A Comparison of Bayesian and Frequentist Model Selection Methods for Factor Analysis Models
We compare the performances of well-known frequentist model fit indices (MFIs) and several Bayesian model selection criteria (MCC) as tools for cross-loading selection in factor analysis under low to moderate sample sizes, cross-loading sizes, and possible violations of distributional assumptions. The Bayesian criteria considered include the Bayes factor (BF), Bayesian Information Criterion (BIC), Deviance Information Criterion (DIC), a Bayesian leave-one-out with Pareto smoothed importance sampling (LOO-PSIS), and a Bayesian variable selection method using the spike-and-slab prior (SSP; Lu, Chow, & Loken, 2016). Simulation results indicate that of the Bayesian measures considered, the BF and the BIC showed the best balance between true positive rates and false positive rates, followed closely by the SSP. The LOO-PSIS and the DIC showed the highest true positive rates among all the measures considered, but with elevated false positive rates. In comparison, likelihood ratio tests (LRTs) are still the preferred frequentist model comparison tool, except for their higher false positive detection rates compared to the BF, BIC and SSP under violations of distributional assumptions. The root mean squared error of approximation (RMSEA) and the Tucker-Lewis index (TLI) at the conventional cut-off of approximate fit impose much more stringent “penalties” on model complexity under conditions with low cross-loading size, low sample size, and high model complexity compared with the LRTs and all other Bayesian MCC. Nevertheless, they provided a reasonable alternative to the LRTs in cases where the models cannot be readily constructed as nested within each other.