Testing Informative Hypotheses in Factor Analysis Models Using Bayes Factors

This study proposes a Bayesian approach to testing informative hypotheses in confirmatory factor analysis (CFA) models. The informative hypothesis, which is formulated by the constrained loadings, can directly represent researchers’ theories or expectations about the tau equivalence in reliability analysis, item-level discriminant validity, and relative importance of indicators. Support for the informative hypothesis is quantified by the Bayes factor. We present the adjusted fractional Bayes factor of which the prior distribution is specified using a part of the data and adjusted according to the hypotheses under evaluation. This Bayes factor is derived and computed using the Markov chain Monte Carlo posterior samples of model parameters. Simulation studies investigate the performance of the proposed Bayes factor. A classic example of CFA models is used to illustrate the construction of the informative hypothesis, the specification of the prior distribution, and the computation and interpretation of the Bayes factor.