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Multivariate Analysis

Multivariate Questions I. Bivariate Analysis: What are the contributions of genetic and environmental factors to the covariance between two traits?Multivariate Analysis: What are the contributions of genetic and environmental factors to the covariance between more than two traits?. Phenotypic Chole

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Multivariate Analysis

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    1. Multivariate Analysis Mx class 2004 HGEN619 10/20/03

    2. Multivariate Questions I Bivariate Analysis: What are the contributions of genetic and environmental factors to the covariance between two traits? Multivariate Analysis: What are the contributions of genetic and environmental factors to the covariance between more than two traits?

    3. Phenotypic Cholesky F1

    4. Phenotypic Cholesky F2

    5. Phenotypic Cholesky

    6. Phenotypic Cholesky

    7. Cholesky Decomposition

    8. Saturated Model Use Cholesky decomposition to estimate covariance matrix Fully saturated Model: Cov P = F*F’ F: Full nvar nvar

    9. Phenotypic Single Factor

    10. Residual Variances

    11. Factor Analysis Explain covariance by limited number of factors Exploratory / Confirmatory Model: Cov P = F*F’ + E*E’ F: Full nvar nfac E: Diag nvar nvar

    12. Twin Data

    13. Genetic Single Factor

    14. Single [Common] Factor X: genetic Full 4 x 1 Full nvar x nfac Y: shared environmental Z: specific environmental

    15. Common Environmental Single Factor

    16. Specific Environmental Single Factor

    17. Residuals partitioned in ACE

    18. Residual Factors T: genetic U: shared environmental V: specific environmental Diag 4 x 4 Diag nvar x nvar

    19. Independent Pathway Model

    20. Path Diagram to Matrices

    21. Independent Pathway I G1: Define matrices Calculation Begin Matrices; X full nvar nfac Free ! common factor genetic path coefficients Y full nvar nfac Free ! common factor shared environment paths Z full nvar nfac Free ! common factor unique environment paths T diag nvar nvar Free ! variable specific genetic paths U diag nvar nvar Free ! variable specific shared env paths V diag nvar nvar Free ! variable specific residual paths M full 1 nvar Free ! means End Matrices; Start … Begin Algebra; A= X*X' + T*T'; ! additive genetic variance components C= Y*Y' + U*U'; ! shared environment variance components E= Z*Z' + V*V'; ! nonshared environment variance components End Algebra; End

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