3. 3. Empirical Evaluations of the "complete" CHC Theory
An acknowledged limitation of Carroll’s (1993, p. 579) three-stratum model was the fact that his inferences regarding the relations between different factors at different levels (strata) emerged from data derived from a diverse array of studies and samples.  None of Carroll’s datasets included the necessary breadth of variables to evaluate, in a single analysis, the general structure of his proposed three-stratum model.   The sample sizes of most studies reviewed by Carroll were modest (median n = 198) and were limited in the breadth of variables analyzed (median number of variables = 19.6) (Roberts, Pallier & Goff, 1999). Some domains were weakly represented (e.g., Ga).  According to Roberts et al. (1999), “no investigator has used confirmatory factor-analytic techniques to determine whether there is empirical support for the structure comprising the most salient aspects (i.e., Strata I and II) of Carroll’s (1993) model” (p. 344).
This past decade has witnessed a number of exploratory and/or confirmatory factor analysis investigations that have included a wider range of CHC construct indicators.  Collectively,these studies provide an opportunity to evaluate and validate the broad strokes of the CHC model (Figure 1e and Table 3).  Other studies, although not specifically designed to evaluate the CHC model, when viewed through a CHC lens provide additional support for major portions of the CHC model.  The factor analytic studies reviewed next were either: (1) designed as per the CHC framework, (2) designed as per the Carroll and/or Cattell-Horn Gf-Gc models, and/or (3) were non-CHC studies that are now interpreted here via a post-hoc CHC lens. Collectively, these studies provide empirical support for the broad strokes of contemporary CHC theory.