After obtaining estimates of the A and E parameters of the
Cholesky decomposition model, the estimated Cholesky path
coeffi cients were converted and rescaled into A and E correlation
matrices for the 22 variables, which then served as the input
to exploratory factor analyses performed in Mplus 5.21. Exploratory
factor analyses were conducted using an unweighted least
squares estimator because of the nonpositive defi nite properties
of the A and E correlation structures. The geomin rotation method
in Mplus was used to obtain the oblique rotation of the chosen
exploratory factor analysis solution. We used oblique rotations
because we wanted to examine the magnitude of the relationship
between the resulting genetic and environmental factors.
The exploratory factor analysis of the genetic correlation matrix
produced four eigenvalues above unity: 9.88, 3.19, 1.85, and 1.53.
A scree plot was consistent with an infl ection break at either three
or four factors. The fourth factor identifi ed a coherent factor of
fi ve disorders (genetic factor 4 below) and so merited retention.
By contrast, a fi fth factor included only one syndrome with a substantial
loading (eating disorders)—a clear sign of overextraction.
Furthermore, the four-factor solution provides a reasonable summary
of the matrix of genetic correlations seen in Table S3 in the
online data supplement.
Exploratory factor analysis of the specifi c environmental correlation
matrix revealed six factors with eigenvalues exceeding unity:
5.17, 2.70, 1.46, 1.34, 1.19, and 1.10. Examining the scree plot suggests
a break between three and four factors. Adding a third factor
identifi ed a coherent bipolar factor with salient loadings on fi ve
disorders (environmental factor 3 below). Adding a fourth factor,
by contrast, identifi ed a minimally coherent factor with loadings
on only two disorders—positive on drug abuse or dependence and
negative on dependent personality disorder. We again saw this as
evidence of overextraction, so we present results from a four-factor
genetic and a three-factor unique environmental solution.