Is the Bifactor Model a Better Model or Is It Just Better at Modeling Implausible Responses? Application of Iteratively Reweighted Least Squares to the Rosenberg Self-Esteem Scale

Although the structure of the Rosenberg Self-Esteem Scale (RSES) has been exhaustively evaluated, questions regarding dimensionality and direction of wording effects continue to be debated. To shed new light on these issues, we ask (a) for what percentage of individuals is a unidimensional model adequate, (b) what additional percentage of individuals can be modeled with multidimensional specifications, and (c) what percentage of individuals respond so inconsistently that they cannot be well modeled? To estimate these percentages, we applied iteratively reweighted least squares (IRLS) to examine the structure of the RSES in a large, publicly available data set. A distance measure, d_s, reflecting a distance between a response pattern and an estimated model, was used for case weighting. We found that a bifactor model provided the best overall model fit, with one general factor and two wording-related group factors. However, on the basis of d_r values, a distance measure based on individual residuals, we concluded that approximately 86% of cases were adequately modeled through a unidimensional structure, and only an additional 3% required a bifactor model. Roughly 11% of cases were judged as “unmodelable” due to their significant residuals in all models considered. Finally, analysis of d_s revealed that some, but not all, of the superior fit of the bifactor model is owed to that model's ability to better accommodate implausible and possibly invalid response patterns, and not necessarily because it better accounts for the effects of direction of wording.