Fortunately, most published papers in which the univariate moderation model was used concern moderation effects of family-level moderators such as SES, parental educational attainment level, or the age of the twins, i.e., variables that are by definition equal in both twins. As we have shown, non-zero semi-partial correlations are not a problem in that case and the false positive rate is rather too low than too high (i.e., the model is slightly conservative). In a few published papers, however, moderators were studied that did show variation between twins (e.g., McCaffery et al. 2008, 2009; Timberlake et al. 2006: moderators under study were educational attainment level of the twins, exercise level of the twins, and the twins’ self-reported religiosity, respectively). Whether the moderation effects reported in these papers are genuine or spurious (i.e., the result of non-zero semi-partial cross-trait cross-twin correlations) depends, as we have shown, on the nature of the correlation between T and M, on the nature of the correlation between M1 and M2, and on the absence or presence of moderation of the covariance between M and T.
