Augmented bifactor models and bifactor-(S-1) models are identical. A comment on Zhang, Luo, Zhang, Sun & Zhang (2023)

In a recent study, Zhang, Luo, Zhang, Sun, and Zhang (2023) proposed the augmented oblique bifactor model as a new methodological contribution, in which an oblique bifactor model is augmented by one or more indicator(s). Zhang et al. (2023) argued that the augmented oblique bifactor model is superior to existing bifactor modeling approaches. In this comment, we show that the augmented oblique bifactor model by Zhang et al. (2023) is identical and therefore indistinguishable from bifactor-(S-1) type of models presented by Eid et al. (2017). The augmentation approach has already been recommended in the original work of Eid et al. (2017) and by Eid (2020). Finally, we highlight strengths of the simulation studies conducted by Zhang et al. (2023), but also show that several of the conclusions drawn by Zhang et al. (2023) are incorrect. We conclude that there are no differences when applying augmented and bifactor-(S-1) type of models.