The genetic SNP score can be incorporated directly into the ACE model described above as a fixed effect. This approach is equivalent to multivariate linear regression except that the model accounts for clustering within families (twin pairs are nested within families) and within subjects over time due to the repeated measurements. Resulting regression coefficient estimates and standard errors are corrected for the non-independent observations. The overall model is a special case of a mixed effects regression (Pinheiro & Bates, 2000), where the variance components are random effects and the SNP score and covariates are fixed effects, with the difference being that we used a variance-covariance matrix structured to account for twin zygosity.
