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Multivariate Twin Analysis Tom Price Frühling Rijsdijk Variable 1 Variable 2 A C E a2a2 c2c2 e2e2 rArA rErE rCrC A C E a1a1 c1c1 e1e1.

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Presentation on theme: "Multivariate Twin Analysis Tom Price Frühling Rijsdijk Variable 1 Variable 2 A C E a2a2 c2c2 e2e2 rArA rErE rCrC A C E a1a1 c1c1 e1e1."— Presentation transcript:

1 Multivariate Twin Analysis Tom Price Frühling Rijsdijk Variable 1 Variable 2 A C E a2a2 c2c2 e2e2 rArA rErE rCrC A C E a1a1 c1c1 e1e1

2 Bivariate Cholesky Decomposition Variable 1Variable 2 V1V1 v1v1 V2V2 v3v3 v2v2

3 Longitudinal Analysis Boomsma & van Baal, 1998 IQ age 5IQ age 7 V1V1 1.0 V2V

4 Another use for the Cholesky IQReading V1V1 V2V2 v1v1 v3v3 v2v2

5 Bivariate Correlated Factors Model Variable 1 Variable 2 V1V1 v1v1 V2V2 v2v2 r

6 y 1 = x 1 y 2 = ( x x 3 2 )r = x 2 / y 2 Bivariate Correlated Factors Model Variable 1Variable 2 V1V1 y1y1 V2V2 y2y2 r Bivariate Cholesky Decomposition Variable 1Variable 2 V1V1 x1x1 V2V2 x3x3 x2x2 Conversion

7 Univariate Twin Model Twin 1 Twin 2 A C E ace A C E ace MZ = 1.0 DZ = 0.5 MZ = 1.0 DZ = 1.0

8 Bivariate Cholesky Decomposition Variable 1 Twin 1Variable 2 Twin 1 A1A1 C1C1 E1E1 x1x1 y1y1 z1z1 A2A2 C2C2 E2E2 x3x3 y3y3 z3z3 x2x2 y2y2 z2z2

9 Childhood IQ Boomsma & van Baal, 1998 IQ age 5IQ age 7 A1A1 C1C1 E1E1 A2A2 E2E2

10 Bivariate Correlated Factors Model Variable 1 Twin 1 Variable 2 Twin 1 A1A1 C1C1 E1E1 a1a1 c1c1 e1e1 A2A2 C2C2 E2E2 a2a2 c2c2 e2e2 rArA rErE rCrC

11 A1A1 E1E1.30 A2A2 E2E2.40 r A = 1.0 Variable 1Variable 2 Variable 1 A1A1 E1E1.90 A2A2 E2E2.80 Variable 2 Genetic Correlation High heritability, low genetic correlation Low heritability, high genetic correlation

12 Full Bivariate Model Variable 1 Twin 1 Variable 2 Twin 1 A1 C1 E1 a1c1e1 A2 C2 E2 a2c2e2 Variable 1 Twin 2 Variable 2 Twin 2 A1 C1 E1 a1c1e1 A2 C2 E2 a2c2e2

13 Conversion J. C. Loehlin, Behavior Genetics, 26, Bivariate Correlated Factors Model Variable 1 Twin 1 A C E a1a1 c1c1 e1e1 rArA rErE rCrC Bivariate Cholesky Decomposition Variable 1 Twin 1 Variable 2 Twin 1 ACE x1x1 y1y1 z1z1 A C E x3x3 y3y3 z3z3 x2x2 y2y2 z2z2 A C E a1a1 c1c1 e1e1 a 1 = x 1 c 1 = y 1 e 1 = z 1 a 2 = ( x x 3 2 ) c 2 = ( y y 3 2 ) e 2 = ( z z 3 2 ) r A = x 2 / a 2 r C = y 2 / c 2 r E = z 2 / e 2

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 Lowernvar nvar Free! genetic parameters Y Lowernvar nvar Free! shared environment parameters Z Lowernvar nvar Free! nonshared environment parameters L Diagnvar nvar Free! variance estimates H Full1 1! scalar.5 O Zeronvar 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.5All Start 1L 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 LabelsPARCA1 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 LabelsPARCA1 VOCAB1 PARCA2 VOCAB2 Matrices= Group 1 Covariances( L | O _ O | L ) & ( A + C + E | + C _ + 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 Unit1 nvar End Matrices; Constrain\d2v( P ) = I;! constrain to unit variance End G5: Calculate genetic / environmental correlations Data Calc Matrices = Group 1 I Idennvar 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; 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


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