentile of the distribution of eigenvalues derived from random data (generated with 1000 iterations). All analyses for the CPM approach were conducted in Mplus and all analyses for the EGFA approach were conducted in R using the OpenMx and Psych packages; bootstrapped confidence intervals for the EGFA path loadings were obtained using 1000 replicates.
