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Introduction to Multivariate Analysis

Introduction to Multivariate Analysis. Frühling Rijsdijk & Shaun Purcell Twin Workshop 2002. ENVIRONMENTS. GENES. ENVIRONMENTS. Relationships. Decomposition of covariance between measures. Depression. Anxiety. Individual. Within. Between. Within. Measure. Between.

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Introduction to Multivariate Analysis

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  1. Introduction to Multivariate Analysis Frühling Rijsdijk & Shaun Purcell Twin Workshop 2002

  2. ENVIRONMENTS GENES ENVIRONMENTS Relationships • Decomposition of covariance between measures Depression Anxiety

  3. Individual Within Between Within Measure Between Multivariate twin data Twin covariance Variance Phenotypic covariance Cross-trait twin covariance

  4. VX1 CX1Y1 CX1X2 CX1Y2 CX1Y1 VY1 CY1X2 CY1Y2 CX2X1 CX2Y1 VX2 CX2Y2 CX1Y2 CY2Y1 CY2X2 VY2 Multivariate twin covariance matrix X1 Y1 X2 Y2 X1 Y1 X2 Y2

  5. 1 / 0.5 1 / 0.5 rG rG A X A Y A X A Y hY hY hX hX X 1 Y1 X 2 Y2 Multivariate model parameters

  6. Correlated factors • Genetic correlation rG • Chain of paths hXrGhY bivariate heritability • Component of phenotypic covariance rXY = hXrGhY +cXrCcY +eXrEeY rG A X A Y hX hY Y1 X 1

  7. A C A SY A SX A 1 A 2 hC hC hSX h2 h1 h3 hSY Y1 Y1 X 1 X 1 Cholesky decomposition rG A X A Y hX hY Y1 X 1

  8. Cholesky • Tests of specificity • If h3 > 0 • genetic influences specific to Y A 1 A 2 h2 h1 h3 Y1 X 1

  9. More than two variables

  10. BGIM module http://statgen.iop.kcl.ac.uk/bgim/

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