提出新方法评估部分探索性因子分析的因子数与结构，提升模型可靠性。
Recovering Latent Structures after Variational Bayesian Variable Selection: Fit Assessment and Factor-Number Selection in Partially Exploratory Factor Analysis
- 用变分贝叶斯变量选择恢复弱指定的因子载荷结构
- 通过增益规则准确识别真实因子数，优于传统指标
- 适用于需灵活建模因子结构的研究者，如心理学量表开发
在部分探索性因子分析（PEFA）中，因子载荷结构和因子数量设定较弱。本文采用正则化变分近似方法（PCFA VA），利用尖峰-平滑先验为未指定载荷分配包含概率，实现结构恢复。研究引入后选择评估框架：将收敛解转化为协方差模型，采用硬选择（阈值化概率生成稀疏模式）或软选择（保留概率作为有效参数权重）。推导出相应的自由度、绝对拟合指标（RMSEA、SRMR、CFI、TLI）及相对准则（AIC、BIC、ELBO）。为确定因子数，提出无量纲增益规则并设持续下降保护机制。模拟结果显示，绝对指标能有效追踪载荷恢复情况并标识因子不足问题；尽管原始准则随因子数波动，增益规则可准确恢复真实维度，其中ELBO版本最稳健。最后，在100项PID-5量表实例中，本模型拟合优于25个构面的验证性模型，并在不同规格下一致恢复主要结构。
原文摘要 · Abstract (English)
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.
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