Recovering bifactor models: A comparison of seven methods.

Abstract

The last decade has witnessed a resurgence of interest in exploratory bifactor analysis models and the concomitant development of new methods to estimate these models. Understandably, due to the rapid pace of developments in this area, existing Monte Carlo comparisons of bifactor analysis have not included the newest methods. To address this issue, we compared the model recovery capabilities of 5 existing methods and 2 newer methods (Waller, 2018a) for exploratory bifactor analysis. Our study expands upon previous work in this area by comparing (a) a greater number of estimation algorithms and (b) by including both nonhierarchical and hierarchical bifactor models in our study design. In aggregate, we conducted almost 3 million exploratory bifactor analyses to identify the most accurate methods. Our results showed that, when compared with the alternatives, the rank-deficient Schmid-Leiman and Direct Schmid-Leiman methods were better able to recover both nonhierarchical and hierarchical bifactor structures.

Appropriate Use of Bifactor Analysis in Psychopathology Research: Appreciating Benefits and Limitations

“…In this example, the general factor is not really a general factor at all, but rather just a group factor that has been shuffled into a different part of the model, cf. (34). In this case, the appropriate conclusion is that the data represent three weakly correlated factors.…”

“…Likewise, it becomes more difficult to assess the differential external validity of the general or group factors since the unique relations of the group factors must be drawn from the residuals (disturbances), rather than the latent group factors themselves. To increase clarity, even when a higher-order model is theoretically preferred, results are often presented in the form of a constrained bifactor model using the Schmid-Leiman transformation (34). In general, we argue that the bifactor model makes testing theoretical hypotheses about general and group factors clearer and more interpretable, even if the conceptual model posits that the general factor directly contributes to the narrow group factors.…”

“…The latter patterns would imply that there is not a coherent group factor separable from the content contained in the general factor. For discussions of best practices in interpreting patterns of factor loadings in bifactor models, see (10,34,57). To enhance comparability across samples, researchers should consider drawing on previous bifactor model results to add additional constraints to the model, such as constraining the relative magnitudes of indicator loadings on general versus group factors, using informative Bayesian priors based on previous studies, or even fixing factor loadings to specific previously estimated values.…”

Factor Analysis and Variance Partitioning in Intelligence Test Research: Clarifying Misconceptions

“…With the SL procedure, correlated group factors are prioritized in the first-order solution (with oblique rotation) and allowed to be freely estimated independent of the influence of g . The ability of the SL procedure to recover group factors is well established (Giordano & Waller, 2020). Decker and colleagues neither acknowledged nor discussed this mathematical capability.…”

The general factor of psychopathology: a comparison with the general factor of intelligence with respect to magnitude and predictive validity

“…This rotation funnels the variance shared among all indicators into a general factor, and the variance unique to subsets of the indicators into uncorrelated specific factors. Simulations indicate that this rotation performs well 38 .…”