We used Genomic SEM16 to perform multivariate GWAS on latent factors that posit different ways that genetic influences impact SUDs and correspond to two models previously estimated by this group18 (Supplementary Table 1a and b). The first model hypothesizes that a shared set of genes influences SUDs along with other externalizing phenotypes, such as attention deficit hyperactivity disorder (ADHD) and substance initiation (see below for further discussion of each phenotype). This shared genetic dimension in shown in Box A of Figure 1. This model also facilitates examination of the genetic influences on each SUD after accounting for what it shares with other SUDs and externalizing traits (Boxes B-E in Figure 1). These influences reflect residual, substance-specific genetic effects after accounting for what is shared with each of the other externalizing indicators, hereafter referred to as “residual-SUD”). The second model hypothesizes that separate, but correlated, dimensions of genetic risk influence SUDs and other externalizing traits, here referred to as behavioral disinhibition (Boxes F and G in Figure 1). In our previous work18, both models emerged as viable candidates; thus, in this study, we carry both forward into the multivariate GWAS analyses to compare their ability to facilitate gene identification for SUDs.