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

2026-07-08 · Source: Computation and Language · Field: Science & Research — Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning, Research Methodology & Innovation · Depth: Expert, quick

Summary

A new post-selection assessment framework is introduced for Partially Exploratory Factor Analysis (PEFA) using regularized variational approximation for Partially Confirmatory Factor Analysis (PCFA VA). This approach recovers latent structures via Bayesian variable selection, employing spike and slab priors to assign inclusion probabilities to unspecified loadings. The framework converts converged solutions into covariance models using either hard or soft selection, deriving degrees of freedom, absolute fit diagnostics (RMSEA, SRMR, CFI, TLI), and relative criteria (AIC, BIC, ELBO). To determine factor numbers, a scale-free gain rule with a sustained drop guard is proposed. Simulations demonstrate that absolute indices successfully track loading recovery and flag underfactoring, while the gain rule accurately recovers true dimensionality, with the ELBO variant proving most robust. A 100-item PID 5 example shows the model fits better than a confirmatory 25-facet model and recovers major structures across disjoint specifications.

Key takeaway

For research scientists applying partially exploratory factor analysis, this framework offers a robust approach to assess model fit and determine factor numbers. You should integrate its post-selection assessment, including absolute fit diagnostics like RMSEA and SRMR, to track loading recovery and avoid underfactoring. Employing the ELBO variant of the proposed scale-free gain rule will provide a more accurate and robust method for identifying true dimensionality in your models.

Key insights

A post-selection framework assesses latent structures in PEFA, improving factor number and loading recovery.

Principles

• Bayesian variable selection with spike and slab priors aids latent structure recovery.
• Absolute fit diagnostics track loading recovery and identify underfactoring.
• A scale-free gain rule robustly determines true dimensionality.

Method

The framework converts converged solutions into covariance models via hard or soft selection, derives degrees of freedom and fit diagnostics, and uses a scale-free gain rule with a sustained drop guard for factor number selection.

In practice

• Use hard or soft selection to convert variational solutions into covariance models.
• Apply RMSEA, SRMR, CFI, TLI to assess loading recovery and detect underfactoring.
• Employ the ELBO variant of the gain rule for robust factor number determination.

Topics

• Partially Exploratory Factor Analysis
• Variational Bayesian Variable Selection
• Model Fit Diagnostics
• Factor Number Selection
• Latent Structure Recovery

Best for: AI Scientist, Research Scientist

Related on AIssential

• Recovering Latent Structures after Variational Bayesian Variable Selection: Fit Assessment and Factor-Number Selection in Partially Exploratory Factor Analysis — A post-selection framework assesses latent structures and determines factor numbers in PEFA using Bayesian variable selection.
• Structured Nonparametric Variational Inference for Dependent Latent Modeling — SN-VI models complex latent variable dependencies using multivariate splines for accurate posterior approximation.
• Asymptotic Signal Subspace Recovery in Softmax Attention Models — Softmax attention mechanisms can rigorously extract hidden signals from high-dimensional noise through gradient-based learning dynamics.
• Occam's Razor is Only as Sharp as Your ELBO — ELBO's model selection behavior depends critically on the approximate posterior's covariance structure.
• Partial Causal Structure Learning for Valid Selective Conformal Inference under Interventions — Selective conformal prediction under interventions can be robustly maintained by learning partial causal structures.
• To select or not to select? — Predictively consistent priors enable complex models to outperform or match simpler selected models without explicit model selection.

See Counsel's argued verdicts on the open AI decisions leaders are weighing →

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by Computation and Language.