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Introduction to Multivariate Analysis

This presentation provides an introduction to multivariate analysis in twin data, focusing on the relationships between depression, anxiety, and individual measures within and between twins. It covers the decomposition of covariance, twin covariance, variance, phenotypic covariance, and cross-trait twin covariance. It also explores the multivariate twin covariance matrix, correlated factors, genetic correlation, heritability, and Cholesky decomposition. The presentation includes tests of specificity and the influence of genetic factors on specific variables.

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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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