Why Do Bi-Factor Models Outperform Higher-Order Factor Models? A Network Perspective.

Bi-factor models of intelligence tend to outperform higher-order factor models statistically. The literature provides the following rivalling explanations: (i) the bi-factor model represents or closely approximates the true underlying data-generating mechanism; (ii) fit indices are biased against the higher-order factor model in favor of the bi-factor model; (iii) a network structure underlies the data. We used a Monte Carlo simulation to investigate the validity and plausibility of each of these explanations, while controlling for their rivals. To this end, we generated 1000 sample data sets according to three competing models-a bi-factor model, a (nested) higher-order factor model, and a (non-nested) network model-with 3000 data sets in total. Parameter values were based on the confirmatory analyses of the Wechsler Scale of Intelligence IV. On each simulated data set, we (1) refitted the three models, (2) obtained the fit statistics, and (3) performed a model selection procedure. We found no evidence that the fit measures themselves are biased, but conclude that biased inferences can arise when approximate or incremental fit indices are used as if they were relative fit measures. The validity of the network explanation was established while the outcomes of our network simulations were consistent with previously reported empirical findings, indicating that the network explanation is also a plausible one. The empirical findings are inconsistent with the (also validated) hypothesis that a bi-factor model is the true model. In future model selection procedures, we recommend that researchers consider network models of intelligence, especially when a higher-order factor model is rejected in favor of a bi-factor model.