Spearman’s Hypothesis Tested Between and Within Genetic Ancestry Groups in the HRS-HCAP Sample

We tested Spearman's hypothesis, that cognitive differences between groups are concentrated on the general factor of intelligence (g), using multi-group confirmatory factor analysis (MGCFA) and the method of correlated vectors (MCV) in the Health and Retirement Study Harmonized Cognitive Assessment Protocol (HRS-HCAP). We examined differences both between European and African ancestry groups (NEuropean_ancestry = 1805, NAfrican_ancestry = 341), defined by both self-identification and genetic ancestry principal components, as well as between gradients of African ancestry within the African ancestry group. A bifactor model with g and three group factors (Memory, Visuospatial Reasoning, and Speed/Attention) achieved partial strict measurement invariance across ancestry groups and also achieved strict invariance across genetic ancestry gradients within the African ancestry group. The weak form of Spearman’s hypothesis fit the ancestry group comparison best. Regarding the intra-African ancestry comparison, where higher African ancestry was associated with lower cognitive scores, while the Δχ² test indicated that weak Spearman’s hypothesis fit better than the contra model, the evidence overall was less decisive. Nonetheless, results from the strict invariance model implied that g explained 63% of the total absolute latent mean differences across ancestry gradients, which was comparable to the proportion explained between the European and African ancestry groups (52.5%). Correlated vectors analyses using both CFA and EFA-derived g-loadings showed strong convergence with observed between-group differences (r = .76) and within-group African ancestry associations (r = .50 to .65). Overall, the results suggest that Spearman's hypothesis extends to genetic ancestry gradients within the admixed African American population.