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### Bivariate analysis

HGEN619 class 2006

Bivariate Questions I

- Univariate Analysis: What are the contributions of additive genetic, dominance/shared environmental and unique environmental factors to the variance?
- Bivariate Analysis: What are the contributions of genetic and environmental factors to the covariance between two traits?

Bivariate Questions II

- Two or more traits can be correlated because they share common genes or common environmental influences
- e.g. Are the same genetic/environmental factors influencing the traits?

- With twin data on multiple traits it is possible to partition the covariation into its genetic and environmental components
- Goal: to understand what factors make sets of variables correlate or co-vary

Bivariate Twin Data

(cross-twin within-trait)

covariance

(within-twin within-trait

co)variance

(cross-twin within-trait)

covariance

cross-twin cross-trait

covariance

Bivariate Twin Covariance Matrix

VX1 CX1X2

CX2X1 VX2

CX1Y1

CX2Y2

CX1Y2

CX2Y1

CY1X1

CY2X2

CY1X2

CY2X1

VY1 CY1Y2

CY2Y1 VY2

DZ Twin Covariance Matrix

a112+e112

.5a112

a21*a11+

e21*e11

a222+a212+

e222+e212

.5a21*a11

.5a222+

.5a212

Cross-Trait Covariances

- Within-twin cross-trait covariances imply common etiological influences
- Cross-twin cross-trait covariances imply familial common etiological influences
- MZ/DZ ratio of cross-twin cross-trait covariances reflects whether common etiological influences are genetic or environmental

Practical Example I

- Dataset: MCV-CVT Study
- 1983-1993
- BMI, skinfolds (bic,tri,calf,sil,ssc)
- Longitudinal: 11 years
- N MZF: 107, DZF: 60

Practical Example II

- Dataset: NL MRI Study
- 1990’s
- Working Memory, Gray & White Matter
- N MZFY: 68, DZF: 21

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