Psicothema 
ISSN EDICIÓN EN PAPEL: 02149915 
2003. Vol. 15, nº 1, pp. 155160 

FACTOR STRUCTURE OF THE SPANISH WAISIII

Luis F. García, Miguel Ángel Ruiz and Francisco José Abad

Universidad Autónoma de Madrid


The Spanish version of the WAISIII scale was published
two year after the American one only. Taking into account the polemic
about the factor structure of the previous versions (WAIS, and WAISR),
it is critical to test what this new scale is assessing. Several structural
models were analysed in the total sample (N = 1369), and in every normative
age group through confirmatory factor analysis procedures. A model with
four firstorder factors (Verbal, Perceptual Organisation, Working Memory
and Processing Speed) presents the best fit in all samples. When a secondorder
factor (identified with the g factor) is added to this model,
the fit indexes also show acceptable values. Results support that g
would be the main cognitive ability assessed by the WAISIII. Implications
for the scores computed after the scale (Total IQ, Verbal IQ, Performance
IQ, and four cognitive indexes) are discussed.
Estructura factorial de la versión española
del WAISIII. Tan solo dos años después de la publicación
en EE.UU. de la tercera versión de la escala Wechsler para adultos
(WAISIII), se adaptó dicha escala en España. Teniendo
en cuenta la polémica sobre la estructura factorial de las versiones
previas, es necesario comprobar qué factores está evaluando
la nueva escala. Con este objetivo diversos modelos estructurales fueron
ajustados tanto en la muestra total (N = 1369) como en cada grupo de
edad. El modelo con cuatro factores de primer orden (Verbal, Organización
perceptiva, Memoria de trabajo y Velocidad de procesamiento) obtuvo
el mejor ajuste en todas las muestras. Por su parte, cuando se añadía
un factor de segundo orden (identificado con g) al modelo anterior,
los índices de ajuste presentaban valores considerados aceptables.
En general, los resultados avalan la conclusión de que g
es la principal aptitud cognitiva evaluada por la versión española
del WAISIII. Se discuten las implicaciones sobre las puntuaciones obtenidas
a partir de la escala (CI total, CI verbal, CI manipulativo así
como cuatro índices cognitivos).


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Fecha recepción: 2102 • Fecha aceptación:
26502
Correspondencia: Luis Francisco García Rodríguez
Facultad de Psicología
Universidad Autónoma de Madrid
28049 Madrid (Spain)
Email: luis.garcia@uam.es




Wechsler’s scales (WPPSI, WISC, WAIS and their successive versions) are probably the psychometric instruments most used to assess cognitive abilities. Nevertheless, they have been continuously criticised due to the instability of the extracted factors, and the lack of agreement regarding their number and nature (Caruso & Cliff, 1998; Geary, & Whitworth, 1988; Kamphaus, Benson, Hutchison, & Platt, 1994; O’Grady, 1989; O’Grady, 1990). In fact, it has been claimed that they should become extinct (Carroll, 1993; Frank, 1983).
Focusing on WAIS scales (WAIS, WAISR, and WAISIII), different structures with one (O’Grady, 1983), two (Verbal and Performance factors; Wechsler, 1955; Siegert, Pattern, Taylor, & McCormick, 1988), or three factors (Verbal Comprehension, Perceptual Organisation, and Freedom from Distractibility; Allen and Thorndike, 1995; Silverstein, 1985) have been defended. Caruso and Cliff (1998) suggest that divergences on how many factors should be extracted, as well as methodological pitfalls, are responsible of such conflictive results. They conclude that the one and twofactor solutions are both plausible, whereas the third factor is not replicable across age groups and, therefore, it is a questionable factor.
The aim of the current study is to look into the factor structure of the Spanish version of the WAISIII. Confirmatory factor analysis will be conducted in order to compare different hypothesised models on the grounds of wellknown fit indexes (Bollen, 1989).
Method
Participants
The Spanish standardisation sample of the WAISIII (N= 1369; TEA, 1999)) was analysed in the present study. The six normative age groups (in years) and the corresponding N (in parentheses) are: 1619 (163); 2024 (153); 2534 (272); 3554 (408); 5569 (237) y 7094 (136). No larger differences than 3% were found between the standardisation sample, and the Spanish census in the percentages of sex, age, residence (urban, intermediate, rural), educational level, and geographic location (Seisdedos & Corral, 1999). So, the standardisation sample is representative of the Spanish population.
Instrument
The WAISIII is an individually administered cognitive scale, shaped by 14 subtests: Vocabulary, Similarities, Information, Comprehension, Arithmetic, Digit span, Letternumber series, Picture completion, Block design, Matrices, Picture arrangement, Object assembly, Coding, and Symbol search.
Three IQ scores (Total IQ, Verbal IQ, Performance IQ), and four cognitive indexes (Verbal Comprehension, Perceptual Organisation, Working Memory, and Processing Speed) are computed after the WAISIII subtests (see TEA, 1999; for details). Reliabilities (Splithalf method) are shown in Table 1.
Procedure
Analyses were performed through the Amos 3.6 statistical package (Arbuckle, 1997). Variancescovariances matrices were used as input data. Parameters were estimated by the Maximum Likelihood method.
Structural models
Five structural models were evaluated (figure 1): Onefactor, oblique twofactor, oblique threefactor, oblique fourfactor, and a model with a secondorder factor.
The onefactor model supposes that only the g factor (Jensen, 1980, 1998) accounts for by the differences on performance on the WAISIII subtests. Following this model, Total IQ would be the only reliable WAISIII score. The oblique 2factor model maintains the classical division between verbal and performance subtests. This model supposes that has sense to compute the Verbal and Performance IQs separately.
A third factor (commonly called Freedom from distractibility) has been identified in previous versions of the Wechsler scales. «Digit span», «Arithmetic», and «Coding» subtests have traditionally loaded on this factor. In the WAISIII, two new subtest theoretically linked with them have been developed («Letternumber series» and «Symbol search»). These new subtests would reinforce this third factor, named «Attention». So, this model contains three factors: Verbal, Perceptual Organisation, and Attention.
According to the authors, the WAISIII is intended to incorporate the advances on cognitive psychology. These efforts are directed to improve the assessment of the working memory. This construct has been presented as the main candidate to explain the differences in the g factor from a cognitive perspective (Colom, 1998; Kyllonen & Christal, 1990; Carpenter, Just, & Shell, 1990). On the other hand, a fourth factor, called Processing Speed, is extracted on the grounds of the strong relationship between the «Coding» and «Symbol search» subtests. So, this model contains four firstorder factors: Verbal, Perceptual Organisation, Working Memory, and Processing Speed.
In all models, factors are hypothesised to be oblique since in previous exploratory factor analysis factor correlations ranged between .644 and .778 (extraction through the Principal Factors method with Promax rotation). The g factor is based on this positive manifold (Spearman, 1923; 1927; Jensen, 1998). g is currently located at the highest order of the structure of cognitive abilities (Carroll, 1993; Colom & AndresPueyo, 1999). Therefore, g could be extracted as a secondorder factor in the WAISIII. So, a fifth model adds one secondorder factor to the oblique fourfactor model as is shown in figure 1 (e).
Regression coefficients of the errors over the subtests (and over the firstorder factors in the model with a secondorder factor) were fixed to 1. Moreover, one loading on every factor was also fixed to 1 as follows (linked factors are in parenthesis):
– Onefactor model: Matrices (g).
– Oblique twofactor: Vocabulary (Verbal), and Block design (Performance).
– Oblique threefactor: Vocabulary (Verbal), Block design (Perceptual Organisation), and Coding (Attention).
– Oblique fourfactor, and the model with a secondorder factor: Vocabulary (Verbal), Block design (Perceptual Organisation), Digit span (Working Memory), and Coding (Processing Speed).
Finally, the g variance was fixed to 1 in the model with a secondorder factor.
Results
Total sample (N = 1369)
Fit indexes obtained in the total sample appear in Table 2.
χ^{2} differences are always significant (α = 0.05). Looking
at other fit indexes only models with four firstorder factors show an acceptable
fit. On the contrary, the onefactor, oblique twofactor, and oblique threefactor
models do not fit well.
Table 3 shows the standardised factor loadings obtained in the total sample. Factor loadings are high in all models, even in the onefactor model. Moreover, factor correlations, and the loadings on the g factor in the model with a secondorder factor are also large. This fact would support that the g factor is the main cognitive ability assessed by the WAISIII. However, the better fit of the oblique fourfactor model suggests that other cognitive abilities also play a significant role.
Age groups
Fit indexes obtained by the five models in every age group
are shown in table 4. Again, the oblique fourfactor model obtains the best
fit in all age groups. Besides, the onefactor, oblique two and, threefactor
models do not reach acceptable values in any age group. However, compared to
the fourfactor model, there are no significant differences in the RMSEA (α
= 0.1) in any age group when a secondorder factor is added. Moreover, such
model also gets a good fit in all age groups. Regarding the standardised solutions,
results obtained in every age group reproduce the pattern presented in table
3.
Discussion
The model with the best fit was always the oblique fourfactor
model. This model obtains the lowest values in the χ^{2} test as
well as in the AIC. Moreover, other fit indexes (RMSEA, GFI, NFI, and CFI) present
acceptable values. Results are congruent with those reported for the American
(Randolph & Thompson, 2000), and Canadian samples (Saklofske, Hildebrand,
& Gorsuch, 2000), where the oblique 4factor model always reached the best
fit. On the other hand, the models with one, two, and three factors, not only
have a worse χ^{2}, but also the remaining fit indexes get unacceptable
values. For instance, the RMSEA is always higher than .1 (Browne & Cudeck,
1993).
We would like to remark that fit indexes are very similar in both models with four firstorder factors. Therefore, extracting a secondorder factor is supported. It could be identified with the g factor (Carroll, 1993, Jensen, 1998; JuanEspinosa, 1997), and would be the main cognitive ability assessed by the WAISIII attending at the loadings on every structural model and the factor correlations. In this way, in a SchmidLeiman hierarchical factor analysis conducted over the total sample (performed through Principal factors with Promax rotation procedure), the g factor accounted for by the 58.193% of the variance, whilst the four group factors altogether accounted for by the 14.107% of the variance only. Moreover, such percentages of variances are replicated in all age groups (JuanEspinosa, García, Escorial, Rebollo, Colom, Abad, in press). Nevertheless, the bad fit of the onefactor model reinforces the current view about the hierarchical nature of the structure of cognitive abilities (Carroll, 1993). Finally, note that factor correlations get large values irrespective of the factor procedure (EFA Vs CFA) used.
Regard to the scores computed after the subtests of the WAISIII, Total IQ as an estimation of the g level, and the four cognitive indexes as measures of lowerorder factors report us useful psychometric information. However, several considerations must be done. Total IQ is computed through the simple summation of tests scores, so it is contaminated by other factors plus test’s specificity, reducing their reliability as an individual’s level estimation of the g factor (Colom, Abad, García, JuanEspinosa, submitted; Escorial, Rebollo, García, Colom, Abad, & JuanEspinosa). A similar critic can be risen regarding the four cognitive indexes. Note that loadings on the g factor are larger than those on the lowerorder factors, so the cognitive indexes are also strongly contaminated by g. Besides, the processing speed index should be interpreted carefully since the reliabilities of the related tests are unknown in the Spanish population. Studies about those indexes should be carrying out to test if they improve the criterion validity of the Total IQ. Finally, Verbal and Performance IQs do not seem to make sense since the oblique twofactor model does not fit well to empirical data. 

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