Note that β 2 = zero, if M1 and M2 are uncorrelated, because then rm1,m2 = rt1,m2 = 0, in which case this extension equals the general univariate model. Note also the similarity between Eqs. 6 and 7 and Eq. 4: the calculation of the regression weights in multiple regression with two predictors resembles the calculation of semi-partial correlations, except for the square root in the denominator. From Eqs. 6 and 7, it can be seen that β 1 and β 2 will only be equal across zygosity groups if both rt2,m1 (= rt1,m2) and rm1,m2 are equal across zygosity, i.e., if neither M and the relation between M and T are affected by genetic factors. In all other situations, β 1 and β 2, and as a result β 0, should be estimated separately in MZ and DZ twins, allowing their values to differ across zygosity. Allowing all three betas in the means model to differ across zygosity will result in a general extended univariate moderation model, the specification of which is independent of the nature of the correlations
