Methodological Considerations in Mediation Analysis and Related Modeling Procedures

In recent years, applications of statistical mediation models have become ubiquitous across the social sciences. The popularity of these models is attributable in part to their utility in facilitating judgements about explanatory theories. For example, in educational research, understanding the process by which an intervention affects student outcomes has significant implications for policy and practice. Of course, there are various design features that researchers must consider when conducting any statistical analysis, including mediation. Features such as multiple groups, small sample sizes, nested data structures, and latent variables are commonly encountered in educational and behavioral studies and can pose additional challenges for applied researchers in terms of model estimation and interpretation. Advanced methodological tools are needed to construct more sophisticated mediation models that are required to accommodate these complex design features. This dissertation is a compilation of three papers that address such methodological issues in mediation analysis. Chapter 1 addresses how to include tests of moderation effects in mediation analysis. It begins by reviewing key elements of mediation and moderation and then discusses methods for integrating the two into a single moderated mediation model. The chapter provides a historical perspective on methodological trends in mediation analysis, setting the stage for subsequent chapters that consider more advanced topics. Chapter 2 extends mediation analysis to the case of nested data structures with small sample sizes and latent variables. It considers multilevel mediation models within the context of the structural equation modeling (SEM) framework and compares the performance of Bayesian and frequentist estimation approaches. Results from a Monte Carlo simulation study are presented which demonstrate the impact of Bayesian priors on indirect effect estimates. Chapter 3 addresses the issue of model selection. Establishing a well-fitting measurement model is a necessary first step in testing mediation in any structural model that includes latent variables. Methods for evaluating model fit are well established in the frequentist framework; however, less work has focused on developing model fit criteria in Bayesian SEM. Applied researchers who wish to conduct mediation analysis with latent variables in the Bayesian framework may find the process of first selecting a measurement model challenging. Chapter 3 discusses recent advances in Bayesian model selection and presents a simulation study that rigorously investigates the performance of various Bayesian model fit indices under different model and data conditions. Taken together, the papers presented in this dissertation synthesize developments in mediation analysis and contribute new understandings to methodological issues that researchers often encounter in applied settings.