Recovering Latent Structures after Variational Bayesian Variable Selection: Fit Assessment and Factor-Number Selection in Partially Exploratory Factor Analysis

2026-07-08 · Source: Takara TLDR - Daily AI Papers · Field: Science & Research — Artificial Intelligence & Machine Learning, Data Science & Analytics, Research Methodology & Innovation · Depth: Expert, medium

Summary

A new post-selection assessment framework is introduced for partially exploratory factor analysis (PEFA), specifically for recovering latent structures after variational Bayesian variable selection. This framework addresses weakly specified loading structures and factor numbers by converting converged solutions from regularized variational approximation (PCFA VA) into covariance models. It employs either hard selection, which thresholds inclusion probabilities into a sparse pattern, or soft selection, which retains them as weights for effective parameter counts. The framework derives degrees of freedom, absolute fit diagnostics like RMSEA, SRMR, CFI, and TLI, and relative criteria such as AIC, BIC, and ELBO. To determine the optimal factor number, a scale-free gain rule with a sustained drop guard is proposed. Simulations confirm that absolute indices effectively track loading recovery and identify under-factoring, while the ELBO variant of the gain rule accurately recovers true dimensionality, outperforming raw criteria that tend to over-factor. A 100-item PID 5 example further validates the model's superior fit compared to a confirmatory 25-facet model.

Key takeaway

For research scientists working with partially exploratory factor analysis, this framework offers a robust approach to assess model fit and determine optimal latent factor numbers. If you are struggling with weakly specified loading structures, consider applying the proposed post-selection assessment, particularly the ELBO variant of the gain rule, to accurately recover true dimensionality. This can lead to more reliable structural models and prevent issues like over-factoring, improving the interpretability and validity of your analyses.

Key insights

A post-selection framework assesses latent structures and determines factor numbers in PEFA using Bayesian variable selection.

Principles

• Absolute fit indices track loading recovery.
• ELBO-based gain rule robustly finds dimensionality.
• Hard or soft selection converts solutions to models.

Method

Convert converged PCFA VA solutions to covariance models via hard (thresholding) or soft (weighted) selection. Derive degrees of freedom, absolute (RMSEA, SRMR, CFI, TLI) and relative (AIC, BIC, ELBO) fit diagnostics. Apply a scale-free gain rule with a sustained drop guard for factor number selection.

In practice

• Apply ELBO gain rule for robust factor number selection.
• Use absolute indices to detect under-factoring.
• Assess model fit with RMSEA, SRMR, CFI, TLI.

Topics

• Partially Exploratory Factor Analysis
• Variational Bayesian Variable Selection
• Latent Structure Recovery
• Factor Number Selection
• Model Fit Assessment
• Spike and Slab Priors
• ELBO Criterion

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Takara TLDR - Daily AI Papers.