CHC theory 101: From general intelligence (g) to CHC theory

Dr. Kevin S. McGrew
Institute for Applied Psychometrics (IAP)
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
CHC introduction &
history:
From g to CHC
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
g
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
PMA2 PMA3 PMA4
G1 G2 G3
g ?

Classification is arguably one of
the most central and generic of
all our conceptual exercises …
without classification, there
could be no advanced
conceptualization, reasoning,
language, data analysis, or for
that matter, social science
research.
(K.D. Bailey, 1994)
The importance of taxonomies and
classification in science

A specialized science of
classification of empirical
entities known as taxonomy
(Bailey, 1994; Prentky, 1994)
is ubiquitous in all fields of
study because it guides our
search for information or
truth.

Bloom's Revised Taxonomy of Learning Objectives

...most disciplines have a common set of terms
and definitions (i.e., a standard nomenclature)
that facilitates communication among professionals
and guards against misinterpretations. In chemistry,
this standard nomenclature is reflected in the Table
of Periodic Elements. Carroll (1993a) has provided
an analogous table for intelligence…..
(Flanagan & McGrew, 1998)

Psychometric approach is the
dominant approach, has inspired the
most research, is used most widely in
practical settings. (p. 77)

John Horn, compared the process of classifying
and categorizing human abilities and
intelligence to “slicing smoke”. (Horn, 1991)

Gf
Gc Gwm
Glr
Gv
Ga
Gs
Gq
Grw
g
I am going to be
your guide for a
“walk in the
clouds” of human
cognitive abilities.
CHC theory will
be our map.

Gs
Ga Gv
Gf
Gq
Grw
Glr
Gwm
Gc
ability
construct
Human cognitive
abilities
are hypothetical
constructs
• Hidden attributes
• Unseen phenomena
• Not visible
• Not directly observable
• Latent
• Are used to explain
behavior

Intelligence scholars
have been trying to
discover/define a
valid “Rosetta Stone”
for describing human
cognitive abilities
since the early 1900’s.
© Institute for Applied
Psychometrics (IAP) Dr. Kevin
McGrew 4-11-14

Figure 1. The Evolution of CHC Intelligence Theory and Assessment Methods

T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
g
Spearman’s general factor model
(T# = designates different test measures)
Latent, hidden, unobservable
ability construct
Factor loadings of tests on latent g ability factor

Thurston’s Multiple Factor (Primary
Mental Abilities) Model
(T# = designates different test measures)
(PMA# = different “primary mental ability”)
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
PMA2 PMA3 PMA4 …etc
…etc
Correlations between latent ability constructs

PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
…etc
G1 G2 G3 …etc
Cattell-Horn Gf-Gc Hierarchical (no g) Model

PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
…etc
…etc
…etc
PMA2 PMA3 PMA4
G2
G1
g
Arrows from g to each test
(rectangle) have been
omitted for readability
Stratum I
Stratum II
Stratum III
Carroll’s Schmid-Leiman
Hierarchical Three-Stratum Model

Carroll and Cattell-Horn Model Comparison
Gq
Quantitative
Knowledge
Grw
Reading/
Writing
Cattell-HornCarroll
Gf
Fluid
Intelligence
Fluid
Intelligence
Gf
Gsm
Short-Term
Memory
Gen.Memory
&Learning
Gy
Gv
Visual
Processing
BroadVisual
Perception
Gv
Gs
Processing
Speed
BroadCognitive
Speediness
Gs
CDS
Correct
DecisionSpeed
Dec/Reaction
Time/Speed
Gt
Glr
Long-Term
Retrieval
BroadRetrieval
Ability
Gr
Ga
Auditory
Processing
BroadAuditory
Perception
Gu
Gc
Crystallized
Intelligence
Crystallized
Intelligence
Gc
g

Consensus Cattell-Horn-Carroll (CHC) Hierarchical Three-Stratum Model
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
…etc
G1 G2 G3
…etc
g?
Stratum I
Stratum II
Stratum III
© Institute for Applied Psychometrics
(IAP) Dr. Kevin McGrew 4-11-14

T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
g
(1a) Spearman’s general Factor model
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
…etc
…etc
…etc
PMA2 PMA3 PMA4
G2
G1
g
Arrows from g to each test
(rectangle) have been
omitted for readability
Stratum I
Stratum II
Stratum III
(1d) Carroll’s Schmid-Leiman Hierarchical Three-Stratum Model
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
…etc
G1 G2 G3 …etc
(1c) Cattell-Horn Gf-Gc Hierarchical Model
Figure 1: Major stages in the evolution of psychometric theories from Spearman’s g to Cattell-Horn-Carroll (CHC) theory
Note: Circles represent
latent factors. Squares
represent manifest
measures (tests; T1..).
Single-headed path
arrows designate factor
loadings. Double
headed arrows designate
latent factor correlations
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
…etc
G1 G2 G3
…etc
g ?
(1e) Consensus Cattell-Horn-Carroll Hierarchical Three-Stratum Model
Stratum I
Stratum II
Stratum III
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
…etc
(1b) Thurston’s Multiple Factor (Primary Mental Abilities) Model
© Institute for
Applied
Psychometrics
(IAP) Dr. Kevin
McGrew 4-11-14

CHC Theory Summary
• Combination of research by Raymond Cattell, John Horn,
and John Carroll
• The most empirically-supported, psychometric-based,
contemporary description of the structure of human
cognitive abilities
• Based on the analyses of hundreds of data sets that were
not restricted to a particular test battery
• The theory describes cognitive abilities as a function of
degree of breadth/generality

Richard Snow (1993):
“John Carroll has done a magnificent thing. He has reviewed and reanalyzed the world’s
literature on individual differences in cognitive abilities…no one else could have done it… it
defines the taxonomy of cognitive differential psychology for many years to come.”
Burns (1994):
Carroll’s book “is simply the finest work of research and scholarship I have read and is destined
to be the classic study and reference work on human abilities for decades to come” (p. 35).
John Horn (1998):
A “tour de force summary and integration” that is the “definitive foundation for current theory”
(p. 58). Horn compared Carroll’s summary to “Mendelyev’s first presentation of a periodic table
of elements in chemistry” (p. 58).
Arthur Jensen (2004):
“…on my first reading this tome, in 1993, I was reminded of the conductor Hans von Bülow’s
exclamation on first reading the full orchestral score of Wagner’s Die Meistersinger, ‘‘It’s
impossible, but there it is!’’
“Carroll’s magnum opus thus distills and synthesizes the results of a century of factor analyses of
mental tests. It is virtually the grand finale of the era of psychometric description and taxonomy
of human cognitive abilities. It is unlikely that his monumental feat will ever be attempted again
by anyone, or that it could be much improved on. It will long be the key reference point and a
solid foundation for the explanatory era of differential psychology that we now see burgeoning
in genetics and the brain sciences” (p. 5).
The verdict is unanimous re: the importance of Carroll’s (1993) work
© Institute for Applied Psychometrics (IAP) Dr.
Kevin McGrew 4-11-14

g
Gf GqGc
SAR
Gsm
Gv Ga
TSR
Glm
Gs CDS Grw
Gkn Gh Gk Go
Gf Gc Gy Gv Gu Gr Gs Gt
Gp Gps
A. Carroll Three-Stratum Model
B. Cattell-Horn Extended Gf-Gc Model
D. Tentatively identified Stratum II
(broad) domains 1
Carroll and Cattell-Horn Broad Ability Correspondence
(vertically-aligned ovals repres ent similar broad domains)
Gf GqGc Gsm Gv Ga Glr Gs Gt Grw
C. Cattell-Horn-Carroll (CHC) Integrated Model
g
Stratum III
(general)
Stratum II
(broad)
Notes. Broad ability factor codes based on Carroll (1993) and Horn
and Blankson (2005). See Table 1 for additional explanation.
80+ Stratum I (narrow) abilities hav e been identified under the Stratum
II broad abilities. They are not listed here due to space limitations
(see Table 1).
Placement of g to the left-side of the Carroll Three-Stratum Model (A)
is consistent with Carroll's (1993) published figures, a placement
reflecting his finding that the broad abilities towards the left (e.g, Gf,
Gc) had the highest loadings on the g-factor. The placement of the
Grw and Gq factors in the Cattell-Horn Extended Gf-Gc Model (B) is not
consistent with this g-broad ability representation as Grw and Gq
ty pically demonstrate high g-loadings. Grw and Gq are placed to the
right in B to reflect their absence in model A.
Gf Fluid reasoning Gkn General (domain-specific) knowledge
Gc Comprehension-knowledge Gh Tactile abilities
Gsm Short-term mem ory Gk Kinesthetic abilities
Gv Visual process ing Go Olfactory abilities
Ga Auditory processing Gp Psychomotor abilities
Glr Long-term storage and retrieval Gps Psychomotor s peed
Gs Process ing speed
Gt Decision and reaction s peed (see Table 1 for definitions)
Grw Reading and writing 1 See McGrew(2004, 2005) for literature rev iew supporting these domains
Gq Quantitative knowledge
CHC Broad (Stratum II) Ability Domains
(Miss ingg-to-broad ability arrows acknowledges that Carroll and Cattell-Horn disagreed on the validity of the general factor)
© Institute for Applied Ps ychom etrics, LLC Kevin S. McGrew 7-22-08

g
General
(stratum I)
The CHC taxonomy of
cognitive abilities –
The three levels
(stratum)Narrow
(stratum III)
Broad
(stratum II)
Gf Gc Gwm
Glr Gv Ga Gs
Gc
Note. WJ IV authors propose that
Gsm be changed to Gwm (McGrew,
LaForte & Schrank, 2014)

g
Gf Gc Gwm
Glr Gv Ga Gs
Gc
Substantive Stage of Test Development:
Develop Test Design and Specification Blueprint
• What is the theoretical domain?
• How should intelligence be defined?
• What intelligence theory has the best validity evidence?
Answer: Cattell-Horn-Carroll (CHC) theory of cognitive abilities
© Institute for Applied
Psychometrics (IAP) Dr.
Kevin McGrew 4-11-14

g
Gf Gc Gwm
Glr Gv Ga Gs
Gc
Substantive Stage of Test Development:
Develop Test Design and Specification Blueprint
What broad & narrow ability domain(s) are to be measured and in what proportion?
How do we define the broad and narrow ability constructs?

Contemporary psychometric research has
converged on the Cattell-Horn-Carroll (CHC) model
of cognitive abilities as the consensus working
taxonomy of human intelligence

g
Gf GqGc
SAR
Gsm Gv Ga
TSR
Glm Gs CDS Grw
Gkn Gh Gk Go
Gf Gc Gy Gv Gu Gr Gs Gt
Gp Gps
A. Carroll Three-Stratum Model
B. Cattell-Horn Extended Gf-Gc Model
D. Tentatively identified Stratum II (broad)
domains
Carroll and Cattell-Horn Broad Ability Correspondence
(vertically-aligned ovals repres ent similar broad domains)
Gf GqGc Gsm Gv Ga Glr Gs Gt Grw
C. Cattell-Horn-Carroll (CHC) Integrated Model
g
Stratum III
(general)
Stratum II (broad)
80+ Stratum I (narrow) abilities have been
identified under the Stratum II broad abilities. They
are not lis ted here due to s pace limitations
(see Table 1)
Gf Fluid reasoning Gkn General (domain-specific) knowledge
Gc Comprehension-knowledge Gh Tactile abilities
Gsm Short-term mem ory Gk Kinesthetic abilities
Gv Visual process ing Go Olfactory abilities
Ga Auditory processing Gp Psychomotor abilities
Glr Long-term storage and retrieval Gps Psychomotor s peed
Gs Cognitive processing s peed
Gt Decision and reaction s peed (see Table 1 for definitions )
Grw Reading and writing
Gq Quantitative knowledge
CHC Broad (Stratum II) Ability Domains
(Miss ingg-to-broad ability arrows acknowledges that Carroll and Cattell-Horn disagreed on the validity of the general factor)

The CHC taxonomy of
cognitive abilities:
Current status
Dr. Kevin S. McGrew
Institute for Applied Psychometrics (IAP)
Gf
Gc Gwm
Glr
Gv
Ga
Gs
Gq
Grw
g

Gf
Gc Gwm
Glr
Gv
Ga
Gs
Gq
Grw
g
The CHC taxonomy of cognitive abilities:
Current Status

Gf
Gc Gwm
Glr
Gv
Ga
Gs
Gq
Grw
g
Contemporary
psychometric
research has
converged on the
Cattell-Horn-Carroll
(CHC) model of
cognitive abilities as
the consensus
working taxonomy
of human
intelligence
© Institute for Applied Psychometrics (IAP)
Dr. Kevin McGrew 4-11-14

CHC model is analogous to the Periodic Table of Elements in Chemistry

OM
PC US UM U8 UR
U1
U9
UP UL
Vz SR MV CS SS CF IM PI LE IL PN
Sensory-MotorDomain-
SpecificAbilities
Sensory
The CHC Periodic
Table of Human
Abilities
Adapted from Schneider & McGrew (2012)
and McGrew, LaForte and Schrank (2014)
I RG RQ
WM MS AC
R3 PT MT
P N R9
R1 R2 R4 R7 IT
MA MM M6 FI FA FE SP F0 NA FW LA FF FX
Ideas Words Figures
Domain-Independent
Capacities
Glr-Learning efficiency
Glr-Retrieval fluency
Broad ability
Narrow ability
KM A3
LD VL K0 LS CM MY
KL K1 A5 MK KF LP BC
V RD RC RS WA SG EU WS
AcquiredKnowledge
Systems
K2
PI P2 P3 P4 P6 P7 A1
U1
U9
UP UL
Motor

OM
PC US UM U8 UR
U1
U9
UP UL
SpecificAbilities
Sensory
The CHC Periodic
Table of Human
Abilities
I RG RQ
WM MS AC
R3 PT MT
P N R9
R1 R2 R4 R7 IT
Ideas Words Figures
Domain-Independent
Capacities
Broad ability
Narrow ability
KM A3
LD VL K0 LS CM MY
AcquiredKnowledge
Systems
K2
PI P2 P3 P4 P6 P7 P8
U1
U9
UP UL
Motor
A1

See
handouts
or provided
PDF copy to
read

OM
PC US UM U8 UR
U1
U9
UP UL
SpecificAbilities
Sensory
The CHC Periodic
Table of Human
Abilities
I RG RQ
WM MS AC
R3 PT MT
P N R9
R1 R2 R4 R7 IT
Ideas Words Figures
Domain-Independent
Capacities
Broad ability
Narrow ability
KM A3
LD VL K0 LS CM MY
AcquiredKnowledge
Systems
K2
U1
U9
UP UL
Motor
PI P2 P3 P4 P6 P7 A1P8

KM A3
LD VL K0 LS CM MY
K1 A5
PC US UM U8 UR
U1
U9
UP UL
AcquiredKnowledge
Systems
SpecificAbilities I RG RQ
WM MS AC
P N R9
Ideas Words Figures
Domain-Independent
Capacities
K2
Broad and Narrow Abilities Most Relevant to the Development of Measures of
Cognitive and Achievement Abilities

KM A3
LD VL K0 LS
K1 A5
PC UM
Vz MV SS
AcquiredKnowledge
Systems
SpecificAbilities I RG RQ
WM MS AC
P N
MA MM NA FW LA
Ideas Words Figures
Domain-Independent
Capacities
K2
Broad and Narrow Abilities Measured by the WJ IV COG, OL and ACH
FI

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CHC theory 101: From general intelligence (g) to CHC theory