Bivariate analysis

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Bivariate analysis

• Mx class 2004

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Univariate ACE model
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Expected Covariance Matrices
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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?

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Two Traits
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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

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Bivariate Twin Data
variance
twin covariance
trait covariance
cross-trait twin covariance
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Bivariate Twin Covariance Matrix
VX1 CX1X2 CX2X1 VX2
CX1Y1 CX2Y2
CX1Y2 CX2Y1
VY1 CY1Y2 CY2Y1 VY2
CY1X1 CY2X2
CY1X2 CY2X1
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Genetic Correlation
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Alternative Representations
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Cholesky Decomposition
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More Variables
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Bivariate AE Model
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MZ Twin Covariance Matrix
a112e112
a112
a222a212 e222e212
a21a11 e21e11
a222a212
a21a11
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DZ Twin Covariance Matrix
a112e112
.5a112
a222a212 e222e212
a21a11 e21e11
.5a222 .5a212
.5a21a11
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Within-Twin Covariances Mx
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Within-Twin Covariances
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Cross-Twin Covariances
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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

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Univariate Expected Covariances
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Univariate Expected Covariances II
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Bivariate Expected Covariances
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Practical Example I

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

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Practical Example II

• Dataset NL MRI Study
• 1990s
• Working Memory, Gray White Matter
• N MZFY 68, DZF 21