Beyond Convergence and Model Fit: Structural Guidance in CFA, EFA, ESEM-T, and Penalized SEM

This study examines how alternative forms of structural guidance shape latent-variable solutions under dense-loading conditions in which all indicators have systematically nonzero cross-loadings. Near-population analyses (N = 1,000,000) compared exact restrictions, empirical rotation, target-guided rotation, and penalization while minimizing sampling fluctuation. CFA produced increasing distortion as departures from independent-clusters structure increased. EFA recovery depended strongly on the rotation criterion, with Geomin ε = 0.50 performing consistently well across both populations. Exploratory structural equation modeling with target rotation recovered the generating structure accurately when targets were sufficiently aligned and remained highly accessible. Penalized structural equation modeling recovery likewise depended on structural alignment, although accurate retained solutions could be difficult to access across starting values. Supplementary repeated-sampling analyses at N = 500 and 2,000 showed that numerical convergence and excellent fit did not guarantee corresponding factor orientations. Overall, the form and alignment of structural guidance jointly shaped admissibility, accessibility, recovery, and orientation stability, with important implications for practice.