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UBC Theses and Dissertations

Distinguish the bifactor and higher-order factor model : a comparison of three RMSEA-related approaches under model misspecification Zhou, Linnan (Paradox)


The bifactor model (BFM) is widely used in psychology, often compared with its nested models like the higher-order factor model (HFM) using fit indices. Previous simulation studies have shown that the BFM tends to outperform the HFM via fit indices, even when the HFM is the data-generating model (Greene et al., 2019; Morgan et al., 2015; Murray & Johnson, 2013). The superior model fit of the BFM has been described as a fit index “bias” rather than an indication of model correctness. Focusing on the root mean square error of approximation (RMSEA), the dominant approaches in the nested model comparison are the simple RMSEA approach (i.e., compare RMSEA of both models) and the ∆RMSEA approach (i.e., calculate the difference between two RMSEA values and use a non-zero cut-off to evaluate). An alternative approach, which uses an RMSEA associated with the chi-square difference test (i.e., RMSEA_D) has also been re-discovered and advocated (Brace, 2020; Savalei, et al., 2023). In the study, I evaluated the performance of three approaches when the true model is the HFM, containing varying degrees of misspecification. The results showed that the simple RMSEA approach was biased in favour of the BFM under minor misspecification, while the ∆RMSEA approach leaned towards HFM, even with severe misspecification. The RMSEA_D approach quantifies the misfit introduced by the HFM for each model misspecification condition without favouring either model. Additionally, I investigated how sample size and model size affect the equivalence test results of RMSEA_D. Recommendations are also made for future nested model comparison.

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