Heterogeneity Boulder, 2004

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

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?

Heterogeneity across groups differences in variance components NOT mean differences group membership continuous heterogeneity

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

Models for Concordant Pairs ModelFull / Heterogeneity Constrained / Homogeneity Group 1a1 c1 e1 Group 2a2 c2 e2a1 c1 e1 Statistics12 Parameters63 Degrees of Freedom 69

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

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

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

Homogeneity Model

Example Homogeneity Model

Homogeneity Model VarianceCovarianceCorrelation MZM MZF DZM DZF DZMF

Heterogeneity Model

Example Heterogeneity Model

Heterogeneity Model VarianceCovarianceCorrelation MZM MZF DZM DZF DZMF0.59 /

Scalar Model

Example Scalar Model

Scalar Model VarianceCovarianceCorrelation MZM MZF DZM DZF DZMF0.98 /

General Model

Example General Model

General Model VarianceCovarianceCorrelation MZM MZF DZM DZF DZMF

Alternative General Model

Example 2 General Model

Summary of Models