Rater Bias & Sibling Interaction Meike Bartels Boulder 2004 Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
Jan 20, 2016
Rater Bias&
Sibling Interaction
Meike Bartels
Boulder 2004
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
GENES (A)
ENVIRONMENT
Nonshared Environment (E)Shared Environment (C)
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
The Univariate Model
TWIN I TWIN II
A EC A EC
1 1/.5
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
Variance Decomposition of AGG based on mother ratings at age 10
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
Aboy .63 (.53-.72)
Agirl .50 (.39-.62)
Cboy .20 (.11- .30)
Cgirl .29 (.18-.40)
Eboy .17 (.15-.19)
Egirl .21 (.18-.23)
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
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
Aggressive Behavior
same rater different rater
RMZ .86 .68
RDZ .49 .34
Variance Decomposition
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
Aggressive Behaviorsame rater different rater
A .74 (A + rater specific view) .68
C .12 (rater bias !!) .00
E .14 (E + rater error) .32
A = 2(rmz-rdz) = 2 (.86-.49) = .74
C = rmz – 2 (rmz-rdz) = .89 – 2( .86-.49) = .14
E = 1- rmz = 1- .86 =.14
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
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
AGGm AGGf
A EC A EC
Cholesky Decomposition
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
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
Rater Bias Model
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
E C A
Reliable trait variance T1
mother rating T1
father rating T1
Rm T1
Rf T1
Mothers Bias
A C E
Reliable trait variance T2
mother rating T2
father rating T2
Rm T2
Rf T2
Fathers Bias
1/ 0.5
1
1 1 1 1
ae c eca
bm bm bfbf
rm bf rm rm
Total variance for an individual
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
+
MRT1
FRT1
=
1
1x a Ax + c Cx + e Ex
Bm
Bf
bm 0
0 bfx
+
Rm
Rf
rm 0
0 rfx
Variance-Covariance Matrices in Mx
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
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' ;
The Mx Script
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
Mx jobs: Raterbias.mx
Data: TAD.dat
Parental Ratings
Agreement and disagreement
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
Parental Disagreement
II. Mother or father specific information
(distinct situations, parental specific relation
with a child)
I. Rater Bias / error (e.g. response style,
different normative standards)
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
Psychometric Multiple Rater Model
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
E C A
Reliable trait variance T1
mother rating T1
father rating T1
A C E
Reliable trait variance T2
father rating T2
mother rating T2
1/ 0.5
1
1 1 1 1
ae c eca
Ef Cf Af
Em Cm Am
Af Cf Ef
Am Cm Em1/ 0.5 1
1/ 0.5 1
em
cm
am
efcf
af afcf
efam
cm
em
Total variance for an individual
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
+
MRT1
FRT1
=
1
1x a Ax + c Cx + e Ex
Am
Af
am 0
0 af
x +
Cm
Cf
cm 0
0 cf
x
Em
Ef
em 0
0 ef
x +
Variance-Covariance Matrices in Mx
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
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' ;
The Mx script
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
Mx jobs: Psychometric.mx
Data: TAD.dat
Different models
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
-2LL df
Cholesky 26564.480 10356
Rater Bias 26631.108 10360
Psychometric 26563.938 10356
Reliable Trait Variance
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
Boys Girls
A .74 .71
C .13 .13
E .13 .16
.63
.20
.17
.50
.29
.21
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
Sibling Interaction / Rater Contrast
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
TWIN I TWIN II
A EC A EC
1 1/.5
s
s
path s implies an interaction between phenotypes
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
Constrast Effect
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
P1 = sP2 + aA1 + cC1 + eE1 P2 = sP1 + aA2 + cC2 + eE2
P1 P2
A1 E1C1 A2 E2C2
1 1/.5
s
s
a c e a c e
Constrast Effect
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
P1
P2
=0 s
s 0
P1
P2
+
a c e 0 0 0
0 0 0 a c e
A1
C1
E1
A2
C2
E2
Matrix expression
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
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
In Mx
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
Begin Matrices;
B full 2 2 ! constrast effect
End Matrices;
Begin Algebra;
P = (I-B)~;
End Algebra
Variance –Covariance Matrix
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
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) /
The Mx-script
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
Mx jobs: Constrast.mx
Data: TAD.dat
Consequences for Variation and Covariation
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
basic model:
s
sP1 P2
X1 X2
x x
P1 = sP2 + xX1 P2 = sP1 + xX2
In Matrices
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
P1
P2
=0 s
s 0
P1
P2
+x 0
0 x
X1
X2
s
sP1 P2
X1 X2
x x
y = By + Gx
Matrix expression
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
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
y= (I-B)-1 Gx
in this case (I-B) is simply
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
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
@
Variance-covariance matrix for P1 and P2
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
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
Remember...
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
s
sP1 P2
X1 X2
x x
We want to standardize variables X1 en X2 to have unit variance and correlation r, so
Σ {xx’} = 1 r
r 1
G =
(I-B)-1 =
Σ {xx’} =
To compute the covariance matrix recall
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
1 r
r 1
x 0
0 x
1 s
s 1
1
1-s2
@
To compute the covariance matrix recall
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
1 + 2sr + s2 r+2s + rs2
r+2s + rs2 1 + 2sr + s2
x2
(1-s2)2
@Σ { yy’} =
Seventeenth International Workshop On Methodology of Twin And Family Studies Boulder, CO, 2004
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 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 Illustrationa2=.5 ; d2 = 0; c2=0; e2=.5
s=0; cooperation >> s=.5; competion >> s=-.5
MZ DZ Unrelated
Var Cov r Var Cov r Var Cov r
None 1 .50 .50 1 .25 .25 1 0 0
Cooperation
3.11 2.89 .93 2.67 2.33 .88 2.22 1.78 .80
Competition
1.33 .44 .33 1.78 -.67 -.38 2.22 -1.78
-.80
Social interactions cause the variance of the phenotype to depend on the degree of relationship of the social actors