Interpretation and Visualization of Moderation Effects and Random Slopes in Multilevel Models

Abstract

Interpretation of complex effects and models can be one of the most challenging and important aspects of quantitative data analysis. The present study tackles this issue for moderation effects, including random slope effects, for multilevel models. To demonstrate the generalization of these procedures beyond the basic multilevel model, the multilevel logistic regression model is used. A moderation effect may be useful when a researcher would like to assess how a particular relationship differs for different groups or different levels of a moderator variable. When the moderator under consideration is a random effect, a random slope model arises. The random slope model has various applications; for example, when observations are nested within individuals comprising a longitudinal design, a random slopes model can be used to assess individual growth trajectories for the subjects in the study. However, these useful effects may be particularly difficult to interpret substantively. Therefore, the present study suggests a method combining the traditional aspects of plotting moderation effects with quantities of interest (QI) computation. Specific suggestions and examples, including R syntax, for associated data visualizations are provided.

Keywords

• moderation
• interaction
• random slopes
• multilevel logistic regression
• interpretation
• r