A finite mixture model for genotype and environment interactions: detecting latent population heterogeneity

Approaches such as DeFries-Fulker extremes regression (LaBuda et al., 1986) are commonly used in genetically informative studies to assess whether familial resemblance varies as a function of the scores of pairs of twins. While useful for detecting such effects, formal modeling of differences in variance components as a function of pairs' trait scores is rarely attempted. We therefore present a finite mixture model which specifies that the population consists of latent groups which may differ in (i) their means, and (ii) the relative impact of genetic and environmental factors on within-group variation and covariation. This model may be considered as a special case of a factor mixture model, which combines the features of a latent class model with those of a latent trait model. Various models for the class membership of twin pairs may be employed, including additive genetic, common environment, specific environment or major locus (QTL) factors. Simulation results based on variance components derived from Turkheimer and colleagues (2003), illustrate the impact of factors such as the difference in group means and variance components on the feasibility of correctly estimating the parameters of the mixture model. Model-fitting analyses estimated group heritability as .49, which is significantly greater than heritability for the rest of the population in early childhood. These results suggest that factor mixture modeling is sufficiently robust for detecting heterogeneous populations even when group mean differences are modest.