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Rater Bias & Sibling Interaction

Seventeenth International Workshop On Methodology of Twin And Family Studies. Boulder, CO, 2004. Rater Bias & Sibling Interaction. Meike Bartels Boulder 2004. Seventeenth International Workshop On Methodology of Twin And Family Studies. Boulder, CO, 2004. GENES (A). ENVIRONMENT.

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Rater Bias & Sibling Interaction

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  1. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 • Rater Bias • & • Sibling Interaction Meike Bartels Boulder 2004

  2. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 GENES (A) ENVIRONMENT Shared Environment (C) Nonshared Environment (E)

  3. 1/.5 1 A C E A C E TWIN I TWIN II Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 The Univariate Model

  4. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Variance Decomposition of AGG based on mother ratings at age 10 Aboy .63 (.53-.72) Agirl .50 (.39-.62) Cboy .20 (.11- .30) Cgirl .29 (.18-.40) Eboy .17 (.15-.19) Egirl .21 (.18-.23)

  5. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Problem Behavior • Questionnaires • ages 3, 5, 7, 10 en 12 • - mother ratings • father ratings • teacher ratings (ages 7, 10, and 12) • self report (ages 12, 14, 16) • Achenbach System of Empirically • Based Assessment (ASEBA)

  6. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Parental Ratings

  7. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 correlations

  8. Aggressive Behavior same rater different rater RMZ .86 .68 RDZ .49 .34 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Twin correlations

  9. Aggressive Behavior same rater different rater A.74 (A + rater specific view) .68 C .12 (rater bias !!) .00 E .14 (E + rater error) .32 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Variance Decomposition A = 2(rmz-rdz) = 2 (.86-.49) = .74 C = rmz – 2 (rmz-rdz) = .89 – 2( .86-.49) = .14 E = 1- rmz = 1- .86 =.14

  10. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Rater Bias influences the C factor • Respons Bias • stereotyping, different normative standards, response style • Projection Bias • Psychopathology of the parent influences his/het judgement of the behavior of the child (Several studies suggest that depression in mothers may lead to their overestimating their children’s symptomology)

  11. A C E A C E AGGm AGGf Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Cholesky Decomposition

  12. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Cholesky Decomposition Boys [=A%(A+C+E)] 1 2 1 0.7254 0.7631 2 0.7631 0.5910 [=C%(A+C+E)] 1 2 1 0.1116 0.1074 2 0.1074 0.2494 [=E%(A+C+E)] 1 2 1 0.1630 0.1295 2 0.1295 0.1596 Girls [=A%(A+C+E)] 1 2 1 0.5157 0.6887 2 0.6887 0.5734 [=C%(A+C+E)] 1 2 1 0.2784 0.1511 2 0.1511 0.2367 [=E%(A+C+E)] 1 2 1 0.2060 0.1602 2 0.1602 0.1900

  13. Rater Bias Model 1 1/ 0.5 E C A A C E Reliable trait variance T1 Reliable trait variance T2 mother rating T1 father rating T1 mother rating T2 father rating T2 Rm T1 Rf T1 Rm T2 Rf T2 Mothers Bias Fathers Bias Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 c c e a a e 1 1 1 1 rm bf rm rm bm bm bf bf

  14. MRT1 FRT1 1 1 + = x + + e A C E c a x x x rm 0 0 rf bm 0 0 bf Bm Bf Rm Rf + x x Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Total variance for an individual

  15. Table 1: CBCL-items of the syndrome Aggressive Behavior for the CBCL/2-3 and CBCL/4-18 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Variance-Covariance Matrices in Mx MZ (S+F | S_ S | S+F) + L*(A+C+E | A+C_ A+C | A+C+E )*L' ; DZ (S+F | S_ S | S+F) + L*(A+C+E | H@A+C_ H@A+C | A+C+E )*L' ;

  16. Table 1: CBCL-items of the syndrome Aggressive Behavior for the CBCL/2-3 and CBCL/4-18 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 The Mx Script Mx jobs: Raterbias.mx Data: TAD.dat

  17. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Parental Ratings Agreement and disagreement

  18. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Parental Disagreement I. Rater Bias / error (e.g. response style, different normative standards) II. Mother or father specific information (distinct situations, parental specific relation with a child)

  19. Psychometric Multiple Rater Model 1 1/ 0.5 E C A A C E c c e a a e Reliable trait variance T1 Reliable trait variance T2 1 1 1 1 mother rating T1 father rating T1 father rating T2 mother rating T2 ef af af ef cf cf am em em am Ef Cf Ef Am Cm Em Am Cm Em Af Cf Af cm cm 1/ 0.5 1 1/ 0.5 1 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004

  20. MRT1 FRT1 1 1 + x + c E e a A C x x x + = em 0 0 ef am 0 0 af cm 0 0 cf Em Ef Am Af Cm Cf x x x + + Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Total variance for an individual

  21. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Variance-Covariance Matrices in Mx MZ (G+S+F | G+S_ G+S | S+F) + L*(A+C+E | A+C_ A+C | A+C+E )*L' ; DZ (G+S+F | H@G+S_ H@G+S | G+S+F) + L*(A+C+E | H@A+C_ H@A+C | A+C+E )*L' ;

  22. Table 1: CBCL-items of the syndrome Aggressive Behavior for the CBCL/2-3 and CBCL/4-18 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 The Mx script Mx jobs: Psychometric.mx Data: TAD.dat

  23. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Different models -2LL df Cholesky 26564.480 10356 Rater Bias 26631.108 10360 Psychometric 26563.938 10356

  24. .63 .20 .17 .50 .29 .21 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Reliable Trait Variance Boys Girls A .74 .71 C .13 .13 E .13 .16

  25. Rater Bias & Rater Specific parts of the total variance Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Boys Girls Am .12 .00 Af .03 .08 Cm .08 .19 Cf .14 .13 Am .07 .10 Af .06 .07

  26. 1/.5 1 A C E A C E s TWIN I TWIN II s Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Sibling Interaction / Rater Contrast path s implies an interaction between phenotypes

  27. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Contrast effect; Sibling Interaction Social Interaction between siblings (Carey, 1986; Eaves, 1976) Behavior of one child has a certain effect on the behavior of his or her co-twin: Cooperation (AP in one twin leads to like-wise behavior in the co-twin) Competition (increased AP in one twin leads to decreased behavior in co-twin)

  28. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Constrast effect; Rater Contrast (Neale and Stevenson, 1989) Behavioral judgement/rating of one child of a twin pair is not independent of the rating of the other child of the twin pair. Rater compares the twins’ behavior against one another. The behavior of one child becomes some kind of ‘standard’ by which the behavior of the co-twin is rated. parents may either stress the similarities or differences between the children

  29. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Constrast effect • Phenotypic Cooperation/ positive rater contrast : • mimics the effects of shared environment • increase the variance of more closely related • individuals (var MZ >> var DZ) • Phenotypic competion/ negative rater contrast: • -mimics the effect of non-additive genetic variance • -increase the variance of more closely related • individuals least (var MZ << var DZ)

  30. 1/.5 1 A1 C1 E1 A2 C2 E2 a a c c e e s P1 P2 s Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Constrast Effect P1 = sP2 + aA1 + cC1 + eE1 P2 = sP1 + aA2 + cC2 + eE2

  31. P1 P2 P1 P2 0 s s 0 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Constrast Effect = + A1 C1 E1 A2 C2 E2 a c e 0 0 0 0 0 0 a c e

  32. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Matrix expression y = By + Gx y – By = Gx (I-B) y = Gx (I-B)-1 (I-B)y = (I-B)-1 Gx y= (I-B)-1 Gx

  33. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 In Mx Begin Matrices; B full 2 2 ! constrast effect End Matrices; Begin Algebra; P = (I-B)~; End Algebra

  34. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Variance –Covariance Matrix MZ: P & ( A + C + E | A + C_ A + C | A + C + E) / DZ: P & ( A + C + E | H@A + C_ H@A + C | A + C + E) /

  35. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 The Mx-script Mx jobs: Constrast.mx Data: TAD.dat

  36. X1 X2 x x s P1 P2 s Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Consequences for Variation and Covariation basic model: P1 = sP2 + xX1 P2 = sP1 + xX2

  37. P1 P2 P1 P2 0 s s 0 X1 X2 = + x 0 0 x X1 X2 x x s P1 P2 s Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 In Matrices y = By + Gx

  38. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Matrix expression y = By + Gx y – By = Gx (I-B) y = Gx (I-B)-1 (I-B)y = (I-B)-1 Gx y= (I-B)-1 Gx

  39. 0 s s 0 1 -s -s 1 1 s s 1 1 0 0 1 - = 1 @ 1-s2 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 y= (I-B)-1 Gx in this case (I-B) is simply Which has determinant: (1*1-s*s) = 1-s2 , so (I-B)-1 is

  40. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Variance-covariance matrix for P1 and P2 Σ { yy’} = { (I-B)-1 Gx} { (I-B)-1 Gx} ‘ = (I-B)-1 G Σ {xx’} G’ (I-B)-1’ in whichΣ {xx’} is covariance matrix of the x variables

  41. 1 r r 1 X1 X2 x x s P1 P2 s Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Remember... We want to standardize variables X1 en X2 to have unit variance and correlation r, so Σ {xx’} =

  42. x 0 0 x 1 s s 1 1 @ 1 r r 1 1-s2 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 To compute the covariance matrix recall G = (I-B)-1 = Σ {xx’} =

  43. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 To compute the covariance matrix recall 1 + 2sr + s2 r+2s + rs2 r+2s + rs2 1 + 2sr + s2 x2 Σ { yy’} = @ (1-s2)2

  44. The effects of sibling interaction on variance and covariance components between pairs of relatives. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 ω represents the scalar 1/(1-s2)2

  45. Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004 Numerical Illustrationa2=.5 ; d2 = 0; c2=0; e2=.5s=0; cooperation >> s=.5; competion >> s=-.5 Social interactions cause the variance of the phenotype to depend on the degree of relationship of the social actors

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