Distributional moderation analysis: Unpacking moderation effects in intervention research.

Moderation and subgroup analyses are well-established statistical tools to evaluate whether intervention effects vary across subpopulations defined by participants' demographic and contextual factors. Moderation effects themselves, however, can be subject to heterogeneity and can manifest in various outcome parameters that go beyond group-specific averages (i.e., means) that are typically the focus of main and moderation effect analyses. The present study introduces distributional moderation analysis using the framework of inflated Generalized Additive Models for Location, Scale, and Shape (GAMLSS) that allows researchers to holistically characterize intervention effect modifiers through simultaneously modeling conditional mean-, variance-, skewness-, and kurtosis-based intervention effects, as well as moderated treatment effects located at the endpoints of the response scale (i.e., floor/ceiling effects). Data from a large-scale randomized controlled trial evaluating the effects of a teacher classroom management program on students' disruptive classroom behavior are used to provide a step-by-step guide for applying distributional moderation analysis in school-based intervention research. Although a traditional mean-focused analysis suggests that the intervention reduced students' average disruptive behavior only for students receiving special education, an evaluation of distributional treatment effects reveals a general decrease in the average disruptive behavior for at-risk students. In addition, distributional moderation analysis suggests that this average decrease is moderated by students' race and that the moderation effect of special education status initially seen in the traditional analysis is not located in the means, but in the chance to show no disruptive behavior patterns at all. Thus, we conclude that distributional moderation analysis constitutes a valuable complementary tool to provide a fine-grained characterization of treatment effect modifiers.