Two-level moderated mediation models with single-level data and new measures of effect sizes

This article proposes a two-level moderated mediation (2moME) model with single level data, and develops measures to quantify the moderated mediation (moME) effect sizes for both the conventional moME model and the 2moME model. A Bayesian approach is developed to estimate and test moME effects and the corresponding effect sizes (ES). Monte Carlo results indicate that (1) the 2moME model yields more accurate estimates of the parameters than the conventional moME model; (2) the 95% credibility interval following the 2moME model covers the moME effects and the ESs more accurately than that following the conventional moME model; and (3) statistical tests for the existence of the moME effects with the 2moME model are more reliable in controlling type I errors than those with the conventional moME model, especially under heteroscedasticity conditions. In addition, the developed measures of ES are more interpretable, and directly answer the questions regarding the extent to which a moderator can account for the change of the mediation effect between the predictor and the outcome variable through the mediator variable. An empirical example illustrates the application of the 2moME model and the ES measures.