1 / 19

Multivariate Twin Analysis

r C. r A. r E. A. C. A. C. E. E. a 2. c 2. e 2. a 1. c 1. e 1. Variable 2. Variable 1. Multivariate Twin Analysis. Tom Price Frühling Rijsdijk. Bivariate Cholesky Decomposition. V 1. V 2. v 1. v 2. v 3. Variable 1. Variable 2. Longitudinal Analysis

tacy
Download Presentation

Multivariate Twin Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. rC rA rE A C A C E E a2 c2 e2 a1 c1 e1 Variable 2 Variable 1 Multivariate Twin Analysis Tom Price Frühling Rijsdijk

  2. Bivariate Cholesky Decomposition V1 V2 v1 v2 v3 Variable 1 Variable 2

  3. Longitudinal Analysis Boomsma & van Baal, 1998 V1 V2 1.0 .63 .78 IQ age 5 IQ age 7

  4. Another use for the Cholesky V1 V2 v1 v2 v3 IQ Reading

  5. Bivariate Correlated Factors Model r V1 V2 v1 v2 Variable 2 Variable 1

  6. Bivariate Cholesky Decomposition V1 V2 x1 x2 x3 Variable 1 Variable 2 Conversion Bivariate Correlated Factors Model r V1 V2 y1 y2 Variable 1 Variable 2 y1 = x1 y2 =  ( x22 + x32) r = x2/ y2

  7. Univariate Twin Model MZ = 1.0 DZ = 0.5 MZ = 1.0 DZ = 1.0 A C A C E E a c e a c e Twin 1 Twin 2

  8. Bivariate Cholesky Decomposition C2 A1 C1 E1 A2 E2 x2 y2 z2 x3 y3 z3 x1 y1 z1 Variable 1 Twin 1 Variable 2 Twin 1

  9. Childhood IQ Boomsma & van Baal, 1998 A1 C1 E1 A2 E2 IQ age 5 IQ age 7

  10. E1 A1 C1 a1 c1 e1 Bivariate Correlated Factors Model rC rA rE E2 A2 C2 a2 c2 e2 Variable 2 Twin 1 Variable 1 Twin 1

  11. Genetic Correlation rA = 1.0 E2 E1 A2 A1 E2 E1 A2 A1 .90 .80 .40 .30 Variable 1 Variable 2 Variable 1 Variable 2 Low heritability, high genetic correlation High heritability, low genetic correlation

  12. E1 A1 E1 C1 A1 C1 a1 c1 e1 a1 c1 e1 Full Bivariate Model E2 A2 E2 C2 A2 C2 a2 c2 e2 a2 c2 e2 Variable 2 Twin 1 Variable 1 Twin 1 Variable 2 Twin 2 Variable 1 Twin 2

  13. Conversion J. C. Loehlin, Behavior Genetics, 26, 65-69. Bivariate Cholesky Decomposition Bivariate Correlated Factors Model rC rA rE C A C E A E A C A C E E x2 y2 z2 x3 y3 z3 a1 c1 e1 a1 c1 e1 x1 y1 z1 Variable 2 Twin 1 Variable 1 Twin 1 Variable 1 Twin 1 Variable 1 Twin 1 a1 = x1 c1 = y1 e1 = z1 a2 =  ( x22 + x32) c2 =  ( y22 + y32) e2 =  (z22+ z32) rA = x2/ a2 rC = y2/ c2 rE = z2/ e2

  14. Practical session 1. Use the TEDS dataset to derive MZ and DZ covariance matrices for the variables PARCA1, VOCAB1, PARCA2, VOCAB2. (The instructors will show you where to find the SPSS dataset and script that you will need.) 2. Insert the covariance matrices into the bivariate correlated factors Mx script. Is the script ready to run yet? What else will you need to do before running the script? 3. Run the Mx script and check the output. Has it run properly or are there error messages? What does the output tell you? 4. Think how you might modify the script to test the data in other ways.

  15. SPSS script to make covariance matrices USE ALL. COMPUTE filter_$=(atwin=1 and zyg=1). VALUE LABELS filter_$ 0 'Not Selected' 1 'Selected'. FORMAT filter_$ (f1.0). FILTER BY filter_$. EXECUTE . REGRESSION VARIABLES (COLLECT) /MISSING LISTWISE /DESCRIPTIVES COVARIANCES /DEPENDENT PARCA1 /METHOD=ENTER VOCAB1 PARCA2 VOCAB2. USE ALL. COMPUTE filter_$=(atwin=1 and zyg=2). VALUE LABELS filter_$ 0 'Not Selected' 1 'Selected'. FORMAT filter_$ (f1.0). FILTER BY filter_$. EXECUTE . REGRESSION VARIABLES (COLLECT) /MISSING LISTWISE /DESCRIPTIVES COVARIANCES /DEPENDENT PARCA1 /METHOD=ENTER VOCAB1 PARCA2 VOCAB2.

  16. Bivariate correlated factors Mx script ! Genetic correlated factors model #Define nvar= 2 G1: Model parameters Data Calc NGroups=4 Begin Matrices; X Lower nvar nvar Free ! genetic parameters Y Lower nvar nvar Free ! shared environment parameters Z Lower nvar nvar Free ! nonshared environment parameters L Diag nvar nvar Free ! variance estimates H Full 1 1 ! scalar .5 O Zero nvar nvar End Matrices; Begin Algebra; A= X * X' ; ! genetic variance/covariance C= Y * Y' ; ! shared environment variance/covariance E= Z * Z' ; ! nonshared environment variance/covariance End Algebra; Start .5 All Start 1 L 1 1 - L nvar nvar End [continued]

  17. Bivariate correlated factors Mx script G2: MZ twin pairs Data NInput_vars= 4 NObservations= XXX Cmatrix Full XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX Labels PARCA1 VOCAB1 PARCA2 VOCAB2 Matrices= Group 1 Covariances ( L | O _ O | L ) & ( A + C + E | A + C _ A + C | A + C + E ) / Option RSidual End [continued]

  18. Bivariate correlated factors Mx script G3: DZ twin pairs Data NInput_vars= 4 NObservations= XXX Cmatrix Full XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX XXX Labels PARCA1 VOCAB1 PARCA2 VOCAB2 Matrices= Group 1 Covariances ( L | O _ O | L ) & ( A + C + E | H@A + C _ H@A + C | A + C + E ) / Option RSidual End [continued]

  19. Bivariate correlated factors Mx script G4: Standardise Estimates by constraining A + C + E = 1 Data Constraint Matrices = Group 1 I Unit 1 nvar End Matrices; Constrain \d2v( P ) = I; ! constrain to unit variance End G5: Calculate genetic / environmental correlations Data Calc Matrices = Group 1 I Iden nvar nvar Begin Algebra; U = \sqrt( I . A )~ * A * \sqrt( I . A )~; ! genetic correlations V = \sqrt( I . C )~ * C * \sqrt( I . C )~; ! SE correlations W = \sqrt( I . E )~ * E * \sqrt( I . E )~; ! NE environment correlations ! NB these are all versions of equation [7] ! another way of writing these equations is : ! U = \stnd( A ) ; etc. End Algebra; Intervals @95 A 1 1 A 2 2 C 1 1 C 2 2 E 1 1 E 2 2 U 2 1 V 2 1 W 2 1 End ! See below for explanations of the matrix equations

More Related