Wechsler Intelligence Scale for Children, developed in 1949 and translated into 25 languages, has been and still is the most employed intelligence assessment tool to evaluate IQ in the processes of identification and diagnosis of intellectual giftedness (Silverman, Reference Silverman and Shavinina2009). Therefore, studies on its validity are an important support to the diagnostic and clinical decisions derived from its use.

Since its inception, several studies have focused on determining how certain clinical or special population groups perform in the different subtests that compose this test and checking whether the scale’s factor structure changes when the evaluated subjects have specific characteristics, such as intellectual giftedness, for example. This fact is of fundamental importance in the population at hand as previous research has revealed significant differences in cognitive profiles obtained with this scale, between children of average intelligence and children of superior intelligence, which may affect the significance of the measured construct in both populations (Kaufman, Reference Kaufman1992, Reference Kaufman1993; National Association for Gifted Children [NAGC], 2010; Rimm, Gilman, & Silverman, Reference Rimm, Gilman, Silverman and VanTassel-Baska2008; Saccuzzo, Johnson, & Russell, Reference Saccuzzo, Johnson and Russell1992; Silverman, Reference Silverman, Genshaft, Bireley and Hollinger1995; Sparrow, Pfeiffer, & Newman, Reference Sparrow, Pfeiffer, Newman, Prifitera, Saklofske and Weiss2005; Sweetland, Reina, & Tatti, Reference Sweetland, Reina and Tatti2006; Volker & Smerbeck, Reference Volker, Smerbeck, Flanagan and Kaufman2009).

Early studies performed with the Wechsler’s Intelligence Scale for Children-Revised (WISC-R; Wechsler, Reference Wechsler1974) sought to determine whether the two-factor structure (Verbal Comprehension and Perceptual Organization) obtained for children of average intelligence also fitted intellectually gifted children. The justification for such research purpose lay in the belief that these children could process information in a qualitatively different manner than those children with average intelligence. Therefore, analyzing the patterns of response to the subtests could provide more information towards the diagnosis and intervention of these children than their IQ score. However, studies carried out with the WISC-R on gifted children reached no conclusion, yielding mixed results, ranging from single factor models to multivariate models.

Specifically, based on data from the 362 children in the American WISC-R standardization sample who scored 120 or above on the verbal, manipulative or full scale IQ indexes, Willson, Gilberg and Reynolds (Reference Willson, Gilberg and Reynolds1982) found that a univariate model called Verbal Ability, was the best fit. These results were confirmed by Macmann, Mueller-Plasket, Barnett, and Siler (Reference Macmann, Mueller-Plasket, Barnett and Siler1991), who conducted a principal component factor analysis with 829 children who had total IQ scores of 120 or above, in which the single factor model (composed of Information, Similarities, Vocabulary and Comprehension) was the most consistent solution.

On the other hand, a two-factor model, similar to the verbal-manipulative dichotomy defended on the WISC-R manual was supported by the work of Sapp, Chissom, and Graham (Reference Sapp, Chissom and Graham1985) and Greenberg, Stewart, and Hansche (Reference Greenberg, Steward and Hansche1986), while Karnes and Brown (Reference Karnes and Brown1980) had defended the existence of a third factor, called Freedom from Distractibility, in a study of 946 children with scores of 120 or above on the verbal, manipulative or full scale IQ indexes.

In addition, Brown and Yakimoski (Reference Brown and Yakimoski1987) proposed a four-factor model for the WISC-R (Perceptual Organization, Verbal Comprehension, Acquisition of Knowledge and Spatial Memory) as the best solution for the group of gifted children, compared with the two-factor model (Verbal Ability and Perceptual Organization) suggested in the same study, for the sample of children of average intelligence. Subsequently, Brown, Hwang, Baron, and Yakimoski (Reference Brown, Hwang, Baron and Yakimoski1991) developed a confirmatory factor analysis with gifted children and children with average intelligence, noting that, for gifted children, the best solution was the three-factor model, while the two-factor model was a better fit for children with average intelligence. In view of the results, these authors concluded that children with giftedness differed from children of average intelligence not only in the magnitude of the scores obtained in the WISC-R, but also in the interrelationships between them and in the cognitive processes associated to the subtests (Brown et al., Reference Brown, Hwang, Baron and Yakimoski1991).

The publication of the third edition of the Wechsler Intelligence Scale for Children (WISC-III; Wechsler, Reference Wechsler1991) allowed for the calculation of four indexes: Verbal Comprehension, Perceptual Organization, Freedom from Distractibility and Processing Speed (Georgas, Weiss, van de Vijver, & Saklofske, Reference Georgas, Weiss, van de Vijver and Saklofske2003; Kush et al., Reference Kush, Watkins, Ward, Ward, Canivez and Worrell2001; Sattler, Reference Sattler2001). However, the calculation of the Freedom from Distractibility and Processing Speed indexes is only possible if two additional subtests are applied: Digit Span and Symbol Search, respectively, hence the full scale IQ score is a combination of indexes of Verbal Comprehension and Perceptual Organization. The factorial structure for gifted children in this version of the scale was studied by Watkins, Greenawalt, and Marcell (Reference Watkins, Greenawalt and Marcell2002) on 505 children (M _{total IQ} = 131.2, SD = 7.25), confirming a two-factor structure. The first factor consisted of Information, Similarities, Vocabulary and Comprehension, while the second showed significant loadings for Picture Completion, Block Design and Object Assembly, with both factors explaining 31.8% of variance. In this model, Picture Arrangement and Arithmetic were not loaded on any factor and Coding showed a negative loading on the verbal factor. These researchers recommended not using the Arithmetic and Coding subtests when testing for intellectual giftedness, as both of them exhibited heavy loadings on processing speed.

Finally, the fourth edition of the scale (WISC-IV; Wechsler, Reference Wechsler2003b) proposes a substantial change by introducing a four-factor structure, eliminating the Freedom from Distractibility index and introducing Working Memory and Processing Speed. Initial studies on its factorial structure carried out on normal population and on children with different suspected psychological problems have confirmed its suitability for the four-factor model (Bodin, Pardini, Burns, & Stevens, Reference Bodin, Pardini, Burns and Stevens2009; Canivez, Reference Canivez2014; Keith, Fine, Taub, Reinolds, & Kranzler, Reference Keith, Fine, Taub, Reynolds and Kranzler2006; Watkins, Reference Watkins2010; Watkins, Wilson, Kotz, Carbone, & Babula, Reference Watkins, Wilson, Kotz, Carbone and Babula2006; Wechsler, Reference Wechsler2003b, Reference Wechsler2005). However, it has not been specifically subjected to a factorial analysis on an intellectually gifted population before until the work of Rowe, Dandridge, Pawlush, Thompson, and Ferrier (Reference Rowe, Dandridge, Pawlush, Thompson and Ferrier2014). These authors conducted an exploratory factor analysis on a sample of 225 children aged between 8 and 12 years with an average IQ of 126.15, yielding a two-factor solution (a Verbal Comprehension factor and a second factor that grouped the remaining subtests except for Block Design and Picture Concepts), a three factor (Verbal Comprehension, a second factor resulting from the combination of Working Memory and Processing Speed, and a third factor consisting in a modified Perceptual Reasoning factor) and a four factor solution (corresponding to the indexes of the scale), which accounted for the 41%, 53% and 63.18% of the variance, respectively. The three solutions showed a relatively acceptable fit, and each of the subtests clearly tended to conform to a single factor, except for Picture Concepts. In order to clarify the results, the authors conducted a second study on a sample of 181 children aged between 6 and 12 years with an average IQ of 126.71. In this case, they conducted confirmatory factor analyses to test the three models obtained in the exploratory factor analysis. For the four-factor model, both a first order solution and a second order solution which included a g factor were tested. The results showed that, among the first order models, the only one that suggested a good fit was the four-factor model. The second order four-factor model obtained very similar results to the first order results, although its χ² value was slightly higher. Therefore, Rowe et al. (Reference Rowe, Dandridge, Pawlush, Thompson and Ferrier2014) concluded that the results supported the first order four-factor solution of the WISC-IV, which establishes the general structure of the scale for gifted children.

However, the four-factor structure of the WISC-IV appears to affect the performance profile of gifted children as it decreases the verbal and perceptual skills loadings from 80% to 60% and increases from 20% to 40% the weight of working memory and processing speed tasks (Rimm, Reference Rimm2010; Silverman, Reference Silverman and Shavinina2009). In fact, the results of several studies have consistently shown the existence of a differential performance profile in these children with significantly lower scores in Working Memory and especially in Processing Speed (Rimm, Reference Rimm2006; Rimm et al., Reference Rimm, Gilman, Silverman and VanTassel-Baska2008; Wasserman, Reference Wasserman2006; Wechsler, Reference Wechsler2003b). Examples include data from 63 children with intellectual giftedness within the standardization studies of this version (Wechsler, Reference Wechsler2003b) which, when compared with an average intelligence group, showed significant differences in the four indexes, remaining high for Verbal Comprehension and Perceptual Reasoning and moderate for Working Memory and Processing Speed. In fact, the Processing Speed score (M = 110.6, SD = 11.5) is the lowest score obtained by the group of children with giftedness. Similar results were obtained by Rimm (Reference Rimm2006), in whose work, the Processing Speed index score was the lowest of the group with an average of 111.9 points. This was also the case of the Gifted Development Centre’s with an even lower score (M = 104.3; Rimm et al., Reference Rimm, Gilman, Silverman and VanTassel-Baska2008). This pattern shows that, in general, these children approach cognitive tasks in a more thoughtful way, which entails negative consequences on the scale’s composite score as it reduces the full scale IQ score.

A possible explanation for this variability in gifted children’s cognitive profiles is given by Spearman’s Law of Diminishing Returns (SLORD; Spearman, Reference Spearman1927), which postulates an inverse relationship between high IQ scores and low correlations between different cognitive skills. This relationship has been proven in numerous studies (Abad, Colom, Juan-Espinosa, & García, Reference Abad, Colom, Juan-Espinosa and García2003; Facon, Reference Facon2003a, Reference Facon2004, Reference Facon2006; Jensen, Reference Jensen2003; Reynolds, Hajovsky, Niileksela, & Keith, Reference Reynolds, Hajovsky, Niileksela and Keith2011).

To avoid potential problems arising from discrepancies between indexes, on the full scale IQ score, the General Ability Index (GAI, Flanagan & Kaufman, Reference Flanagan and Kaufman2004; NAGC, 2010; Raiford, Weiss, Rolfhus, & Coalson, Reference Raiford, Weiss, Rolfhus and Coalson2005; Rimm et al., Reference Rimm, Gilman, Silverman and VanTassel-Baska2008; Weiss, Saklofske, Prifitera, & Holdnack, Reference Weiss, Saklofske, Prifitera and Holdnack2006) has been proposed. This index is obtained by evaluating children with only six of the subtests (Vocabulary, Similarities, Comprehension, Block Design, Matrix Reasoning and Picture Concepts) avoiding the subtests that are part of the indexes of Working Memory and Processing Speed. Flanagan and Kaufman (Reference Flanagan and Kaufman2004) have argued that the full scale IQ score should not be taken into consideration if there is a discrepancy equal to or greater than 23 points (1.5 SD) between different indexes, since distances of such magnitude would indicate that the full scale IQ would not be a unitary construct. The NAGC accepts the use of the General Ability Index as a criterion to gain access to educational programs for gifted children, stating that children with high scores on Verbal Comprehension and Perceptual Reasoning but low scores in Working Memory and Processing Speed can succeed in educational programs for advanced students (NAGC, 2010). The work of Rimm et al. (Reference Rimm, Gilman, Silverman and VanTassel-Baska2008) is an example of the impact of using this index. In their study, the number of children with a full scale IQ greater than 130 increased from 44 to 61 after applying this index. However, in Rowe et al.’s (Reference Rowe, Dandridge, Pawlush, Thompson and Ferrier2014) study, the exploratory factor analysis did not confirm the GAI structure and the four-factor model determined through confirmatory factor analysis yielded Working Memory as the first factor and the one that explained the a highest percentage of variance.

Taking the mentioned information as reference, the objectives of this present study are: (1) Check the fit of different factor models to Spanish intellectually gifted children; (2) Check for discrepancies between the different indexes of the scale in this group of children.

Method

Participants

A total of 87 Spanish children, previously identified as gifted by qualified professionals (full scale IQ ≥ 130) participated in the study, all of whom attended public schools in Granada and Jaén. The children were aged between 6 and 13 years (M _age = 8.51, SD = 2.08). A total of 63.2% of participants were male and 36.8% were female. As can be seen on Table 1, the average IQ level was 141.18 (SD = 9.11). Prior to participation in the study, informed parental consent was obtained and it was ensured that the participating children did not suffer from any psychological or behavioral problems.

Table 1.

Participants according to Age, Gender and IQ

Instruments

Wechsler Intelligence Scale for Children-IV (WISC-IV) (Wechsler, Reference Wechsler2005)

It consists of 15 subtests, 10 core tests and 5 supplemental, which assess the intellectual capacity of children aged between 6 and 16 years. It provides four indexes (Perceptual Reasoning, Verbal Comprehension, Working Memory and Processing Speed) and a full scale IQ score reflects the general cognitive ability of the child. This test’s reliability in terms of its internal consistency for the Spanish adaptation reaches values of between .72 and .95. Concurrent validity has been established through the correlation between the WISC-IV and the Raven Progressive Matrices (Raven, Raven, & Court, Reference Raven, Raven and Court1998) finding correlations between .31 and .61, depending on the indexes, being .54 for the full scale IQ score.

Procedure

Firstly, permission from the Human Research Ethics Committee of the Universidad de Granada was obtained. The selection of participants was carried out through collaboration between the Universidad de Granada and the giftedness associations of Granada and Jaén. All the parents of the participants gave their informed consent. As a criterion for inclusion in the study, participants had to be aged between 6 and 13 years and had to have been diagnosed with intellectual giftedness (full scale IQ ≥ 130). Meanwhile, having any disorder diagnosed with the DSM-IV-TR was established as an exclusion criterion. Based on these criteria, 91 children were evaluated.

The evaluation was performed individually in a single, hour-and-a-half session, by members of the research group. Only the 10 core subtests were applied. Once the evaluation was completed, it was found that 4 of the children did not reach a minimum IQ score of 125, and hence these 4 children were not included into the data analysis. The IQ≥125 cut-off was set taking into account the manual’s measurement error (Wechsler, Reference Wechsler2005) and the work of Flanagan and Kaufman (Reference Flanagan and Kaufman2004). Therefore, the final number of participants in this present study was 87 children.

Design and Statistical Analysis

A factorial design was carried out. The data analysis was performed using SPSS statistical software version 18.0 and the LISREL 8.80 and PRELIS statistical programs. Confirmatory factor analysis, descriptive statistics analysis and an analysis of the frequency of discrepancies between indexes of the WISC-IV were performed.

Results

Since the psychometric validity of the WISC-IV has been extensively reviewed (Wechsler, Reference Wechsler2003b; Reference Wechsler2005), a confirmatory factor analysis was performed to determine the goodness of fit of five models: a two-factor (consisting of the verbal and manipulative subtests) model, another two-factor model according to the General Ability Index structure (including subtests of Verbal Comprehension and Perceptual Reasoning indexes), a first-order four-factor model (consisting of the scale’s four indexes: Verbal Comprehension, Perceptual Reasoning, Working Memory and Processing Speed), a second-order four-factor model with a direct g factor (which is related to the subtests), and finally another second-order four-factor model with an indirect g factor (in this case, g grouped the four indexes). Thus, the proposed models were reviewed using the LISREL 8.80 program and the Unweighted Least Squares (ULS) method was used as the estimation method.

Table 2 presents the goodness of fit indexes obtained for all models. First, the χ² (χ² goodness of fit test, non-significant with p > .05) was acceptable since it yielded no significant differences between the models and the empirical data collected with all models except for the Verbal-Manipulative two-factor model (p = .001). Since χ² is sensitive to sample size, Table 2 also presents the Root Mean Square Error of Approximation (RMSEA) values for each model. Again, satisfactory values (RMSEA < .08) were obtained for all models except for the Verbal-Manipulative two-factor model (RMSEA = .12).

Table 2.

Goodness of Fit Indexes for Analyzed Models

Note: RMSEA = Root Mean Square Error of Approximation; ECVI = Expected Cross-Validation Index; AIC = Akaike Information Criterion; CAIC = Consistent Akaike Information Criterion; NFI = Normed Fit Index; CFI = Comparative Fit Index; IFI = Incremental Fit Index; SRMR = Standardized Root Mean Square Residual; GFI = Goodness of Fit Index; AGFI = Adjusted Goodness of Fit; PGFI = Parsimony Goodness of Fit Index.

When the rest of the goodness of fit indexes were analyzed jointly, it was possible to reconfirm that the Verbal-Manipulative two-factor model was not a valid model. Nevertheless, the other four models successfully reached the cut-off points recommended for all the individual fit indexes: NFI-Normed Fit Index, CFI-Comparative Fit Index, IFI-Incremental Fit Index, RMSEA-Root Mean Square Error of Approximation, GFI-Goodness of Fit Index, AGFI-Adjusted Goodness of Fit (Hair, Anderson, Tatham, & Black, Reference Hair, Anderson, Tatham and Black1999; Marsh, Hau, & Wen, Reference Marsh, Hau and Wen2004).

Moreover, the Expected Cross-Validation Index (ECVI), the Akaike Information criterion (AIC) and the Consistent Akaike information Criterion (CAIC) allow for the comparison between models, making it possible to emplace the four valid models into order of adjustment positions. These comparisons situated the two-factor GAI model and the four-factor with indirect g model as the best fitting models, followed by the first-order four-factor model and lastly, by the four-factor model with direct g. Finally, the Parsimony Goodness of Fit Index (PGFI) allows for the comparison of models in terms of their parsimony, placing the four-factor model with indirect g and first-order four-factor model as the best, while the two-factor GAI model and the four-factor with direct g model were placed at a second level (see Table 2).

As for the standardized residuals, only the four-factor with indirect g model maintained them always below |2.85|, as recommended. Hence, the other models must have had an excess or defect of relationships between the subtests and the factors.

As a conclusion of the above mentioned, it can be said that the two-factor Verbal-Manipulative model failed the analysis, and that the two-factor GAI solution, the four-factors with indirect g and first-order four-factor models showed the more robust fit, while the four-factor with direct g model, though valid, was not as robust as the foregoing. However, the two more robust four-factor models seemed to be more consistent with the theory behind the scale.

Figures 1 and 2 show the standardized factor loadings obtained in the 10 core subtests of the WISC-IV for the first-order four-factor model and for the four-factor with indirect g model. These loadings were significant in all cases, and were acceptable for both models, except for the Picture Concepts (.51 in the first-order four-factor model,.55 in the four-factor with indirect g model), Similarities (.51 in the first-order four-factor model and .45 in the four-factor with indirect g), Comprehension (.36 in the first-order four-factor model and .48 in the four-factor with indirect g model) and Block Design (.55 in the four-factor with indirect g model) subtests.

Figure 1.

Four-factor model of the confirmatory factor analysis.

Note: VC = Verbal Comprehension; PS = Processing Speed; WM = Working Memory; PR = Perceptive Reasoning.

Figure 2.

Four-factor model and second-order factor in the confirmatory factor analysis.

Note: VC = Verbal Comprehension; PS = Processing Speed; WM = Working Memory; PR = Perceptive Reasoning.

In relation to the standardized factor loadings, the two-factor GAI model always provided significant loadings (t >1.96). These were also acceptable (near or above 0.60) in the Vocabulary, Picture Concepts and Matrix Reasoning, but were lower in Similarities (.43), Comprehension (.39) and Block Design (.39), following the trend of previous models.

The reliability of the subtests in the three most robust models was moderate, as is observed through the Squared Multiple Correlation, which shows the proportion of each of the models’ explained variance. In the two-factor GAI model they were: Block Design (.15), Similarities (.18), Picture Concepts (.40), Vocabulary (.78), Matrix Reasoning (.48), and Comprehension (.15). For first-order four-factor model they were: Block Design (.37), Similarities (.26), Digit Span (.33), Picture Concepts (.26), Coding (.64), Vocabulary (.65) Letter-Number Sequencing (.57), Matrix Reasoning (.31), Comprehension (.13), and Symbol Search (.59). For the four-factor with indirect g model they were: Block Design (.30), Similarities (.20), Digit Span (.43), Picture Concepts (.31), Coding (.66), Vocabulary (.72), Letter-Number Sequencing (.45), Matrix Reasoning (.40), Comprehension (.17) and Symbol Search (.57).

The distribution of indexes and subtests analysis showed a slight skewness and kurtosis, where the subtests with a more pronounced skewness and kurtosis were Vocabulary and Comprehension (see Table 3).

Table 3.

Descriptive Statistics, Skewness and Kurtosis of the WISC-IV Subtests

Note: VC = Verbal Comprehension; PS = Processing Speed; WM = Working Memory; PR = Perceptive Reasoning.

Regarding the second objective, verifying whether there were discrepancies between different indexes obtained on this scale, the data showed the existence of such discrepancies. Thus, there was an average difference of 20.38 points between Verbal Comprehension and Processing Speed. Similarly, an average difference of 17.73 points between Perceptual Reasoning and Processing Speedwas observed (see Table 4). Of the four indexes, Verbal Comprehension appeared as the most discriminative indicator of giftedness, with Perceptual Reasoning being the second. Meanwhile, Working Memory, and above all, Processing Speed, showed a lower score (see Table 3). Finally, the frequencies analysis showed that 43.7% of participants had discrepancies between Verbal Comprehension and Processing Speed greater or equal to 23 points, and 34.5% of participants showed discrepancies between Perceptual Reasoning and Processing Speed.

Table 4.

Discrepancy Values Analysis between the WISC-IV Indexes

Note: VC = Verbal Comprehension; PS = Processing Speed; WM = Working Memory; PR = Perceptive Reasoning.