In both the univariate and the bivariate moderation models proposed by Purcell (2002), the moderation effects are modelled directly on the path loadings of the genetic (A), shared environmental (C) and nonshared environmental (E) variance components.2 In this moderation model, the variances of A, C, and E are fixed to 1 (standard identifying scaling), but the path coefficients are modelled as (a + β a M i), (c + β c M i), and (e + β e M i), respectively. In these expressions for the moderated loadings, a, c and e are intercepts, i.e., the parts of the variance components that are independent of moderator M, M i is the value of the moderator for a specific twin i, and β a, β c, and β e, are the regression weights of the moderator for the genetic and the environmental variance components, respectively.3 In the standard homoskedastic ACE-model, the β coefficients are assumed to be zero. In the moderation model proposed by Purcell, the total variance of trait T is thus calculated as:1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}
