Carroll's Three-Stratum (3S) Cognitive Ability Theory at 30 Years: Impact, 3S-CHC Theory Clarification, Structural Replication, and Cognitive-Achievement Psychometric Network Analysis Extension

Abstract

Carroll's treatise on the structure of human cognitive abilities is a milestone in psychometric intelligence research. Thirty years later, Carroll's work continues to influence research on intelligence theories and the development and interpretation of intelligence tests. A historical review of the relations between the 3S and CHC theories necessitates the recommendation that the theories of Cattell, Horn, and Carroll be reframed as a family of obliquely correlated CHC theories-not a single CHC theory. Next, a previously unpublished Carroll exploratory factor analysis of 46 cognitive and achievement tests is presented. A complimentary bifactor analysis is presented that reinforces Carroll's conclusion that his 3S model more accurately represents the structure of human intelligence than two prominent alternative models. Finally, a Carroll-recommended higher-stratum psychometric network analysis (PNA) of CHC cognitive, reading, and math variables is presented. The PNA results demonstrate how PNA can complement factor analysis and serve as a framework for identifying and empirically evaluating cognitive-achievement causal relations and mechanisms (e.g., developmental cascade and investment theories), with an eye toward improved cognitive-achievement intervention research. It is believed that Carroll, given his long-standing interest in school learning, would welcome the integration of theory-driven factor and PNA research.

Keywords: CHC theory; Carroll; Cattell; Gf-Gc; Horn; factor analysis; intelligence; psychometric network analysis; three-stratum theory.

Figure 1

Weighted undirected network structure of eight WJ III CHC cognitive composite measures and one reading (GRWR2) composite measure in the cognitive–reading network model. Note. Numbers are the edge weights greater than or equal to .10 (see key for three-category system of relative weight size). The three most central nodes are designated by black and gray circles on nodes (see manuscript text).

Figure 2

Weighted undirected network structure of eight WJ III CHC cognitive composite measures and one math (GQ2) composite measure in the cognitive–math network model. Note. Numbers are the edge weights greater than or equal to .10 (see key for three-category system of relative weight size). The three most central nodes are designated by black and gray circles on nodes (see manuscript text).

Figure 3

CHC cognitive, reading, and math composite variables (and weights) from Figure 1 and Figure 2 as organized as per the developmental cascade and Cattell investment theories. Note. Bold font indicates direct cognitive path links to achievement composite measures.