Multilevel Factorial Designs With Experiment-Induced Clustering
Factorial experimental designs have many applications in the behavioral sciences. In the context of intervention development, factorial experiments play a critical role in building and optimizing high-quality, multicomponent behavioral interventions. One challenge in implementing factorial experiments in the behavioral sciences is that individuals are often clustered in social or administrative units and may be more similar to each other than to individuals in other clusters. This means that data are dependent within clusters. Power planning resources are available for factorial experiments in which the multilevel structure of the data is due to individuals’ membership in groups that existed before experimentation. However, in many cases clusters are generated in the course of the study itself. Such experiment-induced clustering (EIC) requires different data analysis models and power planning resources from those available for multilevel experimental designs in which clusters exist prior to experimentation. Despite the common occurrence of both experimental designs with EIC and factorial designs, a bridge has yet to be built between EIC and factorial designs. Therefore, resources are limited or nonexistent for planning factorial experiments that involve EIC. This article seeks to bridge this gap by extending prior models for EIC, developed for single-factor experiments, to factorial experiments involving various types of EIC. We also offer power formulas to help investigators decide whether a particular experimental design involving EIC is feasible. We demonstrate that factorial experiments can be powerful and feasible even with EIC. We discuss design considerations and directions for future research.