何时可区分一般因子？非比例性、稳定结构与双因子决策
When Is a General Factor Distinguishable? Non-Proportionality, Stable Structure, and the Bifactor Decision
- Faculty of Education, The University of Hong Kong（香港大学教育学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究探讨何时可区分一般因子，提出两步法用于部分探索性因子分析，通过模拟与实证数据揭示了双因子结构的可区分条件及相关误差特性。
AI中文摘要：
是否需要在相关一阶因子之外增设一个额外的一般维度，这是总体协方差矩阵的属性，而非任何估计量或设计的属性。本研究确立了可判定该属性的条件：若每个聚类内的一般载荷与组载荷成比例，则双因子结构与相关因子协方差等价，因此不存在可区分二者的样本量（命题1）；若每个聚类内的该比例关系均不成立，则每个聚类含3个项目且满足若干温和正则性条件时，不存在带对角唯一性的K因子模型能重现该协方差矩阵（定理1）；二者之间为混合边界，此处通过数值方式定位，取决于聚类抗性。因此可区分性是分级的，由总体与K因子类的距离度量。由于该问题以本身不确定的一阶结构为条件，故在部分探索性因子分析中提出两步法，仅当结构在相邻计数间可重现时才输出该结构，并将未输出视为合法结果。模拟显示，一致计数可能伴随无法重现的结构，且被吸收的局部依赖可模仿一般因子，误差随样本量增大而增长，而稳定性指标保持良好。4个实证数据集展示了可能的结果。
英文摘要：
Whether an added general dimension is necessary beyond correlated first-order factors is a property of population covariance, not an estimator. A bifactor structure is covariance-equivalent to correlated factors when general and group loadings are proportional within every cluster. When every cluster violates proportionality, at least three indicators per cluster and mild conditions rule out exact reproduction by a K-factor model with diagonal uniquenesses. Mixed configurations remain only partly characterized, motivating graded distinguishability. We develop a two-step procedure that delivers a stable first-order structure only when it persists across direct wider-count comparisons, then compares oblique and bifactor representations conditionally on delivery. A preliminary simulation study provides tentative design evidence. A major study develops three non-nested persistence profiles, designates .80/r2 as the practical default, and evaluates the frozen family on held-out replications from the same generators. Within the studied scenarios, anchor-only persistence outperforms anchor-zero, minimum congruence modestly outperforms maximum RMSD, and depth four adds no precision at the fixed .70 cutoff. Held-out results also expose stable-yet-wrong delivery under a weak core and show that the conditional comparison is highly accurate after correct recovery. Four empirical applications illustrate agreement, adjacent-count uncertainty, and non-delivery. Persistence, not count alone, carries the structural decision.
