via E), and are likely to cause problems in the univariate moderation model. After all, these non-zero semi-partial correlations, whether positive or negative, will somehow need to be accommodated in the model. Considering the univariate moderation model as depicted in Fig. 1b, a non-zero semi-partial correlation between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\text{T}}_{1}^{\prime } $$\end{document} and M2 is most likely to be accommodated via the effects that M has on the variance components A and C, i.e., via β a and β c, as these are the only links between M2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\text{T}}_{1}^{\prime } $$\end{document}, and M1 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\text{T}}_{2}^{\prime } $$\end{document}, respectively. In Simulation study 1, we investigated first whether these non-zero semi-partial correlations do indeed cause problems in the univariate moderation model. We expect problems to be greatest if the semi-partial correlation deviates more from zero (i.e., in the case that T and M are correlated via E). Second, we investigated whether these problems indeed manifest themselves mostly through β a and β c.
