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.