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

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

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

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

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

Twin correlations 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

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 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

influences the C factor 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) Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004

Cholesky Decomposition AGGm AGGf A E C 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 0.1116 0.1074 2 0.1074 0.2494 [=E%(A+C+E)] 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 0.2784 0.1511 2 0.1511 0.2367 [=E%(A+C+E)] 1 0.2060 0.1602 2 0.1602 0.1900 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004

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

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

Variance-Covariance Matrices in Mx Table 1: CBCL-items of the syndrome Aggressive Behavior for the CBCL/2-3 and CBCL/4-18 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' ; Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004

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

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

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

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

The Mx script Mx jobs: Psychometric.mx Data: TAD.dat Table 1: CBCL-items of the syndrome Aggressive Behavior for the CBCL/2-3 and CBCL/4-18 The Mx script Mx jobs: Psychometric.mx Data: TAD.dat 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 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 .63 .20 .17 .50 .29 .21 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004

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

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

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

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

(I-B)-1 (I-B)y = (I-B)-1 Gx 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 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 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) / Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004

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

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

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

(I-B)-1 (I-B)y = (I-B)-1 Gx 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 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004

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

Σ { yy’} = { (I-B)-1 Gx} { (I-B)-1 Gx} ‘ 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 which Σ {xx’} is covariance matrix of the x variables Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004

Remember... s P1 P2 X1 X2 x We want to standardize variables X1 en X2 to have unit variance and correlation r, so Σ {xx’} = 1 r r 1 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’} = x 0 0 x 1 s s 1 1 1-s2 @ 1 r r 1 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 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004

ω represents the scalar 1/(1-s2)2 The effects of sibling interaction on variance and covariance components between pairs of relatives. Source Variance Covariance Additive genetic ω(1+2sra+s2)a2 ω(ra+2s+ras2)a2 Dominance ω(1+2srd+s2)d2 ω(rd+2s+rds2)d2 Shared env ω(1+2s+s2)c2 Non-shared env ω(1+s2)e2 ω 2se2 ω represents the scalar 1/(1-s2)2 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004

Numerical Illustration a2=. 5 ; d2 = 0; c2=0; e2= Numerical Illustration a2=.5 ; d2 = 0; c2=0; e2=.5 s=0; cooperation >> s=.5; competion >> s=-.5 MZ DZ Unrelated Var Cov r None 1 .50 .25 Cooperation 3.11 2.89 .93 2.67 2.33 .88 2.22 1.78 .80 Competition 1.33 .44 .33 -.67 -.38 -1.78 -.80 Social interactions cause the variance of the phenotype to depend on the degree of relationship of the social actors Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004