1. Introduction to Multivariate Analysis Frühling Rijsdijk & Shaun Purcell Twin Workshop 2004

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

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

4. X1X1 Multivariate twin covariance matrix X2X2 Y1Y1 Y2Y2 X1X1 X2X2 Y1Y1 Y2Y2 C X1Y2 C X2Y1 C Y1X2 C X1Y2 C X2X1 C X1X2 V X2 V X1 C Y2Y1 C Y1Y2 V Y2 V Y1 C Y2X2 C X2Y2 C X1Y1

5. X1X1 X2X2 Y1Y1 Y2Y2 X1X1 X2X2 Y1Y1 Y2Y2 A+C+E A = [ Ax Ayx ] [ Axy Ay ] Covariance A+C+E | A+C _ A+C | A+C+E / A+C A+C+E A+C

6. Multivariate model parameters X 1 Y1Y1 X 2 Y2Y2 rGrG rGrG A X hXhX hXhX 1 / 0.5 A Y hYhY hYhY 1 / 0.5

7. Correlated factors X 1 Y1Y1 rGrG A X hXhX A Y hYhY Genetic correlation r G Chain of paths h X r G h Y bivariate heritability Component of phenotypic covariance r XY = h X r G h Y + c X r C c Y + e X r E e Y

8. X 1 Y1Y1 rGrG A X hXhX A Y hYhY X 1 Y1Y1 A SX h SX A SY h SY A C hChC hChC X 1 Y1Y1 h1h1 A 2 h3h3 A 1 h2h2 Cholesky decomposition

9. X 1 Y1Y1 h1h1 A 2 h3h3 A 1 h2h2 Tests of specificity –If h 3 > 0 –genetic influences specific to Y

10. More than two variables

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