A comparison of frequentist and bayesian approaches: The power to detect model misspecifications in confirmatory factor analytic models

Abstract

This simulation study was conducted to compare the performances of Frequentist and Bayesian approaches in the context of power to detect model misspecification in terms of omitted cross-loading in CFA models with respect to the several variables (number of omitted cross-loading, magnitude of main loading, number of factors, number of indicators per factor and sample size) and (to) investigate the efficiency of BSEM approach to detect cross-loadings. BSEM approach allows including and estimating certain number of cross-loadings by specifying informative piror with small-variance for cross-loadings in the model. By this way, BSEM approach enables researchers to come up with models that better represent the substantive theory. At this simulation study, model misspecification was considered as major misspecification (cl=0.3) and minor misspecification (cl=0.1) according to the amount of omitted cross-loading. Results of this study revealed that Frequentist approach was so sensitive to minor model misspecification whereas Bayesian approach with non-informative prior was so sensitive to the major model misspecification. Finally, it was concluded that the power of BSEM approach to detect cross-loading varied according to the both amount and number of cross-loadings and for large amount of cross-loading the performance of this approach was so well.