In bivariate analyses, we tested whether genetic and environmental influences on the twins' alcohol use and problem use were correlated with those influencing their friends' use. Given that in the literature there is evidence of both friends influencing an adolescent's alcohol use and vice versa [6], and as the data used in the current analyses were cross-sectional, it was not possible to assume a direction of effect between these variables. As such, a bivariate correlated factors model was fitted to the data (see Fig. 1). This is equivalent to a bivariate Cholesky decomposition model but makes no assumptions about the direction of causation [43]. It gives estimates of the genetic (rG), common environment (rC) and unique environment (rE) correlation between two variables of interest. These correlations are independent of the size of the estimates of genetic and environmental influences on the variables of interest.
