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Practica

Multivariate Modeling Nathan Gillespie &amp; Irene Rebollo Files: <br>athan2008 aggression.dat multi_aggr_2var.mx. Practica. 1. Go thru Mx bivariate script with fine tooth comb

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Practica

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  1. Multivariate ModelingNathan Gillespie & Irene RebolloFiles: \\nathan\2008\aggression.dat multi_aggr_2var.mx

  2. Practica 1. Go thru Mx bivariate script with fine tooth comb 2. Estimate phenotypic correlations, genetic & environmental latent factor correlations, standardized proportions of variance 3. Test AE, CE and E submodels 4. Try your hand at writing a trivariate Cholesky

  3. Bivariate Cholesky Folder: \nathan\2008 Files: multi_aggr_2var.mx aggression.dat Aggression Time 1: 3258 twins in 1991 Aggression Time 2: 3303 twins in 1995 Aggression Time 2: 2984 twins in 1997 Data need to be adjusted for age at interview

  4. Additive genetic path coefficients (X) 1 1 A1 A2 Translate path diagram into a matrix x11 x21 x22 Twin 1 Phenotype 2 Twin 1 Phenotype 1 Twin 1 Twin 1

  5. Additive genetic path coefficients (Y) 1 1 A1 A2 Translate path diagram into a matrix y11 y21 y22 Twin 1 Phenotype 2 Twin 1 Phenotype 1 Twin 1 Twin 1

  6. Additive Genetic Cross-Twin Covariance (DZ) 0.5 0.5 Path Tracing: Within-traits P11-P12 = 0.5a112 P21-P22 = 0.5a222+0.5a212 Cross-traits P11-P22 = 0.5a11a21 P21-P12 = 0.5a21a11 1 1 1 1 A1 A2 A1 A2 a11 a21 a22 a11 a21 a22 P22 P11 P21 P12 Twin 1 Twin 2 N.B. in Mx  = @

  7. Total Within-Twin Covariance Using matrix addition, the total within-twin covariance for the phenotypes is defined as:

  8. Age effects on mean Means M + B*O | M + B*P ; 1 by 4 matrix Recall that: M Full 1 nvar Free ! grand mean phenotypes [1 2] B Full 1 ndef Free ! Age beta [1 1] O full ndef nvar fix ! Age for twin 1 at times 1 & 2 [1 2] P full ndef nvar fix ! Age for twin 2 at times 1 & 2 [1 2] B*O = [1 1] * [1 2] = [Bage] * [age1.1 × age3.1] = [Bage× age1.1 Bage× age3.1] B*P = [1 1] * [1 2] = [Bage] * [age1.2 × age3.2] = [Bage× age1.2 Bage× age3.2]

  9. Age effects on mean Means M + B*O | M + B*P; 1 by 4 matrix M + B*O = [µtwin1var1 + Bage×age1.1 µtwin1var2 + Bage×age3.1] M + B*P = [µtwin2var1 + Bage×age1.2 µtwin2var2 + Bage×age3.2 ]

  10. Predicted Model Twin 1 Twin 2 Within-twin covariance Twin 1 Cross-twin covariance Within-twin covariance Twin 2

  11. Predicted Model Twin 1 Twin 2 Within-twin covariance Cross-twin covariance X*X’ + Y*Y’ + Z*Z’ X*X’ + Y*Y’ Twin 1 Cross-twin covariance Within-twin covariance Twin 2 X*X’ + Y*Y’ + Z*Z’ X*X’ + Y*Y’

  12. Observed phenotypic correlation is the result of correlation at - Genetic level - Common environmental level - Unique environmental level Estimate rg, rc, and re Estimate contribution of rg, rc, and re to phenotypic correlation between phenotype 1 and 2 rG rC 1 1 1 1 A1 A2 C2 C1 A112 C112 A222 C222 Phenotype 1 Phenotype 2 E112 E222 1 1 E1 E2 rE Estimating genetic and environmental correlations

  13. Correlations between latent factors Matrix function in Mx: R = \sqrt(I.A)˜ * A * \sqrt(I.A)˜; Where I is an identity matrix: and I.A = R = \stnd(A);

  14. Proportion of observed phenotypic correlation explained by A, C and E • Begin algebra; K = A%P|C%P|E%P; S = A%(A+C+E)|C%(A+C+E)|E%(A+C+E); End algebra; % is the Mx operator for element division Proportion of the phenotypic correlation due to genetic effects

  15. Run ACE Model

  16. ACE Model Fit

  17. Model comparisons

  18. Write trivariate ACE Model Change nvar Include starting values for 3rd variables Change Select statement to include 3rd variable Change Definition statement 3rd variable ages

  19. ACE Model Fit

  20. Mx scripts http://www.psy.vu.nl/mxbib

  21. rG rC 1 1 1 1 A1 A2 C2 C1 A112 C112 A222 C222 Phenotype 1 Phenotype 2 E112 E222 1 1 E1 E2 rE rph due to A rph due to C rph due to E Genetic contribution to observed correlation (h2xy) is a function of rg and both heritabilities

  22. Observed correlation

  23. + = . 28 * 0 . 79 * 0 . 29 0 . 22 Observed correlation and contributions from A, C and E = . 54 = 1.00 . 05 * . 00 0 . 01 * + = . 67 * 0.44 * 0 . 71 0.31 . Proportion of the observed correlation (or covariance) explained by correlation at the genetic level: 0.01/0.54 = 0.02 Proportion of the observed correlation (or covariance) explained by correlation at the shared environmental level:0.22/0.54 = 0.41 Proportion of the observed correlation (or covariance) explained by correlation at the non-shared environmental level: 0.31/0.54 = 0.57

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