Estimating Generalizability to a Latent Variable Common to All of a Scale's Indicators: A Comparison of Estimators for ω h

Abstract

The extent to which a scale score generalizes to a latent variable common to all of the scale's indicators is indexed by the scale's general factor saturation. Seven techniques for estimating this parameter—omega_hierarchical (ω_h)—are compared in a series of simulated data sets. Primary comparisons were based on 160 artificial data sets simulating perfectly simple and symmetric structures that contained four group factors, and an additional 200 artificial data sets confirmed large standard deviations for two methods in these simulations when a general factor was absent. Major findings were replicated in a series of 40 additional artificial data sets based on the structure of a real scale widely believed to contain three group factors of unequal size and less than perfectly simple structure. The results suggest that alpha and methods based on either the first unrotated principal factor or component should be rejected as estimates of ω_h.