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Social interaction

Social interaction. March 7 th , 2002 Boulder, Colorado John Hewitt. 1.0 or 0.5. 1.0. A. C. E. A. C. E. a. c. e. a. c. e. P 1. P 2. P 1 = aA 1 + cC 1 + eE 1 P 2 = aA 2 + cC 2 + eE 2. In matrix form we can write: A 1 P 1 a c e 0 0 0 C 1

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Social interaction

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  1. Social interaction March 7th, 2002 Boulder, Colorado John Hewitt

  2. 1.0 or 0.5 1.0 A C E A C E a c e a c e P1 P2 P1 = aA1 + cC1 + eE1 P2 = aA2 + cC2 + eE2

  3. In matrix form we can write: A1 P1 a c e 0 0 0 C1 = E1 P2 0 0 0 a c e A2 C2 E2

  4. or as a matrix expression y = Gx

  5. 1.0 or 0.5 1.0 A C E A C E a c e a c e s P1 P2 s P1 = sP2+aA1+cC1+eE1 P2 =sP1+aA2+cC2+eE2

  6. In matrix form we can write: A1 P1 0 s P1 a c e 0 0 0 C1 = + E1 P2 s 0 P2 0 0 0 a c e A2 C2 E2

  7. or as a matrix expression y = By + Gx y-By = Gx (I-B)y = Gx (I-B)-1(I-B)y = (I-B)-1Gx Iy = (I-B)-1Gx y = (I-B)-1Gx

  8. X1 X2 x x s P1 P2 s P1 = sP2+xX1 P2 =sP1+xX2

  9. In matrix form we can write: P1 0 s P1 x 0 X1 = + P2 s 0 P2 0 x X2

  10. or as a matrix expression y = By + Gx y-By = Gx (I-B)y = Gx (I-B)-1(I-B)y = (I-B)-1Gx Iy = (I-B)-1Gx y = (I-B)-1Gx

  11. In this case the matrix (I – B) is 1 -s -s 1 Which has determinant 1-s2. So (I-B)-1 is 1 1 s 1-s2 s 1

  12. So, {yy’} = {(I - B)-1Gx} {(I - B)-1Gx}’ = (I - B)-1G{xx’}G’(I - B)-1’

  13. The effects of sibling interaction on variance and covariance components between pairs of relatives. w represents the scalar 1/(1-s2)2

  14. Effects of strong sibling interaction on the variance and covariance between MZ and DZ and unrelated individuals reared together. The interaction s takes the values 0, 0.5, and –0.5 for no interaction, co-operation, and competition, respectively

  15. Now let’s look at the Mx script for fitting this model to data. The basic program is in your handout and in F:\jkh\siblings\sibint.mx

  16. Model fitting to externalizing scores without social interaction

  17. Model fitting to externalizing scores with social interaction

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