1. Heterogeneity Boulder, 2004

2. 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

3. 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?

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

5. 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

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

7. 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

8. 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

9. 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

10. Homogeneity Model

11. Example Homogeneity Model

12. Homogeneity Model VarianceCovarianceCorrelation MZM0.980.890.91 MZF0.980.890.91 DZM0.980.570.58 DZF0.980.570.58 DZMF0.980.570.58

13. Heterogeneity Model

14. Example Heterogeneity Model

15. 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

16. Scalar Model

17. Example Scalar Model

18. 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

19. General Model

20. Example General Model

21. General Model VarianceCovarianceCorrelation MZM0.980.890.91 MZF0.980.890.91 DZM0.980.570.58 DZF0.980.570.58 DZMF0.980.250.26

22. Alternative General Model

23. Example 2 General Model

24. Summary of Models