Estimating ω_h for structures containing two group factors: Perils and prospects

One of the most serious difficulties in the estimation of omega _hierarchical (ω_h) has not been previously studied. Although it is true that one can impose a set of identifying constraints on one's solution to derive an estimate of ω_h in the two-group factor case, there is the potential for introducing bias into the process of estimating ω_h, depending on the extent to which one's set of identifying constraints corresponds to the structure that actually underlies the scale. The authors demonstrate that this potential bias is only considerable when the ratio of the covariance between items loading on different group factors to the covariance between items loading on the same group factor is low. Four methods for estimating ω_h are compared to each other, and the results suggest that Cronbach's alpha and a method based on the first unrotated principal factor should be rejected as estimates of ω_h.