Extended PedigreesClassic Twin DesignExample DataACE Model ResultsCTD AssumptionsCorrelationsGenetic FactorsEnvironmental FactorsOther FactorsPath Diagram Twins & ParentsCovariance Matrices MZ/DZGenetic Transmission ModelGenetic Transmission ExpectationsCommon Environment ModelCommon Environment ExpectationsCommon Environment ResultsSocial Homogamy ModelSocial Homogamy ExpectationsSocial Homogamy ResultsPhenotypic Assortment ModelPhenotypic Assortment ExpectationsConstraintsPhenotypic Assortment ResultsModel ComparisonsHeritabilityShared EnvironmentLimitationsDominanceSex DifferencesSummaryExtended PedigreesHGEN619 class 2006Classic Twin DesignACE / ADEheterogeneitymultivariate developmentalIssuesgeneralizibility >Additional SiblingsExample DataStudy: Virginia 30,000: twins, parents, sibs, spouses, childrenData: church attendanceVariable: categorical, 6 ordered categories > 5 thresholdsAnalysis: 2 groups, malesACE Model ResultsParameter Estimatesa: 0.44 c: 0.59 e: 0.680Standardized Estimates + Confidence Intervals a2: 0.20 c2: 0.34 e2: 0.46CI 0.01-0.20 0.18-0.49 0.42-0.48Fit StatisticsEstimated parameters: 23Observed statistics: 2807, 1 constraint -2 times log-likelihood of data: 9364.528Degrees of freedom: 2784CTD AssumptionsRandom matingAssortment will increase MZ and DZ correlationsWhen fitting ACE model, with assortment present, C will be overestimatedWhen fitting AE model, with assortment present, A will be overestimatedNo Age ModerationWhen fitting ACE model, with G x age interaction present, C will be overestimatedCorrelationsMm Ff Mf FmMZ .64 .63 _ _DZ .49 .53 .41 _Sibs .41 .47 .39 _P-O .49 .49 .49 .46Spouse _ _ .74 _Genetic FactorsDecreasing 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 factorsSibling and DZ correlations less than half MZ correlations (expectation is DZ=1/4MZ) and zero correlations for other pairs of relatives >> dominanceMZ correlations less than 1 >> specific environmental factorsEnvironmental FactorsSimilar 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)Sibling > parent-offspring correlations >> non-parental environmental factors: in common for siblings, such as school environment, peers, friendsTwin > sibling correlations >> special twin environment: additional similarity due to greater sharing of aspects of the environmentSiblings = parent-offspring correlations > half MZ twins >> cultural transmissionOther FactorsIf cultural transmission based on phenotype of parents for a trait which also has a genetic component >> GE covarianceNon-random mating: source of similarity which may have both genetic and environmental implicationseffects of assortative mating depend on mechanism by which people chose spousesif 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 increasedPath Diagram Twins & ParentsPMP1P2PFEe1Ee1Ee1Ee1PF : Phenotype FatherPM : Phenotype MotherP1 : Phenotype Twin 1P2 : Phenotype Twin 2Covariance Matrices MZ/DZFa T2T1MoFaT 2T 1MoPOOW PPOOV PW'V'O'O'O' O'Fa T 2T1MoFaT 2T 1MoPOOW PPOOU PW'U'O'O'O' O'Variance [P]MZ Covariance [U]DZ Covariance [V]Spousal Covariance [W]Parent-offspring Covariance [O]Genetic Transmission ModelGenetic transmissionFixed at .5Residual Genetic VarianceFixed at .5Equilibrium of variances across generationsPMPmPfAA AAa aa a.5 .5.5.5PF1.51.5Ee1Ee1Ee1Ee1Genetic Transmission ExpectationsW= 0; ! covariance spouseO= .5a2; ! covariance parent-offspringU= a2; ! covariance MZ twinsV= .5a2; ! covariance DZ twinsP= a2+e2;! variance twinsQ= a2+e2;! variance parentsCommon Environment ModelCommon environmentSame for all family membersAssortmentFunction of common environmentPMPmPfAA AA Ca aac cc c.5 .5.5.5PF1.511.5Ee1Ee1Ee1E1aeCommon Environment ExpectationsW= c2; ! covariance spouseO= .5a2 +c2; ! covariance parent-offspringU= a2+c2; ! covariance MZ twinsV= .5a2+c2; ! covariance DZ twinsP= a2+c2+e2;! variance twinsQ= a2+c2+e2;! variance parentsCommon Environment ResultsParameter Estimatesa: 0.26 c: 0.66 e: 0.700Standardized Estimates + Confidence Intervals a2: 0.07 c2: 0.44e2: 0.49CI 0.00-0.18 0.35-0.52 0.44-0.55Fit StatisticsEstimated parameters: 43Observed statistics: 3351, 1 constraint -2 times log-likelihood of data: 10999.249Degrees of freedom: 3308Social Homogamy ModelAssortmentSocialCultural TransmissionFrom C to CNon-parental Shared EnvironmentResidualPMPmPfAA ACCA Ca aa ac cc c.5 .5.5.5PF1r.5111.5Ee1Ee1Ee1Ee1f fdSocial Homogamy ExpectationsW= dc2; ! covariance spouseO= (f+df)c2+.5a2; ! covariance parent-childx= 2f2+2df2+r; ! common environment variance twinsU= a2+xc2; ! covariance MZ twinsV= .5a2+xc2; ! covariance DZ twinsP= a2+xc2+e2; ! variance twinsQ= a2+c2+e2; ! variance parentsConstrain x=1Social Homogamy ResultsParameter 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: 1.00Standardized Estimates + Confidence Intervalsa2: 0.04 r2: 0.13 t2: 0.38 e2: 0.48CI 0.04-0.050.12-0.14 0.23-0.47 0.44-0.49 r2: non-parental shared environment, t2: cultural transmission t2 + r2 =c2Fit Statistics Estimated parameters:46, Obs statistics: 3352, 2 constraints -2 times log-likelihood of data: 10994.427, df: 3306Phenotypic Assortment ModelAssortmentPhenotypicCultural TransmissionFrom P to CNon-parental Shared EnvironmentResidualGenotype-Environment CovariancePMPmPfAA ACCA Ca aa ac cc c.5 .5.5.5PFgr.5gxx.5Ee1Ee1Ee1Ee1f fds sPhenotypic Assortment ExpectationsW= pdp; ! covariance spouseT= ga+sc; ! covariance G-phenotypeO= (pf+wf)c+.5a(1+pd)t;! covariance parent-childJ= asc+csa; ! covariance GEU= ga2+xc2+j; ! covariance MZ twinY= g+.5(t(d+d)t); ! assortmentV= .5ya2+xc2+j; ! covariance DZ twinConstraintsK= .5(g+.5(t(d+d)t')+1);! genetic variance constraintL= .5t(2f+ 2dpf);!
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