ISSN EDICIÓN EN PAPEL: 0214-9915
2003. Vol. 15, nº 1, pp. 155-160
FACTOR STRUCTURE OF THE SPANISH WAIS-III
Luis F. García, Miguel Ángel Ruiz and Francisco José Abad
Universidad Autónoma de Madrid
The Spanish version of the WAIS-III 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 WAIS-R),
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 first-order factors (Verbal, Perceptual Organisation, Working Memory
and Processing Speed) presents the best fit in all samples. When a second-order
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 WAIS-III. 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 WAIS-III. Tan solo dos años después de la publicación
en EE.UU. de la tercera versión de la escala Wechsler para adultos
(WAIS-III), 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 WAIS-III. Se discuten las implicaciones sobre las puntuaciones obtenidas
a partir de la escala (CI total, CI verbal, CI manipulativo así
como cuatro índices cognitivos).
Fecha recepción: 2-1-02 • Fecha aceptación:
Correspondencia: Luis Francisco García Rodríguez
Facultad de Psicología
Universidad Autónoma de Madrid
28049 Madrid (Spain)
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, WAIS-R, and WAIS-III), 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 two-factor 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 WAIS-III. Confirmatory factor analysis will be conducted in order to compare different hypothesised models on the grounds of well-known fit indexes (Bollen, 1989).
The Spanish standardisation sample of the WAIS-III (N= 1369; TEA, 1999)) was analysed in the present study. The six normative age groups (in years) and the corresponding N (in parentheses) are: 16-19 (163); 20-24 (153); 25-34 (272); 35-54 (408); 55-69 (237) y 70-94 (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.
The WAIS-III is an individually administered cognitive scale, shaped by 14 subtests: Vocabulary, Similarities, Information, Comprehension, Arithmetic, Digit span, Letter-number 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 WAIS-III subtests (see TEA, 1999; for details). Reliabilities (Split-half method) are shown in Table 1.
Analyses were performed through the Amos 3.6 statistical package (Arbuckle, 1997). Variances-covariances matrices were used as input data. Parameters were estimated by the Maximum Likelihood method.
Five structural models were evaluated (figure 1): One-factor, oblique two-factor, oblique three-factor, oblique four-factor, and a model with a second-order factor.
The one-factor model supposes that only the g factor (Jensen, 1980, 1998) accounts for by the differences on performance on the WAIS-III subtests. Following this model, Total IQ would be the only reliable WAIS-III score. The oblique 2-factor 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 WAIS-III, two new subtest theoretically linked with them have been developed («Letter-number 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 WAIS-III 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 first-order 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 & Andres-Pueyo, 1999). Therefore, g could be extracted as a second-order factor in the WAIS-III. So, a fifth model adds one second-order factor to the oblique four-factor model as is shown in figure 1 (e).
Regression coefficients of the errors over the subtests (and over the first-order factors in the model with a second-order factor) were fixed to 1. Moreover, one loading on every factor was also fixed to 1 as follows (linked factors are in parenthesis):
– One-factor model: Matrices (g).
– Oblique two-factor: Vocabulary (Verbal), and Block design (Performance).
– Oblique three-factor: Vocabulary (Verbal), Block design (Perceptual Organisation), and Coding (Attention).
– Oblique four-factor, and the model with a second-order 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 second-order factor.
Total sample (N = 1369)
Fit indexes obtained in the total sample appear in Table 2.
χ2 differences are always significant (α = 0.05). Looking
at other fit indexes only models with four first-order factors show an acceptable
fit. On the contrary, the one-factor, oblique two-factor, and oblique three-factor
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 one-factor model. Moreover, factor correlations, and the loadings on the g factor in the model with a second-order factor are also large. This fact would support that the g factor is the main cognitive ability assessed by the WAIS-III. However, the better fit of the oblique four-factor model suggests that other cognitive abilities also play a significant role.
Fit indexes obtained by the five models in every age group
are shown in table 4. Again, the oblique four-factor model obtains the best
fit in all age groups. Besides, the one-factor, oblique two and, three-factor
models do not reach acceptable values in any age group. However, compared to
the four-factor model, there are no significant differences in the RMSEA (α
= 0.1) in any age group when a second-order 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
The model with the best fit was always the oblique four-factor
model. This model obtains the lowest values in the χ2 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 4-factor model always reached the best
fit. On the other hand, the models with one, two, and three factors, not only
have a worse χ2, but also the remaining fit indexes get unacceptable
values. For instance, the RMSEA is always higher than .1 (Browne & Cudeck,
We would like to remark that fit indexes are very similar in both models with four first-order factors. Therefore, extracting a second-order factor is supported. It could be identified with the g factor (Carroll, 1993, Jensen, 1998; Juan-Espinosa, 1997), and would be the main cognitive ability assessed by the WAIS-III attending at the loadings on every structural model and the factor correlations. In this way, in a Schmid-Leiman 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 (Juan-Espinosa, García, Escorial, Rebollo, Colom, Abad, in press). Nevertheless, the bad fit of the one-factor 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 WAIS-III, Total IQ as an estimation of the g level, and the four cognitive indexes as measures of lower-order 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, Juan-Espinosa, submitted; Escorial, Rebollo, García, Colom, Abad, & Juan-Espinosa). A similar critic can be risen regarding the four cognitive indexes. Note that loadings on the g factor are larger than those on the lower-order 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 two-factor model does not fit well to empirical data.
Allen, S.R. & Thorndike, R.M. (1995). Stability of the WAIS-R and the WISC-III factor structures using cross validation of covariance structures. Journal of Clinical Psychology, 51, 648-657.
Arbuckle, J.L. (1997). AMOS 3.6. Smallwaters Corporation.
Browne, M.W. & Cudeck, R. (1993). Alternative ways of assessing fit. In Bollen, K.A. y Scott-Long, J. (Eds.), Testing structural equation models. Newbury Park, CA: Sage Publications.
Bollen, K.A. (1989). Structural equations with latent variables. New York: Wiley.
Carpenter, P.A., Just, M.A. & Shell, P. (1990). What one intelligence test measures: a theoretical account of the processing in the Raven progressive matrices test. Psychological review, 97, 404-431.
Carroll, J.B. (1993). Human cognitive abilities. A survey of factor analytic studies. Cambridge, Cambridge Univ. Press.
Caruso, J.C. & Cliff, N. (1998). The factor structure of the WAIS-R: Replicability across age-groups. Multivariate Behavioural Research, 33, 273-293.
Colom, R. (1998). Psicología de las diferencias individuales [Psychology of Individual Differences]. Madrid: Pirámide.
Colom, R., Abad, F.J., García., L.F. & Juan-Espinosa, M. (submitted). Education, Wechsler’s Full Scale IQ, and g.
Colom, R. & Andrés-Pueyo, A. (1999). El estudio de la inteligencia humana: Recapitulación ante el cambio de milenio. Psicothema, 11(3), 453-476.
Escorial, S., Rebollo, I, García, L.F., Colom, R., Abad, F.J. & Juan-Espinosa, M. (in press). Las aptitudes que se asocian al declive de la inteligencia: Evidencias a partir del WAIS-III. Psicothema.
Frank, G. (1983). The Wechsler enterprise: an assessment of the development, structure, and use of the Wechsler test of intelligence. New York: Pergamon.
Geary, D.C. & Whitworth, R.H. (1988). Dimensional structure of the WAIS-R: A simultaneous multi-sample analysis. Educational and Psychological Measurement, 48, 945-956.
Jensen, A.R. (1980). Bias in mental testing. Londres: Metuen.
Jensen, A.R. (1998). The g factor. London: Praeger.
Juan-Espinosa, M. (1997). Geografía de la inteligencia humana [Geography of human intelligence]. Madrid: Pirámide.
Juan-Espinosa, M., García, L.F., Escorial, S., Rebollo, I., Colom., R. & Abad, F.J. (in press). Age dedifferentiation hypothesis : Evidence from the WAIS-III. Intelligence.
Kamphaus, R.W., Benson, J., Hutchison, S. & Platt, L.O. (1994). Identification of factor models for the WISC-III. Educational and Psychological Measurement, 54, 174-186.
Kyllonen, P. & Christal, R. (1990). Reasoning ability is (little more than) working memory capacity?!. Intelligence, 14, 389-433.
O’Grady, K. (1983). A confirmatory maximum likelihood factor analysis of the WAIS-R. Journal of Consulting and Clinical Psychology, 51, 826-831.
O’Grady, K. (1989). Factor structure of the WISC-R. Multivariate Behavioural Research, 24, 177-193.
O’Grady, K. (1990). A confirmatory maximum likelihood factor analysis of the WPPSI. Personality and Individual Differences, 11, 135-190.
Randolph, A.C. & Thompson, B. (2000). Second-order confirmatory factor analysis of the WAIS-III. Assessment, 7, 237-246.
Saklofske, D.H., Hildebrand, D.K. & Gorsuch, R.L. (2000). Replication of the factor structure of the Wechsler Adult Intelligence Scale-Third Edition with a Canadian sample. Psychological Assessment, 12, 436-439.
Seisdedos, N. & Corral, S. (1999). La representatividad de la muestra normativa (Datos de la adaptación española del WAIS-III) [The representativeness of the standardization sample. (Data from the Spanish version of the WAIS-III)]. Paper presented at the Sixth Congress on Methodology of Social and Health sciences celebrated at Oviedo (Spain).
Siegert, R.J., Pattern, M.D., Taylor, A.J.W. & McCormick, I.A. (1988). Factor analysis of the WAIS-R using the factor replication procedure, FACTOREP. Multivariate Behavioural Research, 23, 481-489.
Silverstein, A.B. (1985). Cluster analysis of the Wechsler Adult Intelligence Scale - Revised. Journal of Clinical Psychology, 41, 98-100.
Spearman, C. (1923). The nature of «intelligence» and the principles of cognition. London: Macmillan.
Spearman, C. (1927). The abilities of man: Their nature and measurement. New York: Macmillan.
TEA, S.A. (1999). WAIS-III: Escala de inteligencia de Wechsler para Adultos. Tercera versión [WAIS-III: Wechsler adult Intelligence scale. Third version]. Madrid: TEA.
Wechsler, D. (1955). Manual for the Wechsler Adult Intelligence scale. New York: Psychological Corporation.