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Heterogeneity Boulder, 2004
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Heterogeneity Questions Are the contributions of genetic and environmental factors equal for different groups, such as sex, age, race, ethnicity, SES, environmental exposure, etc.? Gene x Sex/ Age/ Race / Environment Interaction
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Heterogeneity Questions Is heterogeneity due to differences in the magnitude of the effects (quantitative)? e.g. Are genetic/ environmental contribution of factors greater/smaller in males than in females? Is heterogeneity due to differences in the nature of the effects (qualitative)? e.g. Are there different genetic/environmental factors influencing the trait in males and females?
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Heterogeneity across groups differences in variance components NOT mean differences group membership continuous heterogeneity
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Group Comparisons ComparisonConcordant for group membership Discordant for group membership genderMZ & DZ: MM & FF DZ: opposite sex ageMZ & DZ: young & old nationalityMZ & DZ: OZ & US environmentMZ & DZ: urban & rural MZ & DZ: urban & rural
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Models for Concordant Pairs ModelFull / Heterogeneity Constrained / Homogeneity Group 1a1 c1 e1 Group 2a2 c2 e2a1 c1 e1 Statistics12 Parameters63 Degrees of Freedom 69
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Models for Concordant and Discordant Pairs ModelFull / Heterogeneity Constrained / Homogeneity Group 1a1 c1 e1 Group 2a2 c2 e2a1 c1 e1 Statistics15/18 Parameters63 Degrees of Freedom 9/1212/15
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Models for Concordant and Discordant Pairs ModelScalarGeneral Group 1a1 c1 e1 Group 2a1 c1 e1 ka2 c2 e2 h Statistics15/18 Parameters47 Degrees of Freedom 9/1212/15
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Summary of Models Homogeneity Model: no quantitative, no qualitative differences Heterogeneity Model: quantitative but no qualitative differences Scalar Model: special case of heterogeneity model with proportional quantitative differences General Model: quantitative and qualitative differences
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Homogeneity Model
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Example Homogeneity Model
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Homogeneity Model VarianceCovarianceCorrelation MZM0.980.890.91 MZF0.980.890.91 DZM0.980.570.58 DZF0.980.570.58 DZMF0.980.570.58
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Heterogeneity Model
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Example Heterogeneity Model
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Heterogeneity Model VarianceCovarianceCorrelation MZM0.590.500.85 MZF0.980.890.91 DZM0.590.380.64 DZF0.980.570.58 DZMF0.59 / 0.980.450.59
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Scalar Model
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Example Scalar Model
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Scalar Model VarianceCovarianceCorrelation MZM0.980.890.91 MZF2.202.000.91 DZM0.980.570.58 DZF2.201.280.58 DZMF0.98 / 2.200.850.58
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General Model
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Example General Model
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General Model VarianceCovarianceCorrelation MZM0.980.890.91 MZF0.980.890.91 DZM0.980.570.58 DZF0.980.570.58 DZMF0.980.250.26
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Alternative General Model
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Example 2 General Model
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Summary of Models
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