Consider a moderator M and a trait T, both with variance 1 and mean 0, and measured in a sample of MZ and DZ twins. Suppose that in both M and T, variance components A, C, and E account for 40%, 30%, and 30% of the variance, respectively, and that these percentages are stable across the entire population (i.e., there is no moderation). This implies that rMZt1,t2 = rMZm1,m2 = .7 and rDZt1,t2 = rDZm1,m2 = .5. Now suppose that the cross-trait correlation between T and M equals .24 (i.e., rm1,t1 = rm2,t2 = .24) and that the T–M correlation is either exclusively due to A (loading cross-path equals \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt {.15} $$\end{document}), or to C (loading cross-path equals \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt {.2} $$\end{document}), or to E (loading cross-path equals \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt {.2} $$\end{document}; see Fig. 2a–c).
