As the residual correlation within twin pairs was substantial and stronger in MZ twin pairs, regression models were run as hierarchical linear models using PROC MIXED in SAS (SAS Institute, 2008), with twin pairs and individuals within twin pairs being treated as separate levels. Random intercepts were used to estimate family-level variance components. Both the family-level variance and residual variance were estimated separately for MZ and DZ twin pairs. This yields parameter estimates and test statistics for regression coefficients that are adjusted for the residual ICCs for MZ and DZ twins. All explanatory variables were grand mean centered.
