Bayesian Structural Equation Modeling for Small Samples: A Powerful Approach to Address Grand Challenges for Social Work Research

Background: Children living in Appalachian are underrepresented in health and wellness social work research despite their well-documented economic and health disparities. One of the 12 Grand Challenges for Social Work is to ensure the healthy development for all youth. However, social work research involving the healthy development of youth in Appalachian is scarce. Social work needs a small sample statistical approach to model data where “large” data collection may be difficult or expensive to obtain, such as children residing in economically distressed Appalachian communities.  Bayesian structural equation modeling (BSEM) methods are becoming more popular in social and behavioral science due to the intuitive nature and practical advantages of Bayes Theorem, but applications in social work research are limited.  The purpose of this study is to (1) introduce BSEM, (2) discuss the usefulness of Bayesian methods in small sample social work research, and, (3) illustrate how to apply BSEM in a social work research setting.  

Method: This community-based participatory research study contrasted a confirmatory factor analysis on the electronic health literacy scale (eHEALS) with a sample of rural 7^th grade children (n=137) residing in three economically distressed counties in Appalachian using a commonly applied estimator, maximum likelihood (ML), and a BSEM approach using noninformative, weekly informative, and informative priors.  Model fit and comparison were evaluated by common SEM-Based fit indices and Bayesian fit indices. 

Results: The BSEM results demonstrated empirical support for the 1-factor eHEALS model as a parsimonious and reasonable representation of electronic health literacy. The BSEM produced an excellent fitting model (PPP = .50), whereas the ML-based model showed an acceptable fit for the data, χ²₍₁₇₎ = 32.79 (p = .01), RMSEA (CI) = 0.08 (0.04-0.13), CFI= 0.98, TLI= 0.95.  The use of informative priors improved the PPP for the models. Reasons for this discrepancy between ML and BSEM are discussed along with potential advantages and caveats with BSEM. 

Conclusion: The eHEALS scale demonstrates strong measurement in a limited sample of 7^th grade children residing in Appalachian. The current BSEM study highlights the importance of considering a Bayesian approach when planning and conducting social work research, especially for Grand Challenges research.