3 Genotype $\times$ Environment Interaction

As stated in the introduction of this chapter, genotype $\times$ environment (G $\times$ E) interactions can be detected by estimating components of phenotypic variance conditional on environmental exposures. To do so, MZ and DZ covariance matrices are computed for twins concordant for exposure, concordant for non-exposure , and discordant for exposure, and structural equation models are fitted to the resulting six zygosity groups. The Mx specifications for alternative G $\times$ E interaction models are quite similar to those used in a sex-limitation analysis; however, there are important differences between the two. In a G $\times$ E interaction analysis, the presence of a sixth group provides the information for an additional parameter to be estimated. Further, the nature of alternative hypotheses used to explain heterogeneity across groups differs from those invoked in a sex-limitation analysis. In section 9.3.1 we detail these differences, and in section 9.3.2 we illustrate the method with an application to data on marital status and depression.