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

TLDR

Scale score generalization to a latent common factor is indexed by general factor saturation. The study compares seven techniques for estimating omega hierarchical (ω h) across simulated data sets. The authors evaluated the methods on 160 simulated datasets with four group factors, 200 datasets without a general factor, and 40 datasets modeled after a real scale with three unequal group factors. Alpha and first‑unrotated principal factor or component methods should be rejected as estimates of 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 .