Chunk #3 — Introduction

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A note on false positives and power in G × E modelling of twin data.

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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} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\text{Var}}\left( {{\text{T}}|{\text{M}}_{\text{i}} } \right) = \left( {a + \beta_{a} M_{i} } \right)^{ 2} + \left( {c + \beta_{c} M_{i} } \right)^{ 2} + \left( {e + \beta_{e} M_{i} } \right)^{ 2} $$\end{document}for i = 1, 2, and the expected covariances within MZ and DZ twin pairs are:2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \begin{aligned} {\text{Cov}}_{\text{MZ}} ({\text{T}}_{ 1} ,{\text{T}}_{ 2} |{\text{M}}_{ 1} ,{\text{M}}_{ 2} ) & = (a + \beta_{a} M_{1} )(a + \beta_{a} M_{2} ) + (c + \beta_{c} M_{1} )(c + \beta_{c} M_{2} ) \\ {\text{Cov}}_{\text{DZ}} ({\text{T}}_{ 1} ,{\text{T}}_{ 2} |{\text{ M}}_{ 1} ,{\text{M}}_{ 2} ) & = . 5(a + \beta_{a} M_{1} )(a + \beta_{a} M_{2} ) + (c + \beta_{c} M_{1} )(c + \beta_{c} M_{2} ). \\ \end{aligned} $$\end{document}