Joint confirmatory factor analyses of the DAS and WISC-R

Joumol o,fSrhool Pryrholoqy, Vol 30, pp, 185-195, Pergamon Press Ltd. Printed in the USA.

1992 0 ,992 The Journal

oom4405/92/$5 00 + 00 of School Psychology. Inc.

Joint Confirmatory Factor Analyses of the DAS and WISC-R Brian ]. Stone Wichita

State University

This study investigated the joint factor structure of the Differential Abilities Scale and the Wechsler Intelligence Scale for Children-Revised for 115 children. Theoretically supportable models were compared to determine which model provided the best tit to the data. Competing theoretical models were Spearman’s General factor, Wechsler’s Verbal and Performance (and Freedom From Distractibility) factors, and Elliott’s verbal, nonverbal, spatial, and diagnostic perspective. Elliott’s model provided a significantly better fit to the data than the alternative models. Interestingly, the WISC-R Freedom From Distractibility factor was “pulled apart,” suggesting caution in interpreting it as a single entity.

A three-factor

model has consistently

emerged

as the underlying

structure

of

the Wechsler Intelligence Scale for Children-Revised (WISC-R) for both normal and exceptional subjects (Kaufman, 1979). The three factors are Verbal Comprehension, Perceptual Organization, and Freedom From Distractibility. These three factors have generally been supported across diverse ethnic groups (Reynolds & Kaiser, 1990). While for some lower-ability groups only a Verbal

and Performance

be a basic consensus

factor may emerge (Reschly,

on the three-factor

structure

1980), there seems to

of the WISC-R

(Sattler,

1988). However,

there has been disagreement over what the Freedom From Dis1982). Some advocate a behavioral tractibility factor measures (Kaufman, rather than cognitive interpretation, while others suggest a simple numerical explanation for the factor (Sattler, quential Processing interpretation argument WISC-R

was supported and the Kaufman

in a joint

1988). Still others have argued for a Se(Kaufman & McLean, 1987). The latter factor analysis of data derived from the

Assessment

Battery for Children

(K-ABC)

(Kauf-

man & Kaufman, 1983). However, this position stems from the significant correlations between the three Freedom From Distractibility subtests and the three K-ABC Sequential Processing subtests. Therefore, this argument requires adherence

to Kaufman’s

version of Luria’s theory of processing.

Some

vigorous disagreement exists over this interpretation also (e.g., see Sternberg, 1984). Clearly, the Freedom From Distractibility factor is still open to interpretation. Received January 15, 1991; final revision received May 24, 1991. Address correspondence and reprint requests to Brian J. Stone, Department of Counseling, Educational and School Psychology, Wichita State University, Hubbard Hall 320, Campus Box 123, Wichita, KS 67208.

185

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Journal of School

Psychology

Along these lines, there has been support for the thesis that a three-factor structure underlies the school-age Differential Ability Scales (DAS) “core” subtests (Elliott, 1990). The three DAS factors are operationalized as Verbal, Nonverbal Reasoning, and Spatial Ability composites. Some observers have suggested slightly different interpretations of the factor structure. For example, Keith (1990) recommended that the Nonverbal Reasoning Ability composite be interpreted as a measure of g fluid. In addition, the DAS offers “diagnostic” subtests, which are less g-loaded and hence represent relatively independent abilities. There has been little research concerning the distinct abilities that may underlie the diagnostic subtests. On the surface there are many similarities between the theoretical framework of the WISC-R

and that of the DAS.

Both batteries

possess consistent

factor structures across the school-age range. Both allow for second-order g by providing a full scale composite in some form. Both provide highly similar and clear-cut Verbal factors. Indeed, correlations between Verbal composites of these tests are typically in the middle .8Os (Elliott, 1990). The similarity is further highlighted by content DAS Verbal Ability composite on the WISC-R,

overlap. The two subtests that make up the are Word Definitions (similar to Vocabulary

but with O-l scoring) and Similarities

(roughly equivalent

Similarities on the WISC-R, but with a three-word stimulus). tent overlap is particularly responsible for the high correlation. In spite of these similarities theoretically and operationally. is more inclusive than Elliott’s.

Clearly,

to

con-

the factor structures of the instruments differ Theoretically, Wechsler’s view of intelligence Wechsler

(1974)

proposed that intelligence

is

global and manifested in many forms. Two general forms of intelligence are represented by the Verbal and Performance scales. These scales correlate, as both are representative mentation

of his theory,

of the same underlying Wechsler

global ability.

includes low-g-loaded

In the imple-

subtests in the Full

Scale composite. Elliott (1990) has argued for a more concise view of intelligence. He stated, “Psychometric g is the general ability of an individual to perform complex mental processing that involves conceptualization and the transformation of information” (p. 20). Elliott included only the highest-g-loading subtests in his test composite. Relatively independent from g are the diagnostic subtests, which encompass memory and tasks that entail speed of information processing. These subtests (two verbal, one nonverbal) are not included in any composite. At the school-age level these subtests include Speed of Information Processing, Recall of Objects, and Recall of Digits (similar to Digits Forward from the WISC-R Digit Span). Elliott asserts that inclusion of the diagnostic subtests would render existing composites less interpretable (Elliott, 1990). Operationally, Wechsler and Elliot’s theories differ also in how the nonverbal subtests are grouped. Although all nonverbal subtests are grouped together in the WISC-R Performance scale, Elliott provides two nonverbal DAS

187

Stone

composites: Nonverbal Reasoning Ability, which consists of Matrices and the Sequential and Quantitative Reasoning subtests, and Spatial Ability, which consists

of Recall

of Designs

Design). The DAS and WISC-R metric

implementation.

and Pattern

Construction

(analogous

to Block

offer differing theoretical viewpoints and psychodisagreement remains over the proper

In addition,

interpretation of the WISC-R Freedom From Distractibility factor. Therefore, an empirical analysis of data can shed light on the interpretation of these two instruments. To this ehd,

Keith

(1990)

has suggested

that joint

analysis be used to better understand

what constructs

advantage

for this purpose

of a joint

factor

analysis

confirmatory

factor

the DAS measures.

The

is the convergent

and

discriminant information on construct overlap and independence that can be gained. In addition, using confirmatory factor analysis allows competing theoretical structures to be compared, by dictating the structure of the model and examining the goodness of fit indices. Finally, greater generalizability gained by using a representative sample rather than a clinical group.

is

METHOD Instruments The DAS and WISC-R ies. All nine school-age administered,

are individually DAS

subtests

as were all 12 WISC-R

administered

cognitive ability batter-

(six core and three diagnostic)

were

subtests.

Subjects The

subjects

were

115 normal

children

who were included

in two DAS-

WISC-R concurrent validity studies in the DAS manual (Elliott, 1990). The administrations of the DAS and WISC-R were counterbalanced. Testing was done by qualified psychologists or trained graduate students. The sample was collected during and immediately after DAS standardization. The sample size met Gorsuch’s (1983) suggested 5 : 1 minimum ratio of subjects to variables for factor analysis. The subjects ranged in age from 8 years 0 months through 15 years 11 months (mean age = 11 years 9 months; SD = 2 years 1 month) and included 58 girls and 57 boys. The group was composed Latinos, 9 blacks, cific Islander).

and 5 other (Native

American,

of 92 whites, 9

Asian-American,

and Pa-

PROCEDURE The tit of alternative theoretically viable and competing models was compared. One-, two-, three-, four-, and five-factor models were investigated. A short description of each model and how the subtests were categorized follows.

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Journal of School Psychology

One-factor Two-factor

model. All subtests were forced to load on one factor. model. “Wechsler’s Verbal and Performance”: Subtests

forced to

load by content on either Verbal or Performance factors. Three-factor model. “Wechsler’s Verbal, Performance, and Freedom Distractibility”:

All subtests were classified by verbal,

tentional-numerical content. Four-factor model. “Elliott’s DAS

core plus Freedom

From

nonverbal,

From

or at-

Distractibility”:

All subtest were classified by verbal, nonverbal reasoning/high perceptual organizational, and attentional-numerical content.

g, spatial/

Five-factor model. “Elliott’s DAS core plus diagnostic factors”: Subtests were classified as above, but DAS diagnostic subtests were allowed to form their own separate factors with WISC-R

analogues.

RESULTS The mean WISC-R

Full Scale IQ (FSIQ)

for the sample was 109.1 (SD =

14.7), while the mean DAS composite score (termed “General Conceptual Ability”) was 103.8 (SD = 14.0). The DAS mean underscores the representativeness of the sample. The difference in mean scores between the DAS and the WISC-R reflects the approximate 16-year difference between the two standardizations. The two-factor

model provided

a significant

factor model as seen from the significant

increase

decrease

in fit over the one-

in chi-square

(Table

1).

The three-factor model could not be directly compared with the two-factor model, as it was not a nested model. However, the goodness-of-fit indices improved for the three-factor model compared with the one-factor model. The four-factor model provided a significant factor model. The five-factor model improved

increase in fit over the threethe fit to the data significantly

over the four-factor model, thereby producing the best fit overall. The goodness-of-fit indices for this model were best, as seen from the root mean square residual (RMSR) of .069, the goodness-of-fit the adjusted goodness-of-fit index (AGFI) of ,800.

index (GFI)

of .845, and

Table 1 Goodness of Fit Indices for the Five Models Number of factors One TWO Three FOW Five “Compared

Improved x2

4f

495.2 384.3 331.3 264.3 243.7

189 188 186 183 179

with the one-factor

< < < <

P

GFI

.OOl .OOl ,001 ,001 ,001

,764 789 ,835 ,845

model

,664

fit

AGFI

RMSR

x2

df

P

.589 ,710 ,738 .7?2

,102 ,096 ,087 .071 ,069

110.9 163.9 67.0 20.6

1 3 3 3

< ,001 < .OOl” <.OOl < ,001

,800

189

Stone

As all models reasonable

had RMSRs

of .lO or lower,

fits to the data (Kerlinger,

1986).

all can be said to provide

Consequently,

factor loadings

from all models can be examined. For the purpose of interpretation, factor loadings of .4 and above will be considered significantly large (Gorsuch, 1983). It should be noted that the DAS diagnostic subtest Recall of Objects was constrained to load on the Verbal factor for all models. No WISC-R analogue existed for this visual-verbal

learning/recall

task to load with. There-

fore, to keep factors interpretable with at least two high-loading subtests, Recall of Objects was considered a verbal subtest. Indeed, it loaded between .479 and .482 on the Verbal factor of all models. Table

2 details the factor loadings

of the DAS and WISC-R

for the one- and two-factor

subtests had g loadings

models. All

of .4 and above,

with the

exception of Speed of Information Processing from the DAS and the Coding, Mazes, and Picture Arrangement subtests from the WISC-R. The two-factor solution has four nonverbal subtests that load less than .4. These subtests consist of the four lowest-g-loading

subtests previously mentioned.

Table 2 Factor Loadings and Intercorrelations for the One-Factor and Two-Factor (Wechsler’s Verbal and Performance)

Subtest DAS Word Definitions Similarities Seq & Quant Reasoning Matrices Pattern Construction Recall of Designs Recall of Digits Recall of Objects Speed of Info Process WISC-R Information Similarities Arithmetic Vocabulary Comprehension Digit Span Picture Completion Picture Arrangement Block Design Object Assembly Coding Mazes Note. Factor intercorrelations: 1 2 1 1.0 2 .67 1.0

Spearman’s general factor

.818 ,823 ,714

Wechsler Verbal

,777 .794 .637 ,900 .716 ,534 ,459 .370 .505 ,454 ,211 ,155

g)

scales Performance

,850 ,840 ,654 ,722 .791 ,617

,688 ,528 .422 ,538 ,490 .223

(Spearman Models

,496 ,479 ,304

.793 ,805 ,599 ,925 ,733 508 ,547 ,381 ,773 .629 ,242 ,290

Journal of School Psychology

190

Table 3 shows the loadings when the subtests were constrained to match the accepted three-factor WISC-R solution. Low loadings exist for two subtests on the Perceptual-Organization factor (Picture Arrangement and Mazes, again), and for two subtests on the third factor (Speed of Information Processing and Coding, again). The modification indices indicate that the latter two subtests could improve the fit of the model if allowed to load on the same factor, separate from Arithmetic, Digit Span, and the DAS Recall of Digits. In Table 4 the effects of redistributing the subtests according to the DAS framework can be seen. However, the WISC-R Third factor is kept to help determine

its viability and robustness

as a single component

across test batter-

ies. Picture Arrangement and Mazes had low loadings on the Spatial factor, while Speed of Information Processing and Coding contributed weakly to the Numeric factor. Again, the modification indices suggested that the latter two subtests would increase the fit by forming their own factor.

Table 3 Factor Loadings and Intercorrelations for the Three-Factor Model (Wechsler Three-Factor Interpretation)

Subtest DAS Word Definitions Similarities Seq & Quant Reasoning Matrices Pattern Construction Recall of Designs Recall of Digits Recall of Objects Speed of Info Process WISC-R Information Similarities Arithmetic Vocabulary Comprehension Digit Span Picture Completion Picture Arrangement Block Design Object Assembly Coding Mazes No& Factor Intercorrelations: 1 2 3 1 1.0 2 .66 1.0 3 .64 .70 1.0

Verbal Comprehension

PerceptualOrganization

“Third” factor

,853 ,841 ,662 ,730 .785 ,622 ,785 ,482 ,346

,793 ,805 ,632 ,933 ,736 ,775

,556 ,375 ,765 .617 ,267 ,299

191

Stone

Factor

Table 4 Loadings and Intercorrelations for the Four-Factor Model (Elliott Core Interpretation + WISC-R Third Factor)

Subtest DAS Word Definitions Similarities Seq & Qumt Reasoning Matrices Pattern Construction Recall of Designs Recall of Digits Recall of Objects Speed of Info Process WISC-R Information Similarities Arithmetic Vocabulary Comprehension Digit Span Picture Completion Picture Arrangement Block Design Object Assembly Coding Mazes

Verbal

Nonverbal

Spatial

Numeric

Ability

Reasoning

Ability

Ability

,854 ,845 ,828 ,823 ,852 ,631 .759

,480 .361 ,791 ,808 ,674 ,929

,736 ,741 ,550 .369 ,850 ,624 ,282 .280

Note Factor Intercorrelations: 1 2 3 4 1 1.0 2 .76 1.0 3 .52 .67 1.0 4 .66 .80 .59 1.0

Table

5 shows the loadings

of the best-fitting

model.

Again,

the Verbal

factor is characterized by high loadings from all subtests. Low loadings are seen only with Picture Arrangement and Mazes on the Spatial factor. Table 6 contains the subtest correlation matrix. Pearson product-moment correlations are reported only to the hundredths of the correlation is approximately .09.

place, as the standard

error

DISCUSSION The live-factor DAS model provided the best (albeit only fair) lit to the data. Beyond for the empirical support given to the DAS model, perhaps the most interesting finding was the lack of support for the WISC-R Freedom From Distractibility factor. The fit was improved when Coding was allowed to break off from the traditional WISC-R Third factor and form a separate Processing Speed factor with Speed of Information Processing. Arithmetic and Digit

192

Journal

Factor

of School

Psychology

Table 5 Loadings, Intercorrelations, and Second-order g Loadings for the Five-Factor Model (DAS Interpretation)

Subtest

Verbal Ability

DAS Word Definitions Similarities Seq & Quant Reasoning Matrices Pattern Construction Recall of Designs Recall of Digits Recall of Objects Speed Info Process

Spatial Ability

Numeric Ability

PI-OCtX Speed

,854

,845 ,826 ,824 ,854 ,629

,783 ,480 ,790

WISC-R Information Similarities Arithmetic Vocabulary Comprehension Digit Span Picture Completion Picture Arrangement Block Design Object Assembly Coding Mazes No&-. Factor Intercorrelations: 2 3 1 1 1.0 .76 1.0 2 .52 .67 1.0 3 .66 .77 .57 4 .22 .40 .33 5

Nonverbal Reasoning

,792 ,808 .929 ,735 ,766 ,546 ,370 ,849 ,625 ,554 ,279

4

1.0 .41

5

1.0

Second-order g loadings: Factor g loading 1 ,790 2 ,955 3 ,698 4 ,813 5 ,418

Span formed their own “Numeric Ability” factor with the DAS subtest Recall of Digits. While this derogates interpreting Freedom From Distractibility as an intact entity, it should be noted that both the Processing Speed and Numeric Ability factors probably share a similar attentional influence. However, they would best be interpreted as separate factors. Indeed their correlation was quite modest (.41). Along these lines Woodcock (1990) h as shown evidence that it may be appropriate to split the WISC-R Third factor even further. In his research on g fluid-g crystallized theory, Woodcock put Arithmetic, Digit Span, and Coding on three separatefactors (g quantitative, g short-term memory, and g processing speed, respectively). The three subtests loaded highly on their respective factors (.75, .69, and .58). The present research furthers the possibility that interpretation of the Freedom From Distractibility factor as a single entity is erroneous. It appears that Coding should be considered separate from the

;f:

.63 .51 .74 .61 .35 .32 .35 .35 .34 .09 .04

.70 .63 .50 .45 .33 .28 .36 .41 .09

WISC-R subtests 1. Information 2. Similarities 3. Arithmetic 4. Vocabulary 5 Comprehension 6. Digit Span 7. Picture Completion 8. Picture Arrangement 9. Block Design 10. Object Assembly 11. Coding 12. Mazes

DAS subtests 13. Word Definition 14. Similarities 15. Seq & Quant Reasoning 16. Matrices 17. Pattern Construction 18. Recall of Designs 19. Recall of Digits 20. Recall of Objects 2 1. Speed of Info Process

1

.67 .74 .55 .51 .30 .29 .36 .41 .ll

.46 .72 .62 .38 .34 .27 .36 .33 .07 .04

2

.50 .52 .60 .53 .35 .29 .42 .26 .33

.50 .43 .43 .24 .29 .34 .25 .19 .24

3

.80 .77 .59 .56 .43 .33 .43 .48 .14

.71 .45 .41 .33 .38 .36 .16 .12

4

Zero-Order

.57 .57 .48 .44 .28 .23 .34 .34 .17

.36 .28 .27 .29 .20 .15 .OO

5

7

8

.39 .28 .41 .36 .41 .29 .42 .37 .35 .43 .32 .42 .69 .31 .16 .26 .22 -.04

.25 .23 .24 .19 .27 .20 .16 .25 .15

.27 .32 .41 .45 .75 .51 .32 .30 .20

.53 .12 .22

9

.31 .27 .34 .44 .52 .40 .30 .31 .23

.18 .06

10

.23 .13 .25 .19 .16 .ll .15 .05 .44

.31

11

Table 6 Matrix for DAS and WISC-R

.23 .19 .29 .29 .46 .31 .19 .33 .30 .18 -.04 .13 .25 .21 -.02

6

Correlation

.Ol .OO .24 .23 .20 .37 .20 .13 .02

12

.76 .57 .44 .32 .19 .43 .33 .09

13

Subtests

.54 .58 .33 .27 .33 .37 .15

14

.68 .41 .31 .48 .33 .23

15

.51 .43 .47 .34 .26

16

.52 .43 .29 .31

17

.28 .29 .09

18

.20 .22

19

.11

20

194

Freedom basically

Journal of School Psychology

From Distractibility numeric in scope.

factor, rendering the remaining “Third factor” Indeed, this is consistent with the WISC-III

(Wechsler, 1991) four-factor interpretation of the WISC-R. The Verbal factor appeared robust across all models. Verbal subtest loadings were consistently high on the Verbal factor. The lowest loading was consistently Recall of Objects, which was basically loading on this factor by default. While it had a moderate loading, it clearly did not belong as much as the other subtests in the Verbal factor. Further research should be done with other batteries that might have a similar visual-verbal learning/recall subtest. A better fit was produced when the nonverbal subtests were split into separate factors (Nonverbal Reasoning and Spatial Ability), rather than providing one Performance factor. The WISC-R Perceptual-Organization subtests loaded substantially on the Spatial factor for the most part, although Picture Arrangement and Mazes had consistently low loadings. However, there was no logical justification for loading these two subtests on another factor. Since these two subtests showed low g loadings, load them with the g-saturated Nonverbal Sequential and Quantitative of all the nonverbal subtests.

Reasoning Moreover,

it was not theoretically Reasoning factor.

defensible

to

and Matrices g-loaded the highest the Nonverbal Reasoning factor

possessed the highest second-order g loading of all the factors (see Table 5). This lends support to Keith’s (1990) g fluid interpretation of this composite. Although some might argue for including the Block Design subtest in the Nonverbal Reasoning factor, Woodcock (1990) has shown Block Design to load only .12 on a g fluid factor in his research. Furthermore, constraining Block Design to load on the Spatial Ability factor is consistent with Elliott’s model, which loads Pattern

Construction

with the Spatial Ability rather than

the Nonverbal Reasoning composite. The factor intercorrelations show a strong link between the Verbal and Nonverbal Reasoning factors. Both have high g loadings, and their high correlation (. 76) is probably due to the underlying g factor. Nonverbal Reasoning and the Numeric Ability factor were also highly correlated (. 77), possibly partly because of overlap of numeric content in the Sequential and Quantitative Reasoning subtest with similar content in the Numeric Ability factor. Also, the high correlation would again have been influenced by the high g loadings of each factor. Interestingly, as the Numeric Ability factor is probably a more pure Freedom From Distractibility factor (having had Coding removed), the high g loading of the Numeric Ability factor would argue against a behavioral interpretation of the WISC-R Third factor. Finally, the Processing Speed factor had the lowest correlations with the other four factors and is the most independent (and least g-related) measure of ability. This is consistent with Elliott’s view that the DAS diagnostic subtests provide relatively independent measures of ability. Clearly, by including Processing Speed subtests in an overall g-loaded composite, interpretability of that composite would be affected.

195

Stone

Overall, Indeed,

the results lend support

as the Wechsler

to Elliott’s

interpretation

scales delivered practitioners

of the DAS.

from the bondage

of a

single composite, perhaps the DAS can move us beyond the two (or is it three?) composites of the Wechsler scales. Although g remains with us, the interpretation of other abilities may also prove more useful to practitioners.

ACKNOWLEDGMENTS The author wishes to express his appreciation to Drs. Mark Daniel and Timothy Z. Keith for their helpful suggestions and second-order factor analysis and to The Psychological Corporation for their permission to use copyrighted materials. Any errors of fact or reasoning are the sole responsibility of the author.

REFERENCES Elliott, C. D. (1990). Introductory and technical handbook for the Differential Ability Scales. San Antonio: Psychological Corporation. Gorsuch, F. (1983). Factor analysis. Hillsdale, NJ: Lawrence Erlbaum. Kaufman, A. S. (1979). Intelligent testing with the WZSC-R. New York: Wiley. Kaufman, A. S. (1982). The impact of WISC-R research for school psychologists. In C. R. Reynolds & T. B. Gutkin (Eds.), The handbook of school Psychology (pp. 156177). New York: Wiley. Kaufman, A. S., & Kaufman, N. L. (1983). K auf man Assessment Battery for Children administration and scoring manual. Circle Pines, MN: American Guidance Services. Kaufman, A. S., & McLean, J. E. (1987). Joint factor analysis of the K-ABC and WISC-R with normal children. Journal of School Psychology, 25, 105-l 18. Keith, T. Z. (1990). Confirmatory and hierarchical confirmatory analysis of the Differential Ability Scales. Journal of Psychoeducational Assessment, 8, 391-405. Kerlinger, F. N. (1986). Foundations of behavioral research (3rd ed.). New York: Holt, Rinehart & Winston. Reschly, D. J. (1980). Concepts of bias in assessment and WISC-R research with minorities. In H. Vance & F. Wallbrown (Eds.), WZX-R: Research and interpretation. Washington, DC: National Association of School Psychologists. Reynolds, C. R., & Kaiser, S. M. (1990). Test bias in psychological assessment. In T. B. Gutkin & C. R. Reynolds (Eds.), The handbook of school psychology (2nd ed, pp. 487-525). New York: Wiley. Sattler, J. M. (1988) Assessment of children (3rd ed.). San Diego: Author. analysis and criSternberg, R. J. (1984). The K-ABC: A n information-processing tique. Journal of Special Education, 18, 269-279. Wechsler, D. (1974). Manual for the Wechsler Intelligence Scale for Children-Revised. New York: Psychological Corporation. Woodcock, R. W. (1990). Theoretical foundations of the WJ-R measures of cognitive ability. Journal of Psychoeducational Assessment, 8, 23 1- 158. Wechsler, D. (1991). Manual for the Wechsler Intellectual Scale for Children-Third Edition. San Antonio: Psychological Corporation.