most thorough evaluations of the structure of CHC theory are factor analysis studies of
variables from standardized test batteries administered to large nationally representative samples.
The most comprehensive evaluation of Carrolls three-stratum CHC model is the hierarchical
cross-age (ages 6 through 90 years) multiple-group confirmatory factor analysis of the WJ-R
norm data by Bickley, Keith and Wolfe (1995). Consistent with Carrolls (1993) conclusion
the structure of cognitive abilities is largely the same across ages, Bickley et al. found that the
structure of cognitive abilities, as defined by eight broad abilities (Gf, Gv, Gs, Glr, Gc, Ga, Gsm,
Gq) and a higher-order g ability, was invariant from childhood to late adulthood. Bickley
concluded that this study provides compelling evidence that the three-stratum theory may form
parsimonious model of intelligence. The fact that it is also grounded in a strong foundation of
vast, previous research also lends strong support for the acceptance of the model. (p. 323).
recently, in the large nationally representative WJ III standardization sample, McGrew and
Woodcock (2001) reported a CHC-based confirmatory factor analysis of 50 test variables from
ages six through late adulthood. Support was found for a model consisting of a higher-order g-
factor that subsumed the broad abilities of Gf, Gc, Gv, Ga, Gsm, Glr, Gs, Grw, and Gq.
comparison with four alternative models found the CHC model to be the most plausible
representation of the structure in the data.
Taub and McGrew (in press) used multiple-group confirmatory factor analyses to
evaluate the factorial cross-age invariance of the WJ III Cognitive (COG) Battery from ages 6
through 90+. In addition to supporting the construct validity of a higher-order g and seven
order broad CHC factors (Gf, Gc, Gv, Ga, Gsm, Glr, Gs), Taub and McGrews analyses
supported the invariance of the WJ COG measurement and CHC theoretical frameworks. These
findings are consistent with Bickely et al. (1995) and provide additional support for the validity of
the broad and general stratum abilities of CHC theory (from childhood through adulthood).
particular interest to the current chapter, and representing his last formal publication, Carroll
(2003) applied his factor analytic procedures and skills to an investigation of the structure of the
1989 WJ-R norm data. The purpose of Carrolls analyses was to compare the viability of three
different views of the structure of human cognitive abilities. According to Carroll (2003), these
views can be characterized as:
(1) Standard multifactorial model: This
is the classic view of Spearman (Spearman, 1927,
Spearman & Wynn Jones, 1950) and others (e.g., Carroll, 1993; Thurstone & Thurstone;
1941; Jensen; 1998) that a general (g) intelligence factor exists as well as a variety of less
general broad abilities.
(2) Limited structural analysis model. This model also
posits the presence of higher- order
g ability, as well as lower-order broad abilities, but suggests that fluid intelligence (Gf)
highly correlated with, and may be identical with g. This model is primarily associated
with Gustafsson and others (Gustafsson, 1984, 1989, 200l; Gustafsson & Balke, 1993;
Gustafsson & Undheim, 1996)
(3) Second-stratum multiplicity model. This is
a g-less model that also includes broad
abilities, but suggests that the non-zero intercorrelations among lower-stratum factors do
not support the existence of g. This is largely the view of Horn and Cattell (Cattell,
Horn, 1998; Horn & Noll, 1997)
(2003) judged the WJ-R norm data to be a sufficient dataset for drawing conclusions
about the higher-stratum structure of cognitive abilities (p. 8). Carroll submitted the
16- and 29-
variable WJ-R correlation matrices reported by McGrew, et al. (1991) to the same exploratory
factor analysis Schmid-Leiman procedures used in his 1993 survey. These EFA-based results, in
turn, served as the starting point for a confirmatory analyses intended to compare the three
different structural model views of intelligence vis-à-vis the model comparison statistics provided
by SEM methods.
Carroll (2003) concluded that researchers who are concerned with this structure in one
way or another
.can be assured that a general factor g exists, along with a series of second-
order factors that measure broad special abilities (p. 19). Carroll (2003) further stated
doubt is cast on the view that emphasizes the importance of a Gf factor
discredit the limited structural analysis view and the second-stratum multiplicity view (p. 17).
Interestingly, in these analyses Carroll used the broad ability nomenclature of CHC theory when
reporting support for the broad abilities of Gf, Gc, Gv, Ga, Gsm, Glr, Gs, Gq and Language
(comprised of reading and writing tests; aka., Grw).
most recent morphing of the long line of Stanford-Binet Intelligence scales (Stanford
Binet Intelligence ScalesFifth Edition, SB5; Roid, 2003) was guided extensively by the work of
both Carroll and Horn (see Roid, 2003, p.7-11), consultation from authors of the CHC-designed
WJ-III (see Roid, Woodcock, McGrew, 1997 in Roid, 2003; also see Roid, 2003, p. v,) and a
review of the CHC-organized cross-battery research literature of Flanagan, McGrew and
colleagues (see Roid, 2003, p. 8-9). The result is a CHC-organized battery designed to measure
the broad cognitive abilities of Fluid Reasoning (Gf), Quantitative Reasoning (Gq), Crystallized
Knowledge (Gc), Short-term Memory (Gsm), and Visual Processing (Gv). Not measured
broad abilities of Grw, Ga, Glr, and Gs. Confirmatory factor analysis reported in the
indicates that the five-factor model (Gf, Gq, Gc, Gsm, Gv) was the most plausible model when
compared to four alternativs models (one, two, three, and four-factor models).