The use of factor mixture modeling to investigate population heterogeneity in hierarchical models of intelligence

Spearman’s law of diminishing returns (SLODR) posits that at higher levels of general cognitive ability, the general factor (g) performs less well in explaining individual differences in cognitive test performance. The present study used factor mixture modeling to investigate SLODR in the Kaufman Assessment Battery for Children--Second Edition (KABC-II). Factor mixture modeling was a useful method to study SLODR because group membership was determined based on probabilities derived from the model. A second-order confirmatory factor model, consistent with three-stratum theory (Carroll, 1993), was modeled as a within-class factor structure. The fit of several models with varying number of classes and factorial invariance restrictions were compared. A sex covariate was also included with the models that provided the best fit for the data. The results indicated that a two-class model, which allowed for g mean differences, and class-specific g variances and subtest residual variances, provided the most parsimonious explanation of the data. Consistent with SLODR, the second-order general factor explained less subtest variance and less variance in the first-order factors for those of higher general ability. The standardized subtest residual variances were also larger in the high ability class than in the low ability class. Controlling for g, boys performed higher than girls in visual-spatial ability in each of the low and high ability classes. The findings from this study have implications for future research on the interpretation of intelligence test scores across the ability distribution.