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

2. 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

3. 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

4. Variance Decomposition of AGG based on mother ratings at age 10
Aboy ( )
Agirl ( )
Cboy ( )
Cgirl ( )
Eboy ( )
Egirl ( )
Seventeenth International Workshop On Methodology of Twin And Family Studies
Boulder, CO, 2004

5. 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

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

10. 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

11. Cholesky Decomposition
AGGm
AGGf A E C
Seventeenth International Workshop On Methodology of Twin And Family Studies
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12. Cholesky Decomposition
Boys
[=A%(A+C+E)]
[=C%(A+C+E)]
[=E%(A+C+E)]
Girls
[=A%(A+C+E)]
[=C%(A+C+E)]
[=E%(A+C+E)]
Seventeenth International Workshop On Methodology of Twin And Family Studies
Boulder, CO, 2004

13. 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

14. 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

15. 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 |
| A+C+E )*L' ;
Seventeenth International Workshop On Methodology of Twin And Family Studies
Boulder, CO, 2004

16. 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

17. Agreement and disagreement
Parental Ratings
Agreement and disagreement
Seventeenth International Workshop On Methodology of Twin And Family Studies
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18. 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
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19. 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

20. 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

21. 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 |
| G+S+F) + L*(A+C+E |
| A+C+E )*L' ;
Seventeenth International Workshop On Methodology of Twin And Family Studies
Boulder, CO, 2004

22. 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

23. Different models -2LL df Cholesky 26564.480 10356
Rater Bias
Psychometric
Seventeenth International Workshop On Methodology of Twin And Family Studies
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24. Reliable Trait Variance
Boys Girls A C E
.63
.20
.17
.50
.29
.21
Seventeenth International Workshop On Methodology of Twin And Family Studies
Boulder, CO, 2004

25. Rater Bias & Rater Specific parts of the total variance
Boys Girls Am Af Cm Cf Am Af
Seventeenth International Workshop On Methodology of Twin And Family Studies
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26. 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
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27. 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

28. 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

29. 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

30. 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 + eE P2 = sP1 + aA2 + cC2 + eE2
Seventeenth International Workshop On Methodology of Twin And Family Studies
Boulder, CO, 2004

31. 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
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32. (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

33. 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

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

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

36. Consequences for Variation and Covariation
basic model: s P1 P2 X1 X2 x
P1 = sP2 + xX P2 = sP1 + xX2
Seventeenth International Workshop On Methodology of Twin And Family Studies
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37. 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
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38. (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

39. 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

40. 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

41. 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

42. 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

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

44. 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

45. 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