For these reasons, researchers have resorted to what we call Purcell’s (2002) univariate moderation model (e.g., Bartels et al. 2009; Bartels and Boomsma 2009; Dick et al. 2009; Distel et al. 2010; Grant et al. 2010; Harden et al. 2007; McCaffery et al. 2008, 2009; Taylor et al. 2010; Timberlake et al. 2006; Turkheimer et al. 2003; Wallace et al. 2006). In this model, the moderator M is included in the means model of T as follows:3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \begin{aligned} T_{1}\,=\,\beta_{0} + \beta_{1} *M_{1} , \\ T_{2} = & \beta_{0} + \beta_{1} *M_{2} , \\ \end{aligned} $$\end{document}where T 1 and T 2 are the trait values of twins 1 and 2, M 1 and M 2 are their individual moderator values, β 0 is the intercept, and β 1 is the regression weight for moderator M. The parameters β 0 and β 1 are assumed to be equal across twins within a pair, and across zygosity (Fig. 1b). With 8 parameters (6 to describe the variance part of the model: 3 related, and
