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This study enhances partially exploratory factor analysis (PEFA) by introducing a post-selection assessment framework that utilizes regularized variational approximation for Bayesian variable selection. The authors demonstrate that their method effectively recovers latent structures and accurately determines the number of factors, outperforming traditional confirmatory models in fit assessment. Key findings reveal that their scale-free gain rule and the ELBO variant provide robust recovery of true dimensionality and improved fit diagnostics, as evidenced by simulations and a practical application to a psychological inventory dataset.
A novel assessment framework reveals that traditional methods fail to capture true dimensionality, while a new gain rule accurately recovers latent structures in factor analysis.
In partially exploratory factor analysis (PEFA), the loading structure and factor numbers are weakly specified. The regularized variational approximation for partially confirmatory factor analysis (PCFA VA) recovers this structure via Bayesian variable selection, using spike and slab priors to assign inclusion probabilities to unspecified loadings. This research introduces a post selection assessment framework for this approach. We convert converged solutions into covariance models using either hard selection (thresholding probabilities into a sparse pattern) or soft selection (retaining them as weights for effective parameter counts). We derive the resulting degrees of freedom, absolute fit diagnostics (RMSEA, SRMR, CFI, TLI), and relative criteria (AIC, BIC, ELBO). To determine factor numbers, we propose a scale free gain rule with a sustained drop guard. Simulations show absolute indices successfully track loading recovery and flag under factoring. While raw criteria over factor, our gain rule accurately recovers true dimensionality, with the ELBO variant proving most robust. Finally, a 100 item PID 5 example demonstrates that our model fits better than a confirmatory 25 facet model and concordantly recovers major structures across disjoint specifications.
