Structural Equation Models In Behavior Genetics
Arthur S. Goldberger, University of Wisconsin
Abstract
That IQ is a highly heritable trait has been widely reported.
Rather less well-known are such recent reports in major
scientific journals that the heritability of controllable
life events is 53% among women and 14% among men, while the
heritabilities of inhibition of aggression, openness to
experience, and right-wing authoritarianism are respectively
12%, 40%, and 50%. Milk and soda intake are in part
heritable, but not the intake of fruit juice or diet soda.
These numbers are parameter estimates obtained in structural
models fitted to measures taken on pairs of siblings --
prototypically identical and fraternal twins, raised together
and raised apart. The models are of the random effects type, in which
variances and covariances of an observed trait are specified in terms of
latent factors -- genetic and environmental -- whose prespecified
cross-sibling correlations differ by zygosity and rearing status.
Estimation is by maximum likelihood, with chi-square testing,
and (occasionally) confidence intervals based on empirical likelihood.
For these studies, various issues arise. Those discussed here include:
identification by arbitrary restrictions, non-negativity constraints,
pretest estimation, conditioning of the design matrix, multivariate
modelling via Cholesky decomposition, and, last but not least, the
purpose of structural modeling.