Assessing Essential Unidimensionality of Scales and Structural Coefficient Bias

Percentage of uncontaminated correlations (PUC), explained common variance (ECV), and omega hierarchical (ω_H) have been used to assess the degree to which a scale is essentially unidimensional and to predict structural coefficient bias when a unidimensional measurement model is fit to multidimensional data. The usefulness of these indices has been investigated in the context of bifactor models with balanced structures. This study extends the examination by focusing on bifactor models with unbalanced structures. The maximum and minimum PUC values given the total number of items and factors were derived. The usefulness of PUC, ECV, and ω_H in predicting structural coefficient bias was examined under a variety of structural regression models with bifactor measurement components. Results indicated that the performance of these indices in predicting structural coefficient bias depended on whether the bifactor measurement model had a balanced or unbalanced structure. PUC failed to predict structural coefficient bias when the bifactor model had an unbalanced structure. ECV performed reasonably well, but worse than ω_H.