When Is a General Factor Distinguishable? Non-Proportionality, Stable Structure, and the Bifactor Decision

תקציר מקורי באנגליתarXiv:2608.10731v2 Announce Type: replace-cross Abstract: 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 representation