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.     

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.     

On the factor score controversy

A summary and interpretation of the recent literature on the indeterminacy of factor scores is given in simple terms. A good index of factor score determinacy is the squared multiple correlation of the factor with the observed variables.     

Observations on the factor structure of the WAIS-R

Confirmatory factor analyses (CFAs) revealed 2 important characteristics of the standardization data of the Wechsler Adult Intelligence Scale Revised. One finding was that Digit Symbol fit better on an attentional factor in younger groups, but fit was better when Digit Symbol loaded on a visual-perceptual factor in older groups. A second observation was that specifying correlated errors or a fourth factor to explain covariance between Block Design and Object Assembly improved model fit in all age groups except 70- to 74-year-olds. The results illustrate the value of CFA and have implications for investigating other samples and other Wechsler tests.     

Modeling differentiation of cognitive abilities within the higher-order factor model using moderated factor analysis

Receptive foreign language proficiency is usually measured with reading and listening comprehension tasks. A novel approach to assess such proficiencies – viewing comprehension – is based on the presentation of short instructional videos followed by one or more comprehension questions concerning the preceding video stimulus. In order to evaluate a newly developed viewing comprehension test 485 German high school students completed reading, listening, and viewing comprehension tests, all measuring the receptive proficiency in English as a foreign language. Fluid and crystallized intelligence were measured as predictors of performance. Relative to traditional comprehension tasks, the viewing comprehension task has similar psychometric qualities. The three comprehension tests are very highly but not perfectly correlated with each other. Relations with fluid and crystallized intelligence show systematic differences between the three comprehension tasks. The high overlap between foreign language comprehension measures and between crystallized intelligence and language comprehension ability can be taken as support for a uni-dimensional interpretation. Implications for the assessment of language proficiency are discussed.     

Fitting the factor analysis model

When the covariance matrix (p×P) does not satisfy the formal factor analysis model for m factors, there will be no factor matrix (p×m) such that =(-) is diagonal. The factor analysis model may then be replaced by a tautology where is regarded as the covariance matrix of a set of residual variates. These residual variates are linear combinations of discarded common factors and unique factors and are correlated. Maximum likelihood, alpha and iterated principal factor analysis are compared in terms of the manner in which is defined, a maximum determinant derivation for alpha factor analysis being given. Weighted least squares solutions using residual variances and common variances as weights are derived for comparison with the maximum likelihood and alpha solutions. It is shown that the covariance matrix defined by maximum likelihood factor analysis is Gramian, provided that all diagonal elements are nonnegative. Other methods can define a which is nonGramian even when all diagonal elements are nonnegative.A modified version of this paper forms part of a Ph.D. thesis submitted to the University of South Africa.Presently at the National Institute for Personnel Research, South Africa.     

The determination of the factor loadings of a given test from the known factor loadings of other tests

A technique is indicated by which approximations to the factor loadings of a new test may be obtained if factor loadings of a given group of tests and the correlations of the new test with the other tests are known. The technique is applicable to any orthogonal system and is especially adapted to cases in which a _ji a _jk = 0 wheni k. Application is also made to the simultaneous determination of the factor weights of a group of tests in which no additional common factor is present. The technique is useful in adding tests to a completed factorial solution and in using factorial solutions involving errors to give results which are approximately correct.     

Concurrent validity of the WISC-R factor scores

This study investigated the efficacy of predicting academic achievement as measured by the Wide Range Achievement Test using the factor scores of the Wechsler Intelligence Scale for Children-Revised as potential predictors. Both instruments were administered to 200 school children referred for psychological evaluations. Factor scores for the WISC-R were computed according to equations provided by Gutkin (1978). These factor scores then were regressed in a stepwise manner on the Reading, Spelling, and Arithmetic standard scores from the Wide Range Achievement Test. Stepwise regressions also were performed using the traditional Verbal and Performance IQs as the potential predictors. A comparison was made between the results obtained by use of the factors or the more common scores. The results indicated that the Freedom From Distractibility factor score significantly aided in the prediction of Reading and Spelling achievement and was of primary importance in predicting Arithmetic achievement. When the stepwise results using the different scores were contrasted, the factor scores accounted for appreaciably more variance in Arithmetic than did the traditional Verbal and Performance IQs. Derived regression equations are reported along with a discussion of the interpretability of the Freedom From Distractibility factor.     

Therapist factor in the treatment of insomnia

This quasi-experiment attempted to replicate the finding of Turner and Ascher (1979) in contrasting progressive relaxation, stimulus control and paradoxical intention therapies for the treatment of insomnia using clinicians-in-training as therapists. Progressive relaxation and stimulus control were again shown to be effective, paradoxical intention instructions were not. A significant therapist effect was found which is discrepant with previous findings in the field.     

On the sampling errors of factor loadings

The results of three empirical studies on the sampling fluctuation of centroid factor loadings are reported. The first study is based on data which happened to be available on 8 variables for 700 cases and which were factored to three factors for subsamples. The second study is based on fictitious data for 2500 cases which provided separate analyses on 25 samples for each of three situations: 5 variables, one factor; 5 variables, two factors; and 6 variables, three factors. The third study, based on real data for 9 variables and 7000 cases, involves separate factorization for 35 samples of 200 cases. The three studies agree in showing that the sampling behavior of first centroid factor loadings is much like that of correlation coefficients, whereas the sampling fluctuations for loadings beyond the first are disturbingly large.     

Examining the factor structure of the Psychological Mindedness Scale in the Japanese population through exploratory and confirmatory factor analyses

Psychological mindedness (PM) is a psychological construct that represents the tendency and ability to understand the relationships between thoughts, feelings, and behavior. This study examined the statistical properties, particularly the factor structure, of the Psychological Mindedness Scale (PMS) in a non‐clinical Japanese sample through exploratory and confirmatory factor analysis. The relationship between PMS and depression was also examined for predictive validity. The results suggested that the PMS tested on a Japanese sample contains the following four factors: (a) belief in the benefits of discussing one's problems; (b) access to feelings; (c) openness to new ideas and capacity to change; and (d) interest in the meaning and motivation of own and others' behavior. Whereas the total PM score and Factors 2 and 3 had negative correlations with depression, there was a positive correlation between Factor 4 and depression. The 4‐factor structure of the scale is deemed to be applicable to the Japanese population.     

Evaluating the factor structure of the Psychological Performance Inventory

This study assesses the construct validity of a measure of mental toughness, Loehr's Psychological Performance Inventory. Performers (N = 408, 303 men, 105 women, M age = 24.0 yr., SD = 6.7) drawn from eight sports (artistic rollerskating, basketball, canoeing, golf, rugby league, rugby union, soccer, swimming), and competing at either international, national, county and provincial, or club and regional standards. They completed the 42-item Psychological Performance Inventory during training camps. Principal components analysis provided minimal support for the factor structure. Instead, the exploratory analysis yielded a 4-factor 14-item model (PPI-A). A single factor underlying mental toughness (G(MT)) was identified with higher-order exploratory factor analysis using the Schmid-Leiman procedure. Psychometric analysis of the model, using confirmatory analysis techniques, fitted the data well. Collectively satisfying absolute and incremental fit index benchmarks, the inventory possesses satisfactory psychometric properties, with adequate reliability and convergent and discriminant validity. The results lend preliminary support to the factorial validity and reliability of the model; however, further investigation of its stability is required before recommending practitioners use changes in scores as an index for evaluating effects of training in psychological skills.     

Revisiting the factor structure of the Kirton Adaption-Innovation Inventory

The original Kirton Adaption-Innovation Inventory, used to measure innovative (as opposed to adaptive) individual cognitive styles, has been reported to have three factors: Sufficiency of Originality, Efficiency, and Rule/Group Conformity. In exploring the construct validity of the Kirton Adaption-Innovation Inventory, findings from a 2003 study by Im, Hu, and Toh showed the existence of two subdimensions of the Sufficiency of Originality factor-Idea Generation and Preference for Change. In this study, using a sample of 356 household participants, with an average age of 56.0 yr. (SD = 14.0), average income of dollar 39,700 (SD = dollar 19,200), and average of 15.0 yr. of education (SD = 2), from the Arkansas Household Research Panel, we conducted factor analyses. The results specific to our selected sample indicate that a four-factor model recognizing the two subdimensions of Sufficiency of Originality has a better fit than the original three-factor model.     

The factor structures of the STEM and the STEU

The factor structures of two recently developed measures of emotional intelligence, the Situational Test of Emotional Understanding and Situational Test of Emotion Management (STEU, STEM; MacCann & Roberts, 2008) were examined. The results did not support a factor structure of either measure’s subscales indicated by the approach used in developing the test items, and examination of the factors obtained using parallel analysis to determine the number of factors to extract did not yield interpretable factors. These findings suggest that only total scale scores should be used for these tests, although the general factor extracted from the items was not strong for either test; further development work on these tests is indicated.     

Characteristics factor structures of the Japanese version of the State-Trait Anxiety Inventory: coexistence of positive-negative and state-trait factor structures

Previous factor studies of the State-Trait Anxiety Inventory (STAI; Spielberger, Gorsuch, & Lushene, 1970) have reported certain typical factors that are state-trait (S-T) 2-factor solutions and positively-negatively (P-N) worded item 2-factor solutions in addition to 4-factor solutions (positively and negatively worded state factors, positively and negatively worded trait factors). We explored the possibility that these factor structures are included in a factor space. Responses to the Japanese version of the STAI in a sample of 848 male workers were factor analyzed. The first-order factors obtained from principal-component analysis were almost equal to the previous 4 factors, except for a minor factor, and their second-order factors were the P-N factors. However, the S-T factors were also obtained from the same first-order factors by the oblique Procrustes rotation. Moreover, coexistence of these two 2-factor structures was determined in the same factor space by the orthogonal Procrustes rotation.