1Extended PedigreesHGEN619 class 2006Classic Twin Designn ACE / ADE¨ heterogeneity¨ multivariate ¨ developmentaln Issues¨ generalizibility >Additional Siblings2Example Datan Study: Virginia 30,000: twins, parents, sibs, spouses, childrenn Data: church attendancen Variable: categorical, 6 ordered categories > 5 thresholdsn Analysis: 2 groups, malesACE Model Resultsn Parameter Estimatesa: 0.44 c: 0.59 e: 0.680n Standardized Estimates + Confidence Intervals a2:0.20 c2:0.34 e2:0.46CI 0.01-0.20 0.18-0.49 0.42-0.48n Fit Statistics¨ Estimated parameters: 23¨ Observed statistics: 2807, 1 constraint¨ -2 times log-likelihood of data: 9364.528¨ Degrees of freedom: 27843CTD Assumptionsn Random mating¨ Assortment will increase MZ and DZ correlations¨ When fitting ACE model, with assortment present, C will be overestimated¨ When fitting AE model, with assortment present, A will be overestimatedn No Age Moderation¨ When fitting ACE model, with G x age interaction present, C will be overestimatedCorrelations_.74__Spouse.46.49.49.49P-O_.39.47.41Sibs_.41.53.49DZ__.63.64MZFmMfFfMm4Genetic Factorsn Decreasing correlations with a decreasing genetic relatedness: MZ twins > first-degree relatives (DZ twins, siblings, parent-child pairs) > second-degree relatives (grandparents, half-siblings, avuncular pairs) > more distant relatives such as cousins >> additive genetic factorsn Sibling and DZ correlations less than half MZ correlations (expectation is DZ=1/4MZ) and zero correlations for other pairs of relatives >> dominancen MZ correlations less than 1 >> specific environmental factorsEnvironmental Factorsn Similar sibling, DZ, parent-offspring correlations >> shared environmental factors: increase similarity between people living or having grown up in the same home (first-degree relatives and MZs)n Sibling > parent-offspring correlations >> non-parental environmental factors: in common for siblings, such as school environment, peers, friendsn Twin > sibling correlations >> special twin environment: additional similarity due to greater sharing of aspects of the environmentn Siblings = parent-offspring correlations > half MZ twins >> cultural transmission5Other Factorsn If cultural transmission based on phenotype of parents for a trait which also has a genetic component >> GE covariancen Non-random mating: source of similarity which may have both genetic and environmental implications¨ effects of assortative mating depend on mechanism by which people chose spouses¨ if selection is based on phenotype of partner > correlations between sources of variance in one spouse with those of other spouse induced, genetic and/or environmental covariance between parent-offspring and sibling pairs increased Path Diagram Twins & ParentsPMP1P2PFEe1Ee1Ee1Ee1PF : Phenotype FatherPM : Phenotype MotherP1 : Phenotype Twin 1P2 : Phenotype Twin 26Covariance Matrices MZ/DZFa T2T1MoFaT2T1MoPOOW PPOOV PW'V'O'O'O' O'Fa T2T1MoFaT2T1MoPOOW PPOOU PW'U'O'O'O' O'n Variance [P]n MZ Covariance [U]n DZ Covariance [V]n Spousal Covariance [W]n Parent-offspring Covariance [O]Genetic Transmission Modeln Genetic transmission¨ Fixed at .5n Residual Genetic Variance¨ Fixed at .5¨ Equilibrium of variances across generationsPMPmPfAA AAa aa a.5 .5.5.5PF1.51.5Ee1Ee1Ee1Ee17Genetic Transmission Expectationsn W= 0; ! covariance spousen O= .5a2; ! covariance parent-offspringn U= a2; ! covariance MZ twinsn V= .5a2; ! covariance DZ twinsn P= a2+e2;! variance twinsn Q= a2+e2;! variance parentsCommon Environment Modeln Common environment¨ Same for all family membersn Assortment¨ Function of common environmentPMPmPfAA AA Ca aac cc c.5 .5.5.5PF1.511.5Ee1Ee1Ee1E1ae8Common Environment Expectationsn W= c2; ! covariance spousen O= .5a2+c2; ! covariance parent-offspringn U= a2+c2; ! covariance MZ twinsn V= .5a2+c2; ! covariance DZ twinsn P= a2+c2+e2;! variance twinsn Q= a2+c2+e2;! variance parentsCommon Environment Resultsn Parameter Estimatesa: 0.26 c: 0.66 e: 0.700n Standardized Estimates + Confidence Intervals a2: 0.07 c2: 0.44 e2: 0.49CI 0.00-0.18 0.35-0.52 0.44-0.55n Fit Statistics¨ Estimated parameters: 43¨ Observed statistics: 3351, 1 constraint¨ -2 times log-likelihood of data: 10999.249¨ Degrees of freedom: 33089Social Homogamy Modeln Assortment¨ Socialn Cultural Transmission¨ From C to Cn Non-parental Shared Environment¨ ResidualPMPmPfAA ACCA Ca aa ac cc c.5 .5.5.5PF1r.5111.5Ee1Ee1Ee1Ee1f fdSocial HomogamyExpectationsn W= dc2; ! covariance spousen O= (f+df)c2+.5a2; ! covariance parent-childn x= 2f2+2df2+r; ! common environment variance twinsn U= a2+xc2; ! covariance MZ twinsn V= .5a2+xc2; ! covariance DZ twinsn P= a2+xc2+e2; ! variance twinsn Q= a2+c2+e2; ! variance parents¨ Constrain x=110Social Homogamy Resultsn Parameter Estimatesa: 0.20 c: 0.69 e: 0.69 d: 1.00 f: 0.43 r: 0.26 p: 1.00 q: 1.00 x: 1.00n Standardized Estimates + Confidence Intervalsa2:0.04 r2:0.13 t2:0.38 e2:0.48CI 0.04-0.05 0.12-0.14 0.23-0.47 0.44-0.49r2: non-parental shared environment, t2: cultural transmissiont2 + r2=c2n Fit Statistics ¨ Estimated parameters:46, Obs statistics: 3352, 2 constraints¨ -2 times log-likelihood of data: 10994.427, df: 3306Phenotypic Assortment Modeln Assortment¨ Phenotypicn Cultural Transmission¨ From P to Cn Non-parental Shared Environment¨ Residualn Genotype-Environment CovariancePMPmPfAA ACCA Ca aa ac cc c.5 .5.5.5PFgr.5gxx.5Ee1Ee1Ee1Ee1f fds s11Phenotypic Assortment Expectationsn W= pdp; ! covariance spousen T= ga+sc; ! covariance G-phenotypen O= (pf+wf)c+.5a(1+pd)t;! covariance parent-childn J= asc+csa; ! covariance GEn U= ga2+xc2+j; ! covariance MZ twinn Y= g+.5(t(d+d)t); ! assortmentn V= .5ya2+xc2+j; ! covariance DZ twinConstraintsn K= .5(g+.5(t(d+d)t')+1);¨ ! genetic variance constraintn L= .5t(2f+ 2dpf);¨ ! A-C constraintn M= 2fpf+2fwf+ r;¨ ! common environment variance constraintn Z= ga2+xc2+e2+2asc;¨ ! phenotypic variance constraint12Phenotypic Assortment Resultsn Parameter Estimatesa: 0.46 c: 0.31 e: 0.67 d: 0.58 f: 0.36g: 1.32 p: 1.00 s: 0.42 x: 1.41n Standardized Estimates + Confidence Intervalsa2:0.28 c2:0.14 e2:0.46 s2:0.12CI 0.04-0.60 0.00-0.41 0.41-0.51 -0.02-0.16g2:0.21 d2:0.00 t2:0.04 r2:0.10 CI 0.04-0.39 0.00-0.21 0.00-0.20 0.00-0.23s2: genotype-environment covariance, g2: genetic variance, d2: genetic variance through assortment, d2 +g2 =a2n Fit Statistics ¨ Estimated parameters:48, Obs statistics: 3354, 4 constraints¨ -2 times log-likelihood of
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