Dimensionality assessment in bi-factor structures with multiple general factors: a network psychometrics approach

The accuracy of factor retention methods for structures with one or more general factors, typically encountered in fields like intelligence, personality, and psychopathology, has often been overlooked in dimensionality research. To address this issue, we compared the performance of several factor retention methods in this context, including a new, highly accurate network psychometrics approach. For estimating the number of group factors, these methods were the Kaiser criterion, empirical Kaiser criterion, parallel analysis with principal components (PAPCA) or principal axis, and exploratory graph analysis with Louvain clustering (EGALV). We then estimated the number of general factors using the factor scores of the first-order solution suggested by the best two methods, yielding a “second-order” version of PAPCA (PAPCA-FS) and EGALV (EGALV-FS). Additionally, we examined the direct multi-level solution provided by EGALV. All the methods were evaluated in an extensive simulation manipulating nine variables of interest, including population error. The results indicated that EGALV and PAPCA displayed the best overall performance in retrieving the true number of group factors, the former being more sensitive to high cross-loadings, and the latter to weak group factors and small samples. Regarding the estimation of the number of general factors, both PAPCA-FS and EGALV-FS showed a close to perfect accuracy across all the conditions, whereas EGALV was inaccurate. The methods based on EGA were superior in the conditions most likely to be encountered in practice. Therefore, we highlight the particular usefulness of EGALV (group factors) and EGALV-FS (general factors) for assessing bi-factor and generalized bi-factor structures.