Post-selection assessment framework for partially exploratory factor analysis

This research introduces a post-selection assessment framework for partially exploratory factor analysis (PEFA) using regularized variational approximation with spike and slab priors. The method recovers loading structures and factor numbers by converting converged solutions into covariance models via hard or soft selection.

• Derives degrees of freedom and absolute fit diagnostics including RMSEA, SRMR, CFI, and TLI.
• Calculates relative criteria such as AIC, BIC, and ELBO for model comparison.
• Proposes a scale-free gain rule with a sustained drop guard to determine the number of factors.
• Simulations show absolute indices track loading recovery while the gain rule accurately recovers true dimensionality.

The framework helps users assess model fit and select factor numbers more robustly, as demonstrated by improved performance over confirmatory models in a 100-item PID-5 example.