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 between M and T and M1 and M2. This extension implies that β 0, β 1 and β 2 need to be different across MZ and DZ groups, so that the means models for MZ and DZ twins 1 and 2 become:8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \begin{aligned} {\text{MZ:}}\quad {\text{T}}_{ 1} & = \beta_{{0,{\text{mz}}}} + \beta_{{1,{\text{mz}}}} *{\text{M}}_{ 1} + \beta_{{1,{\text{mz}}}} *{\text{M}}_{ 2} , \\ {\text{T}}_{ 2} & = \beta_{{0,{\text{mz}}}} + \beta_{{1,{\text{mz}}}} *{\text{M}}_{ 2} + \beta_{{2,{\text{mz}}}} *{\text{M}}_{ 1} , \\ \end{aligned} $$\end{document} 9\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \begin{aligned} {\text{DZ:}}\quad {\text{T}}_{ 1} & = \beta_{{0,{\text{dz}}}} + \beta_{{ 1 , {\text{dz}}}} *{\text{M}}_{ 1} + \beta_{{2,{\text{dz}}}} *{\text{M}}_{ 2} , \\ {\text{T}}_{ 2} & = \beta_{{0,{\text{dz}}}} + \beta_{{1,{\text{dz}}}} *{\text{M}}_{ 2} + \beta_{{2,{\text{dz}}}} *{\text{M}}_{ 1} . \\ \end{aligned} $$\end{document}
