1. Fitting Univariate Models to Continuous and Categorical Data
September 9, 2014
Elizabeth Prom-Wormley & Hermine Maes

2. Patterns of Twin Correlation
???
rMZ = 2rDZ
Additive
DZ twins on average share 50% of additive
effects
rMZ = rDZ
Shared Environment
rMZ > 2rDZ
Additive &
Dominance
DZ twins on average share 25% of dominance effects
rDZ > ½ rMZ
Additive & “Shared Environment”
A = 2(rMZ-rDZ)
C = 2rDZ – rMZ
E = 1- rMZ

3. BMI Twin Correlations A = 2(rMZ-rDZ) C = 2rDZ - rMZ E = 1- rMZ 0.30
0.78
A = 2(rMZ-rDZ)
C = 2rDZ - rMZ
E = 1- rMZ
A = 0.96
C = -0.20
E = 0.22
ADE or ACE?

4. Univariate Analysis A Roadmap
1- Use the data to test basic assumptions inherent to standard ACE (ADE) models
Saturated Model
2- Estimate contributions of genetic and environmental effects on the total variance of a phenotype
ADE or ACE Models
3- Test ADE (ACE) submodels to identify and report significant genetic and environmental contributions
AE or E Only Models

5. ADE Model- A Few Considerations
Dominance (D) refers to non-additive genetic effects resulting from interactions between alleles at the same locus
ADE models also include effects of interactions between different loci (epistasis)
In addition to sharing on average 50% of their DNA, DZ twins also share about 25% of effects due to dominance

6. ADE Model Deconstructed Path Coefficients
covA <- mxAlgebra( expression=a %*% t(a), name="A" )
covD <- mxAlgebra( expression=d %*% t(d), name=“D" )
covE <- mxAlgebra( expression=e %*% t(e), name="E" ) a
1 x 1 matrix d
1 x 1 matrix e
1 x 1 matrix

7. ADE Model Deconstructed Variance Components
covA <- mxAlgebra( expression=a %*% t(a), name="A" )
covD <- mxAlgebra( expression=d %*% t(d), name=“D" )
covE <- mxAlgebra( expression=e %*% t(e), name="E" ) a aT *
1 x 1 matrix d dT *
1 x 1 matrix e eT *
1 x 1 matrix

8. ADE Model Deconstructed Means & Covariances
meanG <- mxMatrix( type="Full", nrow=1, ncol=ntv, free=TRUE, values= 20, label="mean", name="expMean" )
covMZ <- mxAlgebra( expression= rbind( cbind (A+D+E , A+D), cbind(A+D , A+D+E)), name="expCovMZ" )
covDZ <- mxAlgebra( expression= rbind( cbind(A+D+E, 0.5%x%A+0.25%x%D), cbind(0.5%x%A+0.25%x%D , A+D+E)), name="expCovDZ" )
expMean
expMean= 1 x 2 matrix T1 T2 T1
A+D+E T2
covMZ & covDZ= 2 x 2 matrix

9. ADE Model Deconstructed Means & Covariances
covMZ <- mxAlgebra( expression= rbind( cbind(A+D+E , A+D), cbind(A+D , A+D+E)), name="expCovMZ" )
covDZ <- mxAlgebra( expression= rbind( cbind(A+D+E, 0.5%x%A+0.25%x%D), cbind(0.5%x%A+0.25%x%D, A+0.25%x%D+E)), name="expCovDZ" ) T2 T1 T2 T1
A+D+E
0.5A T2

10. ADE Model Deconstructed Means & Covariances

11. ADE Model Deconstructed
4 Parameters Estimated
ExpMean
Variance due to A
Variance due to D
Variance due to E

12. Univariate Analysis A Roadmap
1- Use the data to test basic assumptions inherent to standard ACE (ADE) models
Saturated Model
2- Estimate contributions of genetic and environmental effects on the total variance of a phenotype
ADE or ACE Models
3- Test ADE (ACE) submodels to identify and report significant genetic and environmental contributions
AE or E Only Models

13. Testing Specific Questions Please Open twinADEcon.R
‘Full’ ADE Model
Comparison against Saturated
Nested Models
AE Model
Test significance of D
E Model vs AE Model
Test significance of A
E Model vs ADE Model
Test combined significance of A & D

14. AE Model Deconstructed
New Object
Containing
AE Model
Object containing
Full Model
AeModel <- mxModel( AdeFit, name="AE" )
The d
path will not be
estimated
AeModel <- omxSetParameters( AeModel,
labels=“d11", free=FALSE, values=0)
AeFit <- mxRun(AeModel)
Fixing the value of the c path to zero

15. Goodness of Fit Stats ep -2ll df AIC diff -2ll diff p Saturated ADE AE
no! E

16. Goodness-of-Fit Statisticsep
-2ll df
AIC
diff -2ll
diff p
Saturated 10
1767
521.93 -
ADE 4
1773
517.45
7.52 6
0.28 AE 3
1774
519.66
4.21 1
0.06 E 2
1775
528.3
0.00

17. What about the magnitudes of genetic and environmental contributions to BMI?

18. Univariate Analysis A Roadmap
1- Use the data to test basic assumptions inherent to standard ACE (ADE) models
Saturated Model
2- Estimate contributions of genetic and environmental effects on the total variance of a phenotype
ADE or ACE Models
3- Test ADE (ACE) submodels to identify and report significant genetic and environmental contributions
AE or E Only Models

19. Estimated Values a d e c a2 d2 e2 c2
ADE - AE E

20. Estimated Values a d e c a2 d2 e2 ADE 0.57 0.54 0.41 - 0.37 0.22 AE
0.78
0.42 E
0.88
1.00

21. Potential Complications
Assortative Mating
Gene-Environment Correlation
Gene-Environment Interaction
Sex Limitation
Gene-Age Interaction

22. Trying Again with Ordinal Data
Open twinAceOrdS.R

23. Okay, so we have a sense of which model best explains the data
Okay, so we have a sense of which model best explains the data...or do we?

24. BMI Twin Correlations A = 2(rMZ-rDZ) C = 2rDZ - rMZ E = 1- rMZ
0.30
0.78
A = 2(rMZ-rDZ)
C = 2rDZ - rMZ
E = 1- rMZ
ADE or ACE?

25. ACE/ADE Conclusions- Problem Set 1 Due Tuesday, 9/16 at 5pm
Modify twinAdeCon.R and modify to reflect an ACE model
BMI (zygosity groups 1 and 3)
Are additive genetic factors significant?
Are dominance factors significant?
Are specific environmental factors significant?
Are shared environmental factors significant?
Provide results (as tables), provide brief explanations and guide me through your tables
Can also send script used to produce result

26. Goodness-of-Fit Statistics
Model ep
-2ll df
AIC
diff -2ll
diff p
Saturated
ADE
ACE

27. Estimated Values a d e c a2 d2 e2 c2
ADE AE
ACE E

28. Thank You!