On the interpretation of the CHC factor Gc

On the one hand, the factors Gf and Gc in the Cattell-Horn-Carroll (CHC) model of intelligence are hypothesized to represent individual differences in unique psychological or biological capacities. On the other hand, they are interpreted as representing the theoretical variables fluid and crystallized intelligence in investment theory. With respect to Gc, this leads to a theoretical conflict because in investment theory crystallized intelligence is not a capacity but purely a statistical entity. We contend that if CHC factor Gc represents a capacity, it cannot represent crystallized intelligence, and if Gc represents crystallized intelligence, it does not represent a capacity. In addition, from our discussion of Gc, we conclude that in investment theory the factors Gf and g represent one and the same capacity. In support of our theoretical conclusions, we implemented the CHC model in a confirmatory factor analysis of a HCA (Human Cognitive Abilities project) data set. As expected, Gf and g were statistically indistinguishable. Gc was effectively absent, because it was statistically equivalent to verbal comprehension. Factors Gc and g could be removed from the model without any reduction in model fit. We argue that in the CHC taxonomy the factors Gc and g are redundant as explanatory variables.     

Comparative longitudinal structural analyses of the growth and decline of multiple intellectual abilities over the life span.

Latent growth curve techniques and longitudinal data are used to examine predictions from the theory of fluid and crystallized intelligence (Gf-Gc theory; J. L. Horn & R. B. Cattell, 1966, 1967). The data examined are from a sample (N approximately 1,200) measured on the Woodcock-Johnson Psycho-Educational Battery-Revised (WJ-R). The longitudinal structural equation models used are based on latent growth models of age using two-occasion "accelerated" data (e.g., J. J. McArdle & R. Q. Bell, 2000; J. J. McArdle & R. W. Woodcock, 1997). Nonlinear mixed-effects growth models based on a dual exponential rate yield a reasonable fit to all life span cognitive data. These results suggest that most broad cognitive functions fit a generalized curve that rises and falls. Novel multilevel models directly comparing growth curves show that broad fluid reasoning (Gf) and acculturated crystallized knowledge (Gc) have different growth patterns. In all comparisons, any model of cognitive age changes with only a single g factor yields an overly simplistic view of growth and change over age.     

K-ABC simultaneous processing, DAS nonverbal reasoning, and Horn's expanded fluid-crystallized theory.

Horn's distinction between--fluid intelligence (Gf) and visualization (Gv) was investigated with two Nonverbal Reasoning subtests from the Differential Ability Scales and three Simultaneous Processing subtests from the Kaufman Assessment Battery for Children. The sample comprised a predominantly Euro-American groups of 57 normal boys and girls between the ages of 6 and 12 years. Principal factor analysis yielded clear-cut Gf and Gv dimensions. The Gf factor was composed both of Differential Ability Scales and Kaufman-ABC subtests, suggesting that the construct of simultaneous processing is not merely a measure of Gv, as researchers have hypothesized, but also measures Horn's Gf fluid intelligence to a considerable extent.     

The joint WAIS-III and WMS-III factor structure: development and cross-validation of a six-factor model of cognitive functioning

During the standardization of the Wechsler Adult Intelligence Scale (3rd ed.; WAIS-III) and the Wechsler Memory Scale (3rd ed.; WMS-III) the participants in the normative study completed both scales. This "co-norming" methodology set the stage for full integration of the 2 tests and the development of an expanded structure of cognitive functioning. Until now, however, the WAIS-III and WMS-III had not been examined together in a factor analytic study. This article presents a series of confirmatory factor analyses to determine the joint WAIS-III and WMS-III factor structure. Using a structural equation modeling approach, a 6-factor model that included verbal, perceptual, processing speed, working memory, auditory memory, and visual memory constructs provided the best model fit to the data. Allowing select subtests to load simultaneously on 2 factors improved model fit and indicated that some subtests are multifaceted. The results were then replicated in a large cross-validation sample (N = 858).     

Revisiting the factor structure of the WAIS-R: insights through nested factor modeling

Past attempts to model via confirmatory factor analysis (CFA) the Wechsler Adult Intelligence Scale-Revised (WAIS-R) intersubtest covariation have used an oblique factor or a higher order modeling approach. The attempts have failed to yield adequate model fit, based on current CFA recommendations. Using the WAIS-R standardization data, it is demonstrated that the WAIS-R can be better conceptualized as measuring a first-order general factor and three orthogonal group-level factors. The results are discussed in relation to Verbal and Performance Intelligence scoring and failed attempts to find relationships between VIQ/PIQ difference scores and external criteria. Because Arithmetic and Digit Span did not share any variance with the other VIQ subtests, independent of General Intelligence, clinicians should reconsider interpreting a VIQ score that includes information from Arithmetic and Digit Span in nonclinical populations. Researchers are encouraged to model intelligence factors as nested factor models, considering their superior model fit, and the increased clarity in the interpretations of relationships between IQ indices and criteria.     

Why is working memory related to intelligence? Different contributions from storage and processing

Domain-specific contributions of working memory (WM), short-term memory (STM), and executive functioning (EF) to individual differences in intelligence were analysed using a latent variable approach. A sample of 345 participants completed a battery of 24 tests tapping the constructs of interests as comprehensively as possible. Visuospatial and verbal STM and WM tasks were administered along with three subcomponents of EF, namely inhibition, planning, and shifting. Intelligence was assessed by non-verbal/abstract/fluid intelligence (Gf) and verbal/crystallised intelligence (Gc) standardised tests. Structural equation modelling results show that EF is the main predictor of Gf, whereas verbal STM is the main predictor of Gc. Storage and processing providing different contributions to the prediction of Gf and Gc supports the view that both short-term storage and executive functioning account for the relationship between WM and intelligence. This main conclusion stresses the importance of acknowledging core cognitive constructs as being hierarchical systems with general and domain-specific mechanisms.     

Openness, fluid intelligence, and crystallized intelligence: Toward an integrative model

Many studies are concerned with the bivariate relationships between Openness, fluid intelligence (Gf), and crystallized intelligence (Gc). Results suggest an influence of Gf and Openness on Gc. However, the overlap between Gf and Openness is rarely controlled for. Moreover, interaction effects or longitudinal influences are also often neglected. The present two studies aimed to elucidate exactly these interactions and longitudinal influences. Besides a main effect of Gf on Gc, Study 1 (N = 180) revealed an interaction effect between Openness and Gf. Study 2 utilized longitudinal data (N = 172) and identified an effect of Openness on the development of Gf. Gf and Openness predicted Gc 6 years later. A model integrating the results and providing a theoretical framework and outlook is proposed.     

A confirmatory factor analysis of the WISC-III in a clinical sample with cross-validation in the standardization sample.

Maximum likelihood confirmatory factor analysis was applied to the Wechsler Intelligence Scale for Children-Third Edition (WISC-III; Wechsler, 1991) data of a mixed clinical sample of 318 children. Analyses were designed to determine which of nine hypothesized oblique factor solutions could best explain intelligence as measured by the WISC-III in the clinical sample. Competing latent variable models were identified in previous studies, and results in the clinical sample were cross-validated by testing all models in the WISC-III standardization sample (n = 2200). Findings in both the clinical and standardization samples supported a five-factor model including Verbal Comprehension, Constructional Praxis, Visual Reasoning, Freedom from Distractibility, and Processing Speed factors. The Visual Reasoning factor was defined primarily by Picture Arrangement, whereas Mazes did not appear to improve model fit. Potential opportunities and pitfalls with regard to the interpretation of the proposed Visual Reasoning factor are discussed.     

Ability factors and cognitive processes

Several measures of the speed of information processing were related to ability factors derived from the Cattell-Horn theory of fluid and crystallized intelligence. Ninety-one college students took a battery of paper and pencil tests designed to measure four ability factors: fluid intelligence (Gf), crystallized intelligence (Gc), spatial visualization (Gv), and clerical perceptual speed (CPS). They also performed paper and pencil and computerized versions of three information processing tasks: mental rotations, letter matching, and sentence verification. Correlations among the ability measures, among the information processing measures, and between the two domains were analyzed using confirmatory factor analysis. The four ability factors were found to be largely independent in this college population. Speed of letter-matching and sentence verification were highly correlated, but neither was related to speed of mental rotation. Mental rotation speed was strongly correlated with Gv; letter matching speed was correlated with CPS; and sentence verification speed was correlated with both Gc and CPS.     

Factor analysis of the Wechsler adult intelligence scale-revised (WAIS-R): An examination of the standardization sample

Orthogonal and oblique factor analyses were performed using the Wechsler Adult Intelligence Scale-Revised (WAIS-R) standardization sample (Wechsler, 1981). Using objective criteria, it was decided to retain two factors. Evidence for a strong general intelligence (g) factor was found from both the orthogonal and oblique rotations. Whereas the verbal IQ provided an acceptable estimate of the Verbal Comprehension factor, a purer measure was found in the form of a Verbal Comprehension Deviation Quotient containing only the Information, Vocabulary, Comprehension, and Similarities subtests. The performance IQ was found to be an inadequate measure of the Perceptual Organization factor. A Perceptual Organization Deviation Quotient, containing only the Block Design and Object Assembly subtests, was recommended as an effective alternative. Analysis of the variance components for each subtest at every age level revealed that a substantial proportion of subtests at a wide range of age levels evidence either high or intermediate levels of specific variance. These results are discussed in terms of interpreting individual subtest scores and patterns. Each of the study's major findings are compared with prior work done with the Wechsler Adult Intelligence Scale (WAIS) (Wechsler, 1955).     

WAIS-IV subtest covariance structure: conceptual and statistical considerations

D. Wechsler (2008b) reported confirmatory factor analyses (CFAs) with standardization data (ages 16-69 years) for 10 core and 5 supplemental subtests from the Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV). Analyses of the 15 subtests supported 4 hypothesized oblique factors (Verbal Comprehension, Working Memory, Perceptual Reasoning, and Processing Speed) but also revealed unexplained covariance between Block Design and Visual Puzzles (Perceptual Reasoning subtests). That covariance was not included in the final models. Instead, a path was added from Working Memory to Figure Weights (Perceptual Reasoning subtest) to improve fit and achieve a desired factor pattern. The present research with the same data (N = 1,800) showed that the path from Working Memory to Figure Weights increases the association between Working Memory and Matrix Reasoning. Specifying both paths improves model fit and largely eliminates unexplained covariance between Block Design and Visual Puzzles but with the undesirable consequence that Figure Weights and Matrix Reasoning are equally determined by Perceptual Reasoning and Working Memory. An alternative 4-factor model was proposed that explained theory-implied covariance between Block Design and Visual Puzzles and between Arithmetic and Figure Weights while maintaining compatibility with WAIS-IV Index structure. The proposed model compared favorably with a 5-factor model based on Cattell-Horn-Carroll theory. The present findings emphasize that covariance model comparisons should involve considerations of conceptual coherence and theoretical adherence in addition to statistical fit.     

Age, ability, and the role of prior knowledge on the acquisition of new domain knowledge: promising results in a real-world learning environment

Prior knowledge, fluid intelligence (Gf), and crystallized intelligence (Gc) were investigated as predictors of learning new information about cardiovascular disease and xerography with a sample of 199 adults (19 to 68 years). The learning environment included a laboratory multimedia presentation (high-constraint-maximal effort), and a self-directed at-home study component (low-constraint-typical performance). Results indicated that prior knowledge and ability were important predictors of knowledge acquisition for learning. Gc was directly related to learning from the video for both domains. Because the trajectory of Gc stays relatively stable throughout the life span, these findings provide a more optimistic perspective on the relationship between aging and learning than that offered by theories that focus on the role of fluid abilities in learning.     

Bifactor Modeling and the Estimation of Model-Based Reliability in the WAIS-IV

Previous confirmatory factor analytic research that has examined the factor structure of the Wechsler Adult Intelligence Scale–Fourth Edition (WAIS-IV) has endorsed either higher order models or oblique factor models that tend to amalgamate both general factor and index factor sources of systematic variance. An alternative model that has not yet been examined for the WAIS-IV is the bifactor model. Bifactor models allow all subtests to load onto both the general factor and their respective index factor directly. Bifactor models are also particularly amenable to the estimation of model-based reliabilities for both global composite scores (ω _h ) and subscale/index scores (ω _s ). Based on the WAIS-IV normative sample correlation matrices, a bifactor model that did not include any index factor cross loadings or correlated residuals was found to be better fitting than the conventional higher order and oblique factor models. Although the ω _h estimate associated with the full scale intelligence quotient (FSIQ) scores was respectably high (.86), the ω _s estimates associated with the WAIS-IV index scores were very low (.13 to .47). The results are interpreted in the context of the benefits of a bifactor modeling approach. Additionally, in light of the very low levels of unique internal consistency reliabilities associated with the index scores, it is contended that clinical index score interpretations are probably not justifiable.     

Second-Order Confirmatory Factor Analysis of the Reactions to Tests Scale with Cross-Validation

The factor structure of the RTT was evaluated by testing a series of confirmatory factor models including a second-order structure. The results indicated that a reduced 20-item RTT scale fit the data better than the 40-item original RTT and that a second-order structure explained the data very well. The models were cross-validated using several strategies. The reduced RTT was found not to cross-validate in terms of overall fit. However, when the parameter estimates were tested across samples, all parameters were found to be invariant except the item residuals. Because the cross-validation results were not conclusive, the need for additional theoretical and empirical research on the cross-validation of covariance models was discussed.     

Exploratory and confirmatory factor analyses of the Asian American Racism-Related Stress Inventory

The authors conducted exploratory and confirmatory factor analyses of the Asian American Racism-Related Stress Inventory (AARRSI) to further examine the underlying factor structure in a total sample of 1,273 Asian American participants. In the first step of analysis, an exploratory factor analysis with 651 participants yielded a 13-item two-factor solution to the data. In the second step, a confirmatory factor analysis with 622 participants supported both the 13-item two-factor model and the original 29-item three-factor model in the cross-validation sample and generational and ethnicity analyses. The two-factor and three-factor models produced internal consistency estimates ranging from .81 to .95. In addition, the authors examined convergent and criterion related evidence for 13-item and 29-item versions of the AARRSI. Given its brief nature and generally good fit across generational status and ethnicity, the authors suggest that the 13-item AARRSI might be advantageous for research and assessment endeavors.     

Confirmatory factor analysis of the NEPSY for younger and older school-age children

Using the standardization sample from the NEPSY, confirmatory factor analysis was conducted to examine the factor structure for ages 5 through 12 of the NEPSY sample, as well as for the younger (5 to 8 years, n=400) and older (9 to 12 years, n=400) age bands, to explore possible differences in test structure at different developmental epochs. Using four standard fit indices, results indicated that a 5-factor model was less than adequate for the entire sample and produced negative error variance for the younger and older age groups, making any solutions for the two subgroups inadmissible. A 4-factor model without the Attention/Executive Function subtests produced satisfactory fit statistics for the entire sample and the younger group, but did not fit the data as well for the older group. A 1-factor model did not fit well for the full sample. These results indicated that the structure for the NEPSY is not invariant across development, with the 4-factor model best fitting the data for the younger age group and for the entire school-age sample.     

Confirmatory factor analysis of the WPPSI for language-impaired children

The present study used a maximum-likelihood confirmatory factor analysis (CFA) to test the hypothesis that a four-factor model is the most parsimonious explanation of the structure of the WPPSI for language-impaired children. Four separate maximum-likelihood confirmatory factor analyses were performed on a sample of 198 Norwegian language-impaired children tested with the WPPSI, and on the Norwegian (n = 563) and American (n = 1200) standardization samples. A one-factor (general), a two-factor (verbal and performance), three-factor (parallel to the WISC-R) and a four-factor solution composed of "processing dependent" ("knowing how" and "seeing how") and "knowledge dependent" ("knowing that" and "seeing that") were imposed on the average intercorrelation matrices of the 11 WPPSI subtests. Confirmatory factor analysis indicated that the four-factor latent construct model was the most parsimonious explanation of the structure of the WPPSI for language-impaired children, as well as for normally developing children.     

A possible model for understanding the personality‐intelligence interface

Despite the recent increase in the number of studies examining empirical links between personality and intelligence (see Hofstee, 2001; Zeidner & Matthews, 2000), a theoretical integration of ability and nonability traits remains largely unaddressed. This paper presents a possible conceptual framework for understanding the personality‐intelligence interface. In doing so, it conceptualizes three different levels of intelligence, namely, intellectual ability (which comprises both Gf and Gc), IQ test performance and subjectively assessed intelligence (a mediator between personality, intellectual ability and IQ test performance). Although the model draws heavily upon correlation evidence, each of its paths may be tested independently. The presented model may, therefore, be used to explore causation and further develop theoretical approaches to understanding the relation between ability and nonability traits underlying human performance.