The Bifactor Model Fits Better Than the Higher-Order Model in More Than 90% of Comparisons for Mental Abilities Test Batteries

Abstract

The factor structure of mental abilities has most often been depicted using a higher-order model. Under this model, general mental ability (g) is placed at the top of a pyramid, with “loading” arrows going from it to the other factors of intelligence, which in turn go to subtest scores. In contrast, under the bifactor model (also known as the nested factors/direct hierarchical model), each subtest score has its own direct loading on g; the non-g factors (e.g., the broad abilities) do not mediate the relationships of the subtest scores with g. Here we summarized past research that compared the fit of higher-order and bifactor models using confirmatory factor analysis (CFA). We also analyzed additional archival datasets to compare the fit of the two models. Using a total database consisting of 31 test batteries, 58 datasets, and 1,712,509 test takers, we found stronger support for a bifactor model of g than for the traditional higher-order model. Across 166 comparisons, the bifactor model had median increases of 0.076 for the Comparative Fit Index (CFI), 0.083 for the Tucker-Lewis Index (TLI), and 0.078 for the Normed Fit Index (NFI) and decreases of 0.028 for the root mean square error of approximation (RMSEA) and 1343 for the Akaike Information Criterion (AIC). Consequently, researchers should consider using bifactor models when conducting CFAs. The bifactor model also makes the unique contributions of g and the broad abilities to subtest scores more salient to test users.