3 Scalar Effects G $\times$ E Interaction Model

As with the scalar sex-limitation model, the scalar G $\times$ E interaction model equates genetic and environmental effects on exposed twins to be a scalar multiple of similar effects on twins who have not been exposed to a modifying environment. As a consequence, the heritability of a trait remains constant across exposure groups, and there is no evidence for a genotype $\times$ environment interaction. This situation may arise if there is a mean-variance relationship, and an increase in trait mean under a particular environmental condition is accompanied by an increase in phenotypic variation. When this is the case, the ratio of the genetic variance component and environmental variance component is expected to remain the same in different environments. The Mx specification for the scalar G $\times$ E interaction model is identical to that used for the scalar sex-limitation model, except for the addition of MZ discordant pairs. The Mx script in Appendix  illustrates how these pairs may be included.