The higher-order model imposes a proportionality constraint: That is why the bifactor model tends to fit better
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Bifactor model does not always fit better (TLI, BIC, AIC) than higher-order model.

Comparisons based on TLI largely unaffected by sample size (in contrast to χ2, AIC, BIC)

Model fit differences correlate perfectly with proportionality constraint violation.

Other testable statistical distinctions between the models may not exist.

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