Penalized eigenvalue block averaging: Extension to nested model comparison and Monte Carlo evaluations

Testing goodness-of-fit and multi-group nested models in confirmatory factor analysis under non-normality is foundational in psychometrics and related fields. Recently, a penalized eigenvalue block averaging (pEBA) procedure was proposed for testing goodness-of-fit, showing promise in a restricted type I error control simulation study. In this study, we extend the simulation conditions to higher dimensions for latent and observed vectors and evaluate type I error control and power for many pEBA variants and traditional test statistics. All statistics are evaluated in four versions, by crossing the base statistic (ML or Browne's RLS), and whether the asymptotic covariance matrix estimator was bias-corrected or not. We develop pEBA methods in the new setting of nested model comparison, accompanied by extensive Monte Carlo evaluation of their performance in weak invariance testing, including type I error control and power. The best-performing procedure for goodness-of-fit testing was pEBA with four blocks, based on the RLS statistic, using the asymptotic covariance matrix estimator without bias correction. For measurement invariance, pEBA with singleton blocks, using the standard ML statistic and the unbiased estimator for the asymptotic covariance matrix, performed best. The pEBA procedures are available in the newly developed R package semTests.