On the distortion of model fit in comparing the bifactor model and the higher-order factor model

• The distortion of fit may appear perfectly correlated in the setting of Gignac (2016), the relation is in essence nonlinear.
• A pattern of distortion of model fit as found by Gignac is generally expected and not unique to the bifactor versus higher-order factor model comparison.

Gignac (2016) showed that if the constraint by which the higher-order factor model is nested within the bifactor model is violated (the so-called ‘proportionality constraint’), model misfit relates strongly to the magnitude of the violation. In the present paper two clarifications of the results by Gignac are discussed. First, it is noted how the misfit relates to the magnitude of the violation in the simulation study by Gignac. Second, it is argued that such a pattern of distortion of model fit as found by Gignac is generally expected and not unique to the bifactor versus higher-order factor model comparison.