Using Exploratory Bifactor Analysis to Understand the Latent Structure of Multidimensional Psychological Measures: An Example Featuring the WISC-V

Abstract

Exploratory bifactor analysis (EBFA) represents a methodological advancement for implementing a bifactor model in exploratory factor analysis (EFA). However, little is known about how to properly employ the procedure. The current rotation criteria available for EBFA make it more likely to “get stuck” in local minima, contributing to possible group factor collapse, than more traditional EFA rotations. Thus, getting a proper solution is a more complex and involved process than typical EFA and may require a sensitivity analysis. This article examines EBFA through a sensitivity analysis and subsequent simulation of parameters thought to contribute to group factor collapse. Results support the use of sensitivity analysis, as the problematic variable was shown to greatly increase the likelihood of factor collapse. The hypothesis that estimation start values contribute to factor collapse was not supported. Accompanying R syntax for all analyses are provided to facilitate reproducibility.

Keywords:

• Exploratory bifactor analysis
• sensitivity analysis
• Monte Carlo simulation
• Wechsler intelligence scale for children–fifth edition

Notes

¹ Throughout this article, we assume all high-order factor models include multiple first-order factors and a single second-order factor, and all bifactor models include only first-order orthogonal group factors.

² In theory, the general factor could also have both direct and indirect effects on the measured variables (Yung et al., 1999), but there is not a method for examining such a model in EFA.

³ Perceptual Reasoning is a combination of Fluid Reasoning and Visual-Spatial factors.

⁴ The technical manual does not provide the actual factor correlations, so we used the implied correlations from the publisher’s preferred five-factor model.

⁵ The ML objective function is

$log(\mathrm{t}\mathrm{r}\left({\left(\mathbf{\Lambda }{\mathbf{\Lambda }}^{\prime }+{\mathbf{U}}^2\right)}^{-1}\mathbf{R}\right)-log\left(\left|{\left(\mathbf{\Lambda }{\mathbf{\Lambda }}^{\prime }+{\mathbf{U}}^2\right)}^{-1}\mathbf{R}\right|\right)-p,$

where U² are the variable uniqueness’s, R is the sample correlation matrix, tr() the matrix trace function, and p is the number of measured variables.

⁶ Based on the factor loadings, the communality reported by Dombrowski et al. (2015, Table 3, p. 198) for Cancellation in the five-factor solution should be .49.