Augmented Bifactor Models and Bifactor-(S-1) Models are Identical. A Comment on Zhang, Luo, Zhang, Sun & Zhang (2023)

Figures & data

Figure 1. (A) Augmented oblique bifactor model by Zhang et al. (2023) using one augmenting indicator. (B) Bifactor-(S*I-1) model by Eid et al. (2017) with one reference indicator. (C) Augmented orthogonal bifactor model with one augmenting indicator. (D) Bifactor-(S-1) model by Eid et al. (2017) and Eid (2020) with two reference indicators.

Figure 2. Figure shows a bifactor-(S-1) model in which two additional indicators are used to directly measure general hyperactivity-impulsivity factor (GF-HI) and three specific reference factors for hyperactivity-impulsivity assessed in specific situations (SRF-HI1, SRF-HI2, SRF-HI3). Y_ij: observed variables, E_ij: error variables, λ_ij: factor loadings, i: indicator, j: facet. The above figure was taken from Eid (2020, see his Figure 2c on page 898).

Figure 3. Flowchart taken from Eid (2020, see Figure 2 on page 899).

Zhang, B., Luo, J., Zhang, S., Sun, T., & Zhang, D. C. (2023). Improving the statistical performance of oblique bifactor measurement and predictive models: An augmentation approach. Structural Equation Modeling: A Multidisciplinary Journal, 31, 233–252. https://doi.org/10.1080/10705511.2023.2222229

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Eid, M., Geiser, C., Koch, T., & Heene, M. (2017). Anomalous results in g-factor models: Explanations and alternatives. Psychological Methods, 22, 541–562. https://doi.org/10.1037/met0000083

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Eid, M. (2020). Multi-faceted constructs in abnormal psychology: Implications of the bifactor S-1 model for individual clinical assessment. Journal of Abnormal Child Psychology, 48, 895–900. https://doi.org/10.1007/s10802-020-00624-9

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