Advantages in Bayesian Approaches to Confirmatory Factor Analysis

To conduct rigorous evaluations of preventive interventions, it is foundational to establish the psychometric or measurement quality of the measures. Confirmatory factor analysis (CFA) is a popular method of modeling and evaluating measurement quality. Such analyses are typically conducted within a frequentist framework, which can pose challenges in an applied research setting due to the strong conditions required to establish measurement quality (e.g., sufficient sample size, exact measurement invariance (MI), and high sensitivity to group differences). An alternative set of approaches involves Bayesian methods, which offer several advantages. However, they remain underutilized by prevention scientists. The main goal of this paper is to illustrate several of the advantages that Bayesian methods offer in the context of analyses of data from the Alabama Parenting Questionnaire (APQ) through five examples. We illustrate the advantages of Bayesian methods over maximum likelihood in terms of result interpretation, and highlight how Bayesian methods allow us to express uncertainty in ways we always intended, avoiding misconceptions associated with frequentist approaches (Example 1). We also show how Bayesian methods help to avoid estimation problems (Example 2), examine parameter MI in both conventional and more flexible ways (Examples 3 and 4), and incorporate substantive prior information into our analysis (Example 5). By highlighting these advantages, we aim to motivate prevention researchers to consider using Bayesian methods for CFA and other analyses.