Multilevel mediation analysis: The effects of omitted variables in the 1-1-1 model

Multilevel mediation analysis examines the indirect effect of an independent variable on an outcome achieved by targeting and changing an intervening variable in clustered data. We study analytically and through simulation the effects of an omitted variable at level 2 on a 1-1-1 mediation model for a randomized experiment conducted within clusters in which the treatment, mediator, and outcome are all measured at level 1. When the residuals in the equations for the mediator and the outcome variables are fully orthogonal, the two methods of calculating the indirect effect (ab, c - c') are equivalent at the between- and within-cluster levels. Omitting a variable at level 2 changes the interpretation of the indirect effect and will induce correlations between the random intercepts or random slopes. The equality of within-cluster ab and c - c' no longer holds. Correlation between random slopes implies that the within-cluster indirect effect is conditional, interpretable at the grand mean level of the omitted variable.