In the present study, we first estimated the genetic correlations among the 10 indicators in our proposed model. Next, we tested a series of a priori specified models to investigate the genetic architecture of externalizing phenotypes and SUDs. We chose these models to reflect alternative conceptualizations of the relationships between externalizing and SUDs in the existing literature. Namely, that SUDs are a subset of externalizing36 (common factor model); that externalizing and SUDs are separable, but correlated, constructs26–28 (EXT-ARF model); that all forms of substance involvement are distinct from, but correlated with, externalizing traits reflecting behavioural disinhibition37 (BD-SUB model); that SUDs are a subset of externalizing with meaningful residual variance (EXT-resARF model); and that behavioural disinhibition and substance use are specific representations of a broad liability to externalizing36 (bifactor model). As such, we tested the following models:
