Lower-level mediation with binary measures

Abstract

In recent literature, researchers have put a lot of time and effort in expanding mediation to multilevel settings. Unfortunately, such extensions are often limited to continuous settings, whereas research on multilevel mediation with binary mediators and outcomes remains rather sparse. Additionally, in lower-level mediation, the effect of the lower-level mediator on the outcome may oftentimes be confounded by an (un)measured upper-level variable. When such confounding is left unaddressed, the effect of the mediator, and hence the causal mediation effects themselves, will be estimated with bias. In linear settings, bias due to unmeasured additive upper-level confounding is often remedied by separating the effect of the mediator into a within- and between-cluster component. However, this solution is no longer valid when considering binary outcome measures. To assess the severity of this transgression, we aim to tackle lower-level mediation in binary settings from a counterfactual point of view, with a special focus on small clusters. We do this by 1) providing non-parametrical identification assumptions of the direct and indirect effect, 2) parametrically identifying these effects based on appropriate modelling equations, 3) considering estimation models for the mediator and the outcome, and 4) estimating the causal effects through an imputation algorithm that samples counterfactuals. Since steps three and four can be completed in various ways, we compare the performance of three different estimation models (an uncentered and centred separate modelling method, and a joint approach), and two different ways of predicting random effects (marginally versus conditionally). Employing simulations, we observe that the joint approach combined with a marginal generation of random effects performs best when sample sizes are sufficiently large. Additionally, we illustrate our findings with data from a crossover study that assesses the impact of experimentally induced goal conflict on the helping behaviour of partners of individuals with chronic pain.