1. ACE Problems
Greg Carey
BGA, 2009
Minneapolis, MN

2. Thought Experiment 1:
Future technology identifies all loci and alleles that contribute to a phenotype.
Genotype a very large sample for all these loci.
Code the alleles for additive effects.
Regress the phenotypes on the additive codes.
Predicted values of the phenotypes are the additive genetic values = numerical estimates of latent variable A.

3. ^ P A11 A1i Locus 1 A21 A2j Locus 2 An1 Ank Locus n a11 a1i a21 a2j
  
A11
A1i
Locus 1
A21
A2j
Locus 2
An1
Ank
Locus n P
a11
a1i
a21
a2j
an1
ank ^

4. Assumption 1:
Phenotypes are influenced by concrete environmental events or Xs.

5. Thought Experiment 2:
Measure all the Xs for a large sample of individuals.
Regress the phenotype on all the Xs.
Predicted values equal the total environmental values = numerical estimates of the sum of latent variables C + E.

6. X1 X2 Xn b1 b2 bn ^ P

7. Problem at Hand:
If (C + E) = SbiXi, we should be able to find weights for C and weights for E so that: (1) C and E are uncorrelated in an individual; (2) the Es for siblings are uncorrelated.

8. X11 E1
X12 C1 P1

9. Necessary Condition 1:
Every X variable can be placed into one of two mutually exclusive classes—those predicting E and those predicting C.
(X variables can be either green or red).

10. X1e E1
X1c C1 P1

11. Necessary Condition 2:
X variables predicting the unique environment cannot be correlated with X variables predicting the common environment within an individual.
(No magenta correlations).

12. P1
X1e E1
X1c C1
X2c C2
X2e E2 P2

13. Necessary Condition 3:
No sibling correlations among the Xs for the unique environment.
(Green Xs cannot correlate across siblings or no green correlational paths).

14. P1
X1e E1
X1c C1
X2c C2
X2e E2 P2

15. Necessary Condition 4:
No X for sib 1’s unique environment can correlate with any X for sib 2’s common environment.
(No magenta correlational paths)

16. P1
X1e E1
X1c C1
X2c C2
X2e E2 P2

17. Necessary Condition 5:
When C1 = C2,

18. Necessary Condition 5: When C1 = C2,
(With some algebra), a red X for sib 1 and its counterpart for sib 2 must correlate 1.0.

19. X11e
X1ke
X1c
X12
Xjc
X21e
X2ke E1 C E2 P1 P2

20. ACE Model Assumption:
Select any X variable.

21. ACE Model Assumption: Select any X variable.
That X must correlate either 0.0 or 1.0 for the relatives.

22. ACE Model Assumption: Select any X variable.
That X must correlate either 0.0 or 1.0 for the relatives.
It is not possible to have an X that correlates, say, .43 between sibs.

23. ACE Model Assumption:
Conversely, if peer substance abuse correlates .38 among sibs, then

24. ACE Model Assumption:
Conversely, if peer substance abuse correlates .38 among sibs, then
Peer substance abuse can NOT be an environmental influence on substance abuse.

25. What Happened?
In the beginning,

26. What Happened?
In the beginning, there was G1, G2, E1, and E2 (Jinks & Fulker, 1970).

27. What Happened?
In the beginning, there was G1, G2, E1, and E2 (Jinks & Fulker, 1970).
E2 variance component morphed into variable C in path analysis.

28. What Happened?
In the beginning, there was G1, G2, E1, and E2 (Jinks & Fulker, 1970).
E2 variance component morphed into variable C in path analysis.
E1 variance component morphed into variable E in path analysis.

29. What Happened?
In the beginning, there was G1, G2, E1, and E2 (Jinks & Fulker, 1970).
E2 variance component morphed into variable C in path analysis.
E1 variance component morphed into variable E in path analysis.
Variance components G1 and G2 were eliminated and replaced with variable A.

30. What Happened?
In the process, we overlooked the fact that correlation (variance components) does not necessarily imply causality.

31. School
Pupil1
Pupil2
Res1
Res2

32. Can legitimately calculate:
Variance component for School.

33. Can legitimately calculate:
Variance component for School.
Orthogonal variance component for Error.

34. Can legitimately calculate:
Variance component for School.
Orthogonal variance component for Error.
Test of significance of the variance component for School.

35. Can legitimately calculate:
Variance component for School.
Orthogonal variance component for Error.
Test of significance of the variance component for School.
Intraclass correlation for School.

36. But is this causal?

37. But is this causal?
Not necessarily!

38. School
Pupil1
Pupil2
Res1
Res2
Family1
Family2

39. How Important Is This?
For the simple analysis of a single phenotype, no problem.
For some models of GE correlation, how does a variable (G) correlate with a variance component?
What about multivariate models?

41. Solution?

42. Common and Unique Environment
Solution?
Common and Unique Environment

43. Shared and Nonshared Environment
Solution?
Shared and Nonshared Environment

44. Use Total Environment = C + E
Solution?
Use Total Environment = C + E

45. P1 b A1 E1 a e P2 E2 A2 h

46. $5,000 prize

47. $5,000 prize
Bouchard Prize

48. $5,000 prize
Bouchard Prize
Prove me wrong or irrelevant

49. $5,000 prize
Bouchard Prize
Prove me wrong or irrelevant
Equations, not words