5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \theta _{{jk}} = a{\text{1}}_{k} + a{\text{2}}_{{jk}} + c_{k} + e_{{jk}} , $$\end{document}where ck denotes the environmental effect for being a member of family k, and ejk denotes the environmental effect of being individual j in family k. The genetic component is split into a1 and a2 to model the different genetic correlations amongst monozygotic (MZ) and dizygotic (DZ) twins (cf. Jinks and Fulker 1970). The genetic correlation in MZ twins is usually assumed 1.0 and in DZ twins 0.5, in other words, the genetic covariance in MZ twins is twice as large as in DZ twins. Therefore, if we let the random effect a1 be constant within all families and we let a2 vary within families only for DZ twins (but be constant for MZ twins), and then fix the variances of a1 and a2 to be equal, the genetic covariance in MZ twins will be twice as large as in DZ twins. The variance of a1 and a2 together, VAR(a1) + VAR(a2) = 2 * VAR(a1) can then be
