The limitations of model fit in comparing the bi-factor versus higher-order models of human cognitive ability structure

We addressed the question of whether the bi-factor or higher-order model is the more appropriate model of human cognitive ability structure. In previously published nested confirmatory factor analyses, the bi-factor model tended to be better fitting than the higher-order model; however, these studies did not consider a possible inherent statistical bias favouring the fit of the bi-factor model. In our own analyses and consistent with previous empirical results, the bi-factor model was also better fitting than the higher-order model. However, simulation results suggested that the comparison of bi-factor and higher-order models is substantially biased in favour of the bi-factor model when, as is commonly the case in CFA analyses, there is unmodelled complexity. These results suggest that decisions as to which model to adopt either as a substantive description of human cognitive ability structure or as a measurement model in empirical analyses should not rely on which is better fitting.