Confirmatory Factor Analysis (CFA) using Bayesian estimation achieved better model fit than with Maximum Likelihood (ML) and thereby provided construct validity for a lymphedema knowledge survey

Background: Model fit for a CFA is used to determine construct validity including the hypothesised underlying dimensionality. Frequentist CFA approaches such as maximum likelihood (ML) estimation often provide poor model fit as a result of unrealistically constraining most item-item residual covariances to zero. Bayesian CFA allows greater flexibility and maintains substantive theory by allowing item-item covariances to vary from zero using uninformed priors with zero means. Methods: We used data from an 11-item survey testing knowledge of lymphedema to estimate a hypothesised one-factor solution using both Bayesian and ML CFA with Mplus software. Results: Model fit was poor for both Bayesian and ML CFA when all covariances were constrained to zero. The addition of 6 covariances based on identification of 4 closely related survey items improved model fit but was still sub-optimal for both approaches. A Bayesian CFA with all item-item covariances allowed to vary around zero provided excellent fit and the only 3 large (beta>0.3) and significant (p<0.05) covariances were a subset of the previously identified 6 covariances. In contrast, good model fit was only obtained using ML when 8 item-item covariances were included which were statistically identified using modification indices rather than substantive knowledge. Conclusion: Bayesian estimation provided a one factor model with excellent fit and maintained substantive theory. ML estimation required inclusion of several item-item covariances which were not all identifiable using survey item knowledge alone. Bayesian CFA provides a more flexible and perhaps more realistic method for assessment of construct validity than ML methods.