Multiple raters March 7 th, 2002 Boulder, Colorado John Hewitt

Multiple raters For example, parental ratings of their children’s behavior Consider parental ratings of children’s internalizing behavior problems based on the Child Behavior Checklist (CBCL)

Twin `correlations’ for young boys SAME PARENT DIFFERENT PARENT rMZ rDZ Genetic: `a 2 ’44%30% Shared Env: `c 2 ’34%12% Non-shared E : `e 2 ’22%58%

What influences `c 2 ’ and `e 2 ’ ? Rated by same parent `a 2 ’ 44% `c 2 ’34% shared env and rater bias `e 2 ’22% non-shared env and rater error

What influences `c 2 ’ and `e 2 ’ ? Rated by different parent `a 2 ’ 30% `c 2 ’12% shared env `e 2 ’58% non-shared env and rater bias and rater error

We can analyze this situation when we have multiple informants.

MZ twinsTwin 1Twin 2 MoFaMoFa Twin 1 Mo Twin 1 Fa Twin 2 Mo Twin 2 Fa1.00

DZ twinsTwin 1Twin 2 MoFaMoFa Twin 1 Mo Twin 1 Fa Twin 2 Mo Twin 2 Fa1.00

Possible approaches to these bivariate data? 1. Cholesky or `biometrical model’ FaMo

Common pathway or `psychometric’ model MoFa

T1T2 MoT1FaT1FaT2MoT2 ACEECA Fa bias Mo bias Residual RRR or 0.5 a a c c ee 11 alpha bm bf rmrf rm

If alpha=1, bm=bf=b, rm=rf=r then Cov MZ, mothers’ ratings = a 2 + c 2 + b 2 Cov DZ, mothers’ ratings = 0.5a 2 + c 2 + b 2 Variance = a 2 + c 2 + b 2 + e 2 + r 2 shared env non-shared env and rater bias and rater error

See script in handout and in F:\jkh\raters\ratingboys.mx

Output matrices from ratingboys.mxo MATRIXPARAMETER AXa 2 =.2674a=.5171 CYc 2 =.1204c=.3470 EZe 2 =.0419e=.2046 BR bm=.3098 bf=.5158 bm 2 =.0960 bf 2 =.2660 FJ rm=.2601 rf=.4172 rm 2 =.0676 rf 2 =.1741 S alpha= observed stats – 8 estimated parameters = 12 df Chi-square=8.967, p = 0.706

T1 MoT1FaT1 ACE Fa bias Mo bias Residual R Parameter estimates Path coefficients

VARIANCE COMPONENTS OF MOTHERS’ RATINGS Reliable trait variance V A = a 2 = (62%) V C = c 2 = (28%) V E = e 2 = (10%) Subtotal= (73%) Maternal bias= (16%) Maternal residual= (11%) Subtotal= Total= (100%)