chc theory 101: from general intelligence (g) to chc theory

Dr. Kevin S. McGrewInstitute 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 termsand definitions (i.e., a standard nomenclature)that facilitates communication among professionalsand guards against misinterpretations. In chemistry,this standard nomenclature is reflected in the Tableof Periodic Elements. Carroll (1993a) has providedan analogous table for intelligence…..

(Flanagan & McGrew, 1998)



A Good Taxonomy:

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)


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I am going to be your guide for a “walk in the clouds” of human cognitive abilities.

CHC theory will be our map.

Gs

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GrwGlr

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abilityconstruct

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, unobservableability 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

G2G1

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

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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


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

G2G1

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 representlatent 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


g

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Gs CDS Grw

Gkn Gh Gk Go

Gf Gc Gy Gv Gu Gr Gs Gt

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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 represent 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 have 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 typically 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) knowledgeGc Comprehension-knowledge Gh Tactile abilitiesGsm Short-term memory Gk Kinesthetic abilitiesGv Visual processing Go Olfactory abilitiesGa Auditory processing Gp Psychomotor abilitiesGlr Long-term storage and retrieval Gps Psychomotor speedGs Processing speedGt Decision and reaction speed (see Table 1 for definitions)

Grw Reading and writing 1 See McGrew (2004, 2005) for literature review supporting these domains

Gq Quantitative knowledge

CHC Broad (Stratum II) Ability Domains

(Missing g-to-broad ability arrows acknowledges that Carroll and Cattell-Horn disagreed on the validity of the general factor)

© Institute for Applied Psychometrics, 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


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?© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14

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 GqGcSARGsm Gv Ga

TSRGlm 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 represent 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 listed here due to space limitations(see Table 1)

Gf Fluid reasoning Gkn General (domain-specific) knowledgeGc Comprehension-knowledge Gh Tactile abilitiesGsm Short-term memory Gk Kinesthetic abilitiesGv Visual processing Go Olfactory abilitiesGa Auditory processing Gp Psychomotor abilitiesGlr Long-term storage and retrieval Gps Psychomotor speedGs Cognitive processing speedGt Decision and reaction speed (see Table 1 for definitions)Grw Reading and writingGq Quantitative knowledge

CHC Broad (Stratum II) Ability Domains

(Missing g-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. McGrewInstitute for Applied Psychometrics (IAP)

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Gf

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Gs

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The CHC taxonomy of cognitive abilities: Current Status


GfGc Gwm

Glr

Gv

Ga

Gs

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Contemporary psychometric research has

converged on the Cattell-Horn-Carroll

(CHC) model of cognitive abilities as

the consensus working taxonomy of human intelligence


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

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The CHC Periodic Table of Human

AbilitiesAdapted from Schneider & McGrew (2012) and McGrew, LaForte and Schrank (2014)

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Gs P N R9

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Ideas Words Figures

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Glr-Learning efficiency

Glr-Retrieval fluency

Broad ability

Narrow ability

© Institute for Applied Psychometrics (IAP)Dr. Kevin McGrew 3-28-14

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See handouts

or provided PDF copy to

read


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Broad and Narrow Abilities Most Relevant to the Development of Measures of Cognitive and Achievement Abilities

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Broad and Narrow Abilities Measured by the WJ IV COG, OL and ACH

FI


chc theory 101: from general intelligence (g) to chc theory

Education

mcgrew institute

kevin mcgrew

g model institute

stratum model institute

science institute

flanagan mcgrew

pma2 pma3 pma4 g2 g1

readability stratum