For each moderator, we ran a bivariate Cholesky model with moderation (shown in Figure 1). The bivariate Cholesky model extends the classic twin design and allows for partitioning both the variance of each phenotype and their covariance. The variance and the covariance are partitioned into three sources [additive genetic factors (A), shared environmental factors (C), and unique environmental factors (E)] based on the relationship between the monozygotic and dizygotic twin correlations. Moderation can be assessed in the bivariate model on the A, C, and E influences unique to the behavioral outcome and those shared with the moderator. Along with the a, c and e path estimates, β parameters (indicating the moderating effect of the moderator variable on each path) are also estimated. If the β parameter is significantly different from zero this indicates the existence of moderation on that pathway and the value of β indicates the magnitude of the moderation. Moderation effects were tested first on the shared paths to determine whether it was appropriate to use the extended univariate model. If the moderation on the shared paths was
