rater bias & sibling interaction

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)


The Univariate Model

TWIN I TWIN II

A EC A EC

1 1/.5


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)

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)


Parental Ratings


correlations


Twin correlations


Aggressive Behavior

same rater different rater

RMZ .86 .68

RDZ .49 .34

Variance Decomposition


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)


Cholesky Decomposition


AGGm AGGf

A EC A EC

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

Rater Bias Model


E C A

Reliable trait variance T1

mother rating T1

father rating T1

Rm T1

Rf T1

Mothers Bias

A C E


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


+

MRT1

FRT1

=

1

1x a Ax + c Cx + e Ex

Bm

Bf

bm 0

0 bfx

+

Rm

Rf

rm 0

0 rfx

The Mx Script


Mx jobs: Raterbias.mx

Data: TAD.dat

Parental Ratings

Agreement and disagreement


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)


Psychometric Multiple Rater Model


E C A


mother rating T1

father rating T1

A C E


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


+

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 +

The Mx script


Mx jobs: Psychometric.mx

Data: TAD.dat

Different models


-2LL df

Cholesky 26564.480 10356

Rater Bias 26631.108 10360

Psychometric 26563.938 10356

Reliable Trait Variance


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


Boys Girls

Am .12 .00

Af .03 .08

Cm .08 .19

Cf .14 .13

Am .07 .10

Af .06 .07

Sibling Interaction / Rater Contrast


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)


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


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)


Constrast Effect


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


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


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


Begin Matrices;

B full 2 2 ! constrast effect

End Matrices;

Begin Algebra;

P = (I-B)~;

End Algebra

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) /

The Mx-script


Mx jobs: Constrast.mx

Data: TAD.dat

Consequences for Variation and Covariation


basic model:

s

sP1 P2

X1 X2

x x

P1 = sP2 + xX1 P2 = sP1 + xX2

In Matrices


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


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


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


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...


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


1 r

r 1

x 0

0 x

1 s

s 1

1

1-s2

@

To compute the covariance matrix recall


1 + 2sr + s2 r+2s + rs2

r+2s + rs2 1 + 2sr + s2

x2

(1-s2)2

@Σ { yy’} =


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


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

rater bias & sibling interaction

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