Bimodality in the Berlin model of intelligence structure (BIS): A replication study

Person. inditid.

SO191-8869(96)00129-8

Dilf: Vol. 21, No. 6. pp. 987-1005, 1996 Copyright % 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0191-8869196 $15.00+0.00

BIMODALITY IN THE BERLIN MODEL OF INTELLIGENCE STRUCTURE (BIS): A REPLICATION STUDY Valentin Bucik’* and Aljoscha C. Neubauer’ ‘Departmentof ‘Department

Psychology, of Psychology,

University of Ljubljana, ASkerEeva 2, 1000 Ljubljana, Slovenia and University of Graz, UniversitZitsplatz Z/III. A-8010 Graz, Austria (Received 4 January 1996)

bimodal structure of intelligence as proposed in the ‘Berlin model of intelligence structure’ (BIS) (J%ger, 1982) and measured by the BIS-4 test was analysed in a sample of I82 subjects. According to this theory two modalities characterize the structure, both emerging from results in 45 mental tasks and containing a total of seven components: Operations (processing speed, memory, creativity, processing capacity), and contents (verbal, numerical, figural ability), as well as the general factor (g). Exploratory analysis following Jager’s approach revealed the existence of four operations and three contents. The simultaneous examination of the bimodality in the structure of the BIS was performed by means of confirmatory factor analysis. The theoretically proposed bimodal model (four operations and three contents) was compared with a unimodal model involving seven correlated factors of the same level and with other alternative unimodal models. In these analyses a slight superiority of operations over contents was observed. The reasons for our preference of the bimodal BIS structure compared to other unimodal solutions are clarified and the role of operations and contents in the construct of intelligence is discussed. Copyright 0 1996 Elsevier Science Ltd. Summary-The

INTRODUCTION The researcher studying human cognitive abilities who is interested not only in individual differences in general intelligence, but also in the differential structure of the mental capacity, is confronted with numerous well-known theories of the intelligence structure. These models give an insight into a hierarchically organised construct, intelligence. As Carroll (1993) pointed out, the majority of the models were created as a consequential outcome of the development of exploratory factor analysis, where we try to find latent dimensions in a set of observed variables, which can best account for the variability in the correlation matrix. But the extracted factors are not always clearly interpretable, as they merely represent the successive explanations of the amount of variance remaining in particular steps of extraction. Therefore, we try to reach the so called ‘simple structure’ by means of an orthogonal or oblique rotation of factor axes (Thurstone & Thurstone, 1941), so that each observed variable is highly loaded only on one factor, simultaneously having as low loadings as possible on all other extracted factors. The main feature of most models dealing with the structure of intelligence according to these rules is that the total variance of each observed variable-test, task or item-included in the model is partitioned into a variance explained by at least one general factor, by one group or primary factor, and a variance specific for an observed variable. Different models of the structure of intellect offered distinct solutions in determining the structural part of the intelligence: one ‘general’ and a set of ‘specific’ factors in Spearman’s two-factor model (Spearman, 1927); seven ‘primary’ factors in Thurstone’s model of cognitive abilities (Thurstone, 1938); 120, 150 or more possible independent factors in Guilford’s three-dimensional (‘operations, products, contents’) structure-of-intellect model (Guilford, 1967); one ‘general’ and two ‘major group’ factors, a series of ‘minor group’ factors and numerous ‘specific’ factors in Vernon’s hierarchical model of intelligence (Vernon, 1961); simplex (‘complexity’) and circumplex (‘content’) ordering principles of abilities in Guttman’s radex model of intelligence (Guttman, 1970); eight principal components (‘calculating skills, visual perception, convergent thinking, convergent verbal factor, divergent thinking, divergent verbal factor, associative memory, memory span’) in Pawlik’s hierarchical model (Pawlik, 1982, cited from Jsger, 1984); higher-order and lower-order factors in

*To whom all correspondence

should be addressed. 987

Valentin Bucik and Aljoscha C. Neubauer

988

Al general intelligence

K performances

Figural

Numerical Fig. 1. Jlger’s

M

F

Verbal

B

E

V N

K

Processing speed Memory

Creativity Processing capacity

bimodal model of intelligence structure (B, processing ‘speed; M, memory; E, creativity; processing capacity; F, figural ability; V, verbal ability; N, numerical ability).

K,

the Cattell and Horn hierarchical model of cognitive abilities (Cattell, 1971; Horn, 1985), if we limit the list only to best-known models. However, the Gustafsson’s HILI model (Gustafsson, 1984, 1988), Jensen’s arguments on the nature of g (Jensen, 1986, 1987) and the extensive work of Carroll (1993), pointed to an integrated hierarchical model for intelligence with g at the apex that accommodates many of the views that might have been seen as exclusive. At the beginning of the 1980s Jgger presented his model of the structure of intellect (Jgger, 1982, 1984; see also Jgger, 1973). He declared it a descriptive bimodal hierarchical model, which does not lean on firm theoretical presumptions, the characteristic actually representative for most factoranalytic models. The model, called BIS (Berlin model of intelligence structure), emphasized seven principal, general components or bundles of abilities, inhabited in two modalities, ‘operations’ and ‘contents’. The modalities were conceived as different facets or aspects of classification of various intellectual capabilities. The first one was considered as a group of processes that are taking place while solving the cognitive tasks. It included four classes, ‘processing speed’, ‘memory’, ‘creativity’ and ‘processing capacity’. The content modality comprised the classes of verbal, numerical and figural bundles of abilities, in which operations are being performed. The model is presented in Fig. 1. The seven principal components, which can be gained from the Operations by Contents matrix in the BIS, are described as follows: Operation based components: Processing speed (Bearbeitungsgeschwindigkeit-B): working speed, ease of perception and concentration capacity which are decisive in solving tasks of low difficulty levels. Memory (Merkfghigkeit-M): active storage into short-term memory and recognition or reproduction of verbal, numerical and figural material. Creativity (Einfallsreichtum-E): fluid, flexible and original production of ideas, requiring the availability of diverse information, wealth of imagination and ability to see many different sides, variations, reasons, and possibilities in problem-oriented-not purely imaginative-solutions. Processing capacity (VerarbeitungskapazitHt-K): the processing of complex information in tasks that are not immediately solvable, but rather require the S to establish diverse relations and use exact formal-logical reasoning about relevant problem solving information.

Bimodality

in the BIS

989

Content based components: Figural ability (F): visually based thinking; the ability to understand clearly relations and plasticity in figural material, forms, shapes, patterns in tasks, appertaining to different operations, Verbal ability (V): language based thinking; it plays a role in all groups of tasks in different operations that are linked to language. Numerical ability (N): number based thinking; it plays a role in all groups of tasks in different operations that are linked to numerical material. Therefore, the Ss capacity to process the verbal material is assumed to be determined by both his/her processing capacity (K) and verbal ability (V). As an integral or aggregate of all components, the factor of general intelligence, or g, (AI, Allgemeine Intelligenz) can also be obtained. Jager (1984) points out that other than in Guilford’s structure of intellect model there are no primary constructs or theoretically determined abilities in the cells of the two-dimensional matrix, but multi- (bi-) factorial determined performance-level cognitive capabilities. Regarding their hierarchical level the seven BIS components could be located between Vernon’s primary factors of intelligence and his higher-order factors v : ed (verbal-educational), k : m (practical-mechanical) (Vernon, 1961); or between Cattell’s first-order factors and g, and gc (Cattell, 1971). The BE was presented as the final result of a broad exploratory-inductive research project. Analogous to lexical and taxonomic approaches in some studies of the structure of personality, Jager and his co-workers tried to find a structure of intelligence by applying a large set of cognitive tasks drawn from the research literature on intelligence and creativity. They did not succeed in confirming the expected structure (e.g. Thurstone’s verbal, numeral and spatial classes that were often found in other studies) by using the usual exploratory factor- and cluster-analytic agglomerate technics; furthermore, various alternative factor solutions could not be shown to be clearly and unequivocally interpretable. For that reason Jager chose 48 variables or problems from a large pool of diverse cognitive tasks, each of which was relatively easy to cross-classify regarding the operational and content modalities. In this arrangement each of 48 measured variables could be classified in one of the operation and one of the content-based classes at the same time. Both modalities formed the four by three matrix with 12 cells, each representing the specific intellectual capability and containing four cognitive tasks. The list of tasks within each cell, used by Jager in the former versions of the test for BIS in his original studies (cf. Jager, 1982, p. 218) was rather similar to the list in BIS-4 test presented in Table 1 in the next section of this paper. Jager tried to confirm the bimodal structure in the BIS by extensive analyses in a sample of 545 Berlin secondary school graduates (Jager, 1982). He used the method of aggregation of cognitive tasks over operations or over contents to obtain reliable and valid confirmations of the proposed structure (see also Wittmann, 1988; Wittmann & Matt, 1986). With the aggregation of the standardized results in the tasks (z-scores) over the content modality he separated 16 aggregates, or ‘operation-homogeneous’ results, which have been averaged over verbal, numerical and figural tasks. The factorisation of those 16 scores gave a distinct four-factor solution in which the factors could easily be interpreted as the presupposed operations. By aggregating tasks over the operation modality he obtained 12 ‘content-homogeneous’ aggregates, which-in a subsequent factor analysis-produced three content factors. The method of aggregation of variables therefore allowed a confirmation of the proposed BIS structure. By the side of the successive approach Jager tried to test the stability of the bimodal structure of the BIS also simultaneously via aggregating tasks in the 3 x 4 matrix into eight operation-homogeneous and six content-homogeneous groups. The clear and concise structure of four operation and three content classes emerged from exploratory factorand cluster-analyses, although it was clearly pointed out that a smaller number of measured variables in each aggregate (three and four, respectively) should be considered in making conclusions about the structure. By retesting 347 Ss (from the pool of 545 secondary school graduates tested in the first study) after four years Jager could also demonstrate a high temporal stability of the BIS model (Jager, 1984). In addition, Pfister and Jager (1992) showed the stability of the model in the same sample, using a so-called topographic analysis that determines the correlational structure of BIS items via multidimensional scaling. Schmidt (1984) argued that the elementary presumption of the exploratory factor-analytic tech-

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Valentin Bucik and Aljoscha C. Neubauer

nits, the simple structure as the rotation criterion, is the principal reason why it is difficult to prove the bimodal structure in the Berlin model of intelligence, simultaneously. Instead, he suggested the use of confirmatory factor analysis. First, the theoretically justifiable alternative solutions are needed for confirmatory analysis. Second, this approach enables testing of the goodness of fit of each of these models, so the alternative solutions are directly statistically comparable. Finally, they provide the means for the simultaneous testing of multi-modal solutions, like the BIS model. In Schmidt’s analysis of Jager sample of 545 Ss (1984) he compared the goodness of fit of the bimodal BIS model and three alternative models: (a) a model in which the observed variables or cognitive tasks in the test of BIS would reflect three content-based factors from the BIS structure; (b) a model with four operative components; and (c) a model in which each of the observed variables is attributed to two factors, the ones that showed the highest correlation with the observed variable in the exploratory factor analysis. By means of the latter model Schmidt tried to verify the concurrent value of both the theoretically postulated, confirmatory provable model, and the outcome of the conventional exploratory factor analysis, translated into confirmatory factor analysis terminology. He found that the presumed BIS model is acceptable regarding the goodness of fit indices. Both three-factorial (content-based) and four-factorial (operational) solutions were clearly rejected, with the three-factor model expressing a worse fit to the data than the four-factor model. The bimodal Berlin model and the alternative exploratory seven-factor showed almost equally sufficient metric characteristics as the differences in overall goodness of fit indices were negligible. Yet, Jager’s observation was confirmed that the seven-factor solution, obtained by exploratory factor analysis of the observed variables (Principal axes analysis, Varimax rotation), was very difficult to interpret as a theoretically justifiable structure. Therefore, Schmidt concluded that the BIS model is for essential psychological reasons more expedient for the description of the data than the exploratory unimodal seven-factor model, which is statistically equivalent (Schmidt, 1984). Huldi (1992) reports a validation study of the BIS, in a sample of 521 high school students in Switzerland. A new version of the original test for BIS (BIS-4) was applied. The hypothesised theoretical structure of intelligence was confirmed with different structure-analytic methods (factor analysis and multidimensional scaling). Promising results of the validation studies of the BIS are presumably one of the reasons that the model is recently being used more often in the field of studying the structure of intellect, and especially the relationships between components of cognitive processes. The BIS test was employed in studies investigating the relation of intelligence to other constructs such as complex problem solving or processing capacity (Hormann & Thomas, 1989; Hussy, 1989, 1991; Strohschneider, 1991; Stil3, Oberauer & Kersting, 1993) cognitive strategies (Doll & Mayr, 1987) or working memory (Oberauer, 1993). The model was also used in studies on the relation between mental speed and intelligence (Beauducel & Brocke, 1993; Neubauer & Bucik, 1996) and in assessing creative abilities (Kiinig, 1986). Unfortunately, the test for the Berlin intelligence structure model is only available in the German language and, to our knowledge, there are only two translations and adaptations of the test: A kit of tests for the BIS was translated into Brazilian-Portuguese (Kleine & Jager, 1987, 1989) and Chilean-Spanish (Rosas, 1991). The replications of the BIS model in other cultural and language environments were successful and the differential as well as predictive validity were shown to be satisfactory. However, for the purpose of further validation of the model it would be necessary to have a test for the BIS available at least in the English language, too. The purpose of our study was to check the validity of the bimodality in the Berlin model of intelligence structure in our sample, which was less restricted regarding age and educational level than former validation studies of the BIS. As we used a new, modified test for the BIS (the BIS-4test) we were also interested in its psychometric quality and replicability of the classical BISstructure.

METHOD Subjects A total of 182 respondd:nts participated in the study, 103 females and 79 males, ranging in age from 18 to 54 years (M = 28.93, SD = 8.21). Ss were recruited via an advertisement in a local

Bimodality in the BIS

991

Table 1. The classification of the 45 tasks in the BIS-4 test

zs

Number-symbol test

KW

OE BD

Old English Striking through letters (strike through all ‘x’)

T-G uw

OG

Orientation memory

ST

FM

WM

WE

Memorizing forms (company symbols) Memorizing the path

ZF ZK OJ LO

CH FA BG AN AW

Classification of words (strike through all plants) Part-whole Uncompleted words

XG

For s greater

SI

RZ

Divisive by seven Calculation signs (putting them into equations)

Sensible text (memorizing and reproducing details) Memorizing words

ZP

Memorizing pairs of numbers

zz

PS

Fantasy language (memorizing pairs)

zw

Two-syllable numbers (encoding and reproducing) Number recognition (five-syllable numbers)

Symbol competition

ES

ZR

Symbol combining (as many abstract figures as possible) Object designing (proposed geom. figures + real objects) Layout (creating as many logotypes as possible)

AM

Specdic traits (which a salesman should not have) Possible uses of the object Masselon (three words-many sentences) Insight test (explaining presented social situation)

ZG TN

Inventing telephone numbers (according to logical rules)

Charkov (completing the progressing string of figures) Choosing the geom. figure Bongard (two groups of figulres. each with six patterns) Analogies (figural)

SL

Logical conclusions (syllogisms)

ZN

Numerical senes

TM SV

Facts vs opinions Comparing conclusions (proper conclusions) Word analogies

BR TL

Series of letters Table reading

RD

Vocabulary (one of four words doesn’t belong)

SC

Computation reasoning (simple text tasks) Estimations (calculating on the basis of simple consideration)

Complex unwinding (spatial comprehensiveness)

MA IT

WA ws

DR

Puzzle with numbers (inventing pattern of numbers) Divergent computing (finding equations x + y*z = 60) Equations with numbers

The abbreviations represent the German names of the components and tasks.

newspaper in Graz (Austria), in which they were offered the opportunity to receive information about their IQ and their strengths and weaknesses concerning specific intellectual abilities. Materials andprocedure The test for the BZS (BIS-4). For testing the Ss abilities according to the Berlin model of intelligence structure the most recent BIS-4 test was used.* This modified and adapted test only differs from the former version in the number of mental tasks (the number of tasks in each of 12 cells is not equal) and in that some of the tasks were replaced with newer ones, but the structure of the BIS was assumed to remain unchanged. The test includes a total of 45 tasks as observed variables. Each combination of operations processing speed (B) and memory (M) with three content based components (figural, verbal, and numerical), is measured by means of three tasks, for measurement of creativity (E) there are four tasks for each content based component, and processing capacity (K) is assessed by means of five tasks for each content based component. The names of the tasks and their classification in the operations by contents matrix are shown in Table 1. The test is divided into three test books. in each test book the tasks representing each operation and/or content are balanced. There are strict time limits for all tasks. At the beginning of each task the specific requirements of the following problem are demonstrated in a practice trial. The test administrator performs this training task together with the Ss to avoid misunderstandings. The administration of each test book took about 45 min and there were 10 min breaks between the three test books. The duration of the complete BIS-4 test was about 3 h. The test was administered in groups of maximally 20 Ss. According to the procedure suggested by Jager (I 982, 1984) the scores for all seven components in the BIS-4-test (processing speed, memory, creativity, processing capacity, figural ability, verbal ability, and numerical ability), and for the g-score were computed by means of aggregating normalized z-scores. First, for each of the 45 tasks z-scores were calculated, subsequently a mean z-

*Thanks are due to A. 0. J%ger and A. Beauducel for their permission M. Huldi for providing us with the materials on the test.

to use the BIS-4 test in our study, and to F. Stall and

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Valentin Bucik and Aljoscha C. Neubauer

score for each of 12 cells in the BIS was computed by averaging the z-scores of all tasks in the corresponding cell. Then, mean z-scores for each operational component and each content based component were calculated by averaging the aggregated z-score for the corresponding row or column in the BIS (e.g. the z-score for the figural component was computed by averaging the zscores from the cells in the first column-B-figural, M-figural, E-figural, and K-figural; the z-scores from the memory component was computed by averaging the z-scores from the cells in the second row-M-figural, M-verbal, and M-numerical (cf. Table 1). Finally, a score for general intelligence (AI) was obtained by averaging z-scores from all 12 cells in the BIS. Raven’s Advanced Progressive Matrices. To compare the BIS-4 results with the outcomes of the well-known psychometric intelligence test, we also included Raven’s Advanced Progressive Matrices (APM, Raven, 1958). The test was administered with a 10 min time-limit for Set I and a 20 min time-limit for Set II.*

RESULTS

AND

DISCUSSION

Initial statistics In Table 2 the raw data from the 45 tasks in the BIS-4 are presented: means, standard deviations, minimal and maximal values, skewness and kurtosis with their statistical significance. For reasons of comparison the results from the psychometric study of BIS-4 on the sample of 510 secondary school students in Switzerland (M. Huldi, personal communication, 27 July 1994) can also be found in Table 2. It can be seen from the data that absolute values of variables vary in a broad range. In some tasks the S can reach more than 20 points, while some other tasks have only five to 10 items. For this reason some scores expressed distinct platokurtic distributions. This weakness of some of the BIS-4 tasks will be dealt with later. Regarding the comparison of our Austrian sample with the Swiss sample (CH) the means display a high degree of similarity in both countries. The only exception are some of E tasks. The performance of Ss in one group of these tasks (AM, EF, IT, OJ and ZK) was scored by counting all valid or correct answers and not only the number of preliminary stated categories of answers, which a S expressed in his or her answer, as it was done in the Swiss sample. This led to higher scores on these five tasks in our sample. Aggregated BIS-component scores were obtained via z-transformations, so all seven components and the general-intelligence-score have a mean of 0, while the size of SDS depends largely on the degree of aggregation of z-values of scores in particular tasks that have a mean of 0 and SD of 1. The values showing that there are no significant deviations from normality in the distributions of BIS scores are also presented in Table 2. The scores from Raven’s APM (sum of Set I and Set II) ranged between 11 and 41, and were almost normally distributed-displaying a slight left asymmetry in an expected direction (skewness = - 1.04) with a mean of 30.99 and an SD of 5.64. The intercorrelations of BIS components and their correlations with the APM are shown in Table 3. Operational components should correlate substantially with content based components, because they were aggregated through the same sets of tasks, hence they bear a large amount of common variance. The correlations between operations and contents are, therefore, not presented. The correlations within the content based components and within the operational components are significant. A trend of lower correlations of the memory component with other operational components can be found. Correlations between the BIS components and the APM are substantial and in a remarkable accordance with the results of Beauducel and Brocke (1993). The correlations with the APM in their study conducted on a sample of 72 students were 0.59, 0.51, 0.30, 0.76,0.67, 0.53, 0.59, and 0.71 for B, M, E, K, F, V, N, and AI, respectively. As expected, K and F showed the highest, and M the lowest relation to the APM also in our study. This leads to the conclusion that the APM, like many other tests considered to be good measures ofg, is actually a good measure of KF rather than of general intelligence (‘Allgemeine Intelligenz’) as defined and evaluated in BIS.

* Frearson and Eysenck (1986) reported unpublished min and untimed procedures are highly correlated on relative standing in the APM.

studies by H. J. Eysenck and J. C. Raven which showed that 20, 40 (around 0.93, demonstrating that time limitations have little influence

993

Bimodality in the BIS Table 2. Initial statistics (Mean, SD, Minimum, Maximum, Skewness. Kurtosis, and their statistical significance) of the raw scores in 45 BIS-4 tasks, the aggregated BlS-components and general intelligence Task

Mean

SD

zs

39.96 32.60 52.13 28.92 12.95 31.40 22.51 13.42 12.63 16.87 12.40 18.35 II .53 7.64 11.41 5.91 6.71 4.18 7.59 8.31 6.19 4.12 12.66 8.75 3.14 Il.85 4.47 Il.75 8.02 8.42 3.15 3.09 2.03 3.20 2.54 9.50 9.95 5.04 4.00 7.99 4.14 4.61 3.24 3.20 4.86 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

7.50 6.25 8.18 5.55 3.34 7.79 6.73 4.69 4.45 4.56 3.02 5.68 3.49 2.29 4.36 2.44 2.32 I .79 2.81 2.90 2.68 1.64 4.56 2.81 I .27 3.89 I .99 4.28 3.43 2.85 I .83 1.50 1.19 1.72 I .40 3.66 3.39 2.09 2.21 2.91 2.40 1.99 1.23 I.42 1.73 5.14 5.55 7.43 9.46 8.52 8.57 8.49 22.14

OE BD KW TG UW XC SI RZ OG FM WE ST WM PS ZP zz zw ZF ZK OJ LO ES AM MA IT ZR DR ZG TN CH FA BG AN AW SL TM AV WA ws ZN BR TL RD SC B M E K F V N Al

Min.

Max.

Skew.

Kurt.

Mean CH

21.00 I I .oo 32.00 6.00 0.00 9.00 6.00 3.00 I .oo 2.00 5.00 3.00 2.00 3.00 1.00 0.00 0.00 0.00 2.00 3.00 2.00 1.00 2.00 2.00 0.00 2.00 0.00 3.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 - 16.06 - 16.46 -17.13 -25.77 - 24.23 - 20.40 -21.42 -51.37

61.00 49.00 76.00 43.00 20.00 52.00 40.00 25.00 20.00 26.00 20.00 31.00 21.00 15.00 20.00 12.00 12.00 8.00 18.00 19.00 16.00 10.00 28.00 16.00 6.00 23.00 9.00 27.00 19.00 I7 00 6.00 6.00 5.00 8.00 5.00 16.00 16.00 10.00 14.00 16.00 9.00 8.00 6.00 6.00 7.00 13.36 17.19 21.60 20.54 20.19 22.47 18.80 53.92

0.27 -0.14 0.20 -0.42 -1.14’ -0.34 0.16 0.12 -0.41 -0.55’ 0.12 0.03 0.02 0.26 0.10 0.13 -0.01 0.07 0.78* 0.77* 0.51 0.44 0.54’ 0.29 -0.01 0.36 0.04 0.35 0.30 0.05 -0.23 0.18 0.51 0.05 -0.04 -0.12 -0.29 -0.09 0.42 0.30 0.17 0.11 0.02 -0.00 -0.63’ -0.15 0.14 0.26 -0.23 -0.14 -0.18 -0.24 -0.33

-0.01 0.42 - 0.09 0.88 I .66* 0.20 -0.11 -0.62 -0.28 0.70 -0.32 -0.36 -0.25 -0.07 - 0.63 -0.16 0.37 -0.64’ 0.97 0.69 0.15 0.26 0.35 -0.06 0.11 -0.10 -0.44 0.14 0.41 0.37 -0.91* -0.82’ -0.38 - 0.47 -0.95’ -0.59 -0.53 -0.60 0.91 -0.24 -0.92; -0.66* -0.41 -0.86’ -0.30 -0.31 0.34 0.30 -0.36 -0.22 -049 -0.42 -0.41

36.27 37.16 55.58 29.29 12.50 27.29 23.19 14.20 13.32 17.69 13.38 18.81 10.72 8.54 12.29 6.37 7.09 4.18 5.72 8.50 5.31 5.06 6.35 5.89 3.38 6.94 5.47 13.45 8.29 8.89 3.17 3.23 2.34 3.47 9.43 10.32 9.50 4.61 3.94 7.43 5.52 4.89 3.30 3.32 4.71

*P < 0.01. The last column represents average scores in BIS-4 in Switzerland (Huldi. personal communication, 27 July 1994. see Tables 1 and 3 for the explanation of abbreviations of the names of tasks and components, and text for the explanation of Huldi’s data).

Table 3. lntercorrelatrons of the BlS operations and contents and their correlations APM (all coefficients are statistically significant, P < 0.01)

M E K V N APM

B

M

E

0.51 0.56 0.62

0.41 0.45

0.56

0.49

0.37

0.48

with the

K

F

V

N

Al

0.76

0.67 0.64 0.67

0.68 0.47

0.60

0.66

B, processing speed; M, memory; E. creativity; K, processing capacity; F, figural ability, V. verbal ability: N, numerical ability; Al, general intelligence; N = 182.

994

Valentin Bucik and Aljoscha C. Neubauer Table 4. Rotated factor matrix of 12 aggregated variables: operations by contents cells (PC extraction. four-factor solution. Varimax rotation. loadings >0.50 are highlighted)

BF BV BN MF MV MN EF EV EN KF KV KN % of total “alriance Factor

Fl

F2

F3

F4

h’

0.24 0.11 0.53 0.49 0.05 0.09 0.21 0.10 0.61 0.87 0.56 0.79 22.67 K

0.01 0.27 0.26 0.59 0.75 0.86 0.04 0.23 0.12 -0.01 0.20 0.19 16.15 M

0.28 0.33 -0.02 0.15 0.12 0.13 0.87 0.82 0.48 0.19 0.25 0.1 I 16.73 E

0.74 0.76 0.62 0.01 0.39 0.07 0.14 0.24 0.17 0.10 0.48 0.27 17.37 B

0.68 0.76 0.74 0.61 0.73 0.77 0.82 0.79 0.66 0.79 0.65 0.75 72.92

B, processing speed; M. memory; E, creativity; K, processing capacity; F, figural ability; V, verbal ability; N, numerical ability; h*, communalities from four factors.

The correlation between the APM scores and the first unrotated factor in PCA of scores in 45 BIS4 tasks (Y= 0.71) does not deviate substantially from the correlation between APM score and BISAI in Table 3. It should be pointed out that the advantage of measuring g via BIS-AI compared to other tests for g is not only due to the quantity but also the selection of 45 tasks of great variety. Exploratory

analysis of the structure

In an exploratory investigation of the structure of intelligence we could not uncover a clear and theoretically interpretable seven-factor solution in the set of 45 BIS4 tasks, and the same was true with four- and three- factor solutions. Some tasks could not be linked unequivocally to one of the factors to which they should belong according to their operational and content characteristics. It might be argued that these troubles could be due to the metric shortcomings of some of the tasks in BIS-4. Actually, tasks in BIS-4 should be regraded as items, as for instance in the APM or in other intelligence tests. The first unrotated principal component factor in factoring 45 tasks accounted for 26.5% of the variance. This factor is not very strong in explanation in comparison to other test batteries (e.g. WAIS-R in which g factor emerges clearly). But this could also be a consequence of psychometric problems of some tasks in BIS-4. Consequently, in the next step we performed the exploratory factor analysis on the aggregated data. We calculated 12 aggregated scores from the 12 cells of the operations by contents matrix, where each cell represents a group of tasks, typical for a combination of one operation and one content (e.g. the cell EV is the average of z-scores of the results on the tasks measuring creativity in the verbal domain). Here, the unrotated principal component factor explained 44.6% of the variance. In searching for simple structure, only in the rotated four-factor solution the aggregated variables could be interpreted in accordance to BIS components. The four factors could be recognized as operations, although the structure is not clear. The solution is shown in Table 4. This result conforms to Jager’s observations (Jager, 1982, 1984) when submitting the BIS-4 tasks to factor analysis: The extracted factors primarily reflected the distinction between operations and not that of contents. We followed Jager’s deduction that if operation-specific variance is stronger and we want to get homogeneous information with respect to contents, it is necessary to suppress operation-specific variance by means of aggregating the BIS-4 tasks over operations but within contents. Similarly vice versa, if we want to have a clear picture of the operations, then content-specific variance should be suppressed by aggregating the tasks over contents and within operations. The procedure of aggregating the tasks in the BIS4 over contents to obtain the operationhomogeneous parcels is shown in Fig. 2. The factorization of operation-homogeneous aggregated variables gave a distinct four-factor solution, with each group of operational variables encompassing a distinct factor. The rotated factor

Bimodality in the BIS F

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matrix is shown in Table 5. This result, which is similar to findings in Jager’s above mentioned studies, shows that if we suppress content specific variance the four operations emerge clearly. The hierarchy of the power of explanation of four operational components (in order: K, E, M, and B) shows that processing capacity (K) seems to play a slightly more important role in the BIS structure than other components although the differences are rather small. It can be seen from the factor matrix in Table 5, that, in spite of the fact that the variables included in the analysis are aggregated over contents, there are some loadings that do not conform to the expected simple structure. Table 5. Rotated factor matrix of the IS operation-homogeneous variables (PC extraction, Varimax rotation, loadings >0.50 are highlighted; the first unrotated principal factor explained 48.1% of variance, the portions of other extracted factors were 10.4, 9.5 and 6.7%) Factor Variable BOPI BOP2 BOP3 MOP1 MOP2 MOP3 EOPI EOP2 EOP3 EOP4 KOPI KOP2 KOP3 KOP4 KOP5 % of total variance Factor

Fl

F2

F3

F4

h’

0.21 0.22 0.43 0.25 0.18 0.09 0.18 0.27 0.17 0.26 0.81 0.77 0.76 0.78 0.74 23.84 K

0.17 0.20 0.26 0.03 0.13 0.24 0.82 0.73 0.71 0.83 0.18 0.20 0.11 0.27 0.30 19.00 E

0.14 0.28 0.21 0.82 0.83 0.80 0.09 0.11 0.29 0. IO 0.18 0.14 0.17 0.20 0.12 16.11 M

0.83 0.79 0.69 0.26 0.11 0.17 0.13 0.35 0.28 0.08 0.25 0.25 0.23 0.15 0.17 15.84 B

0.79 0.80 0.78 0.81 0.76 0.74 0.72 0.75 0.69 0.77 0.79 0.71 0.68 0.75 0.68 74.79

B, processing speed; M, memory; E. creativity; communalities from four factors.

K, processing

capacity;

h’.

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Valentin Bucik and Aljoscha C. Neubauer

I

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The procedure of gaining the content-homogeneous cells by aggregating the BIS4 tasks over operations is shown in Fig. 3, and the clear three factor solution, showing three content based factors, is presented in Table 6. There are no distinctive differences between the portions of explained variance from the F, V and N factors. Compared to Jager’s results (1984) we obtained a larger explanatory power of components (Jager obtained 21.9,20.7 and 23.2% of explained variance for F, V and N components, respectively). This is an encouraging resuit especially with respect to the fact that the sample in our study was smaller (182 vs 545) and that our sample was more heterogeneous regarding age as well as educational level. Confirmatory

analysis of the structure

Exploratory analysis of the structure of intelligence in our sample produced results quite similar to those of other studies analysing the structure of intelligence with the original version of the BIS test (Jager, 1982, 1984; Kleine & Jager, 1987, 1989; Pfister & Jager, 1992). However, Schmidt (1984) argued that exploratory factor analytic techniques are inappropriate for examining bimodality in a

Table 6. Rotated factor matrix of the content-homogeneous variables (PC extraction, Varimax rotation, loadings >0.50 are highlighted; the first unrotated principal component factor explained 61.4% of variance, the portions of other extracted factors were 10.2 and 8.2%) Factor variable FCOI FC02 FC03 VCOI vco2 vco3 NC01 NC02 NC03 % of total \i,ariance Factor

Fl

F2

F3

h’

0.75 0.80 0.86 0.28 0.38 0.24 0.25 0.16 0.48 24.48 F

0.32 0.25 0.25 0.80 0.76 0.82 0.22 0.40 0.31 28.33 V

0.21 0.27 0.22 0.31 0.23 0.3 I 0.86 0.78 0.66 26.97 N

0.72 0.78 0.86 0.82 0.71 0.82 0.85 0.79 0.77 79.78

F, figural ability; V, verbal ability; N. numerical nalities from three factors,

ability; h’ commu-

Bimodality in the BIS

997

structure of intelligence simultaneously, where each variable could be significantly loaded on more than one factor. The main idea behind exploratory factor analysis is that by means of rotation we are trying to find a simple structure with a high loading of each variable on only one factor and as small loadings as possible on all other factors. On the other hand, if we don’t search for a simple structure, and if we, therefore, omit rotation of the axes, we usually do not get a clear insight into the structure at all. Tables 5 and 6 indicate slight difficulties in obtaining the simple structure with the exploratory analyses: Certain portions of the variance in a structure can not be located clearly in the three- or four-factor solutions. The shortcomings of the exploratory approach can be easily over-ridden by means of confirmatory procedures where an analysis of multi-modal structures is possible. In addition, the goodness of fit of each of the proposed solutions can be statistically determined; different models may differ in their rate of the explained variance although they have the same factor measurement and structural loadings. The development of a structure can be investigated hierarchically by comparing the goodness of fit of the ‘nested’ models (i.e. the models that have the same input data matrix and where the group of free parameters of a more restricted model is a subgroup (or subset) of free parameters of a less restrictive model: one model is nested in another model, if this is the same model with one or more additionally fixed parameters). With this approach a structure can be improved by releasing particular restrictions or including additional factors in the model. Following Schmidt’s (1984) analysis of the BIS we tried to check the goodness of fit of the theoretically proposed bimodal BIS model compared to other possible models that could be a priori postulated or built according to exploratory analysis. Starting with the variancecovariance matrix of results in 45 tasks of the BIS-4, we tested seven alternative models of intelligence structure by means of confirmatory factor analysis (with the maximum likelihood method for estimation of parameters), provided by the LISREL 8 program (Jiireskog & Siirbom, 1993): Model 1: The original theoretical model proposed by Jager (1984). In this model seven structural factors were proposed (four operations and three contents). All factors were of the same hierarchical level, with each manifest variable reflecting two of the factors, according to the theoretical presumptions (one operational component and one content based component). The correlations between the seven components were set to be free. Model 2: A model with 45 manifest variables reflecting four inter-related operational components. Each variable was assumed to have a loading in only one of the operations according to the BIS model. Model 3: A model with 45 manifest variables reflecting three inter-related content based components with each variable representing only one content in the BIS model. Model 4: The basis of this alternative unimodal model was the exploratory analysis (PC, Varimax rotation) of the 45 manifest variables with seven factors extracted. The two highest loadings of each variable, representing the reflectance of two factors were set to be free, no matter how high these two loadings were. All other paths between the manifest variables and factors were fixed at level 0. This model was actually an outcome of exploratory analysis transformed in a confirmatory LISREL model, based on the presumption that 45 tasks reflect seven unimodal factors, and satisfying the condition that each task represents two factors as it is assumed in the BIS (the factor matrix is presented in Appendix A). Modef 5: The difference between this model and Model 4 was in the method of factor rotation. Considering the nature of the phenomena measured with 45 tasks it seemed a reasonable decision to examine the structure, in which latent components were allowed to correlate with each other. A PC analysis with Oblimin rotation served as the basis for this model. All other conditions remained the same as in Model 4 (the factor matrix is shown in Appendix B). Model 6: This was an alternative unimodal exploratory model, differing from Model 4 in the way the paths between manifest variables and constructs were established. Exploratory factor analysis (PC, Varimax rotation) with seven factors extracted was performed with the additional criterion that only loadings greater than 0.35 were taken into account to avoid possible artifactual paths between latent and manifest variables. Consequently, each task could have had the theoretical chance to reflect nil to seven factors. As was shown in the analysis, most tasks had loadings higher than 0.35 on one or two factors. These paths from factors to variables in the model were allowed to be free, all others were fixed at zero. The constraint, present in the BIS model and also in Models

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Bucik and Aljoscha

C. Neubauer

Table 7. Overall goodness-of-fit indices of seven alternative confirmatory factor analytic models. and the null model. including 45 BE-4 tasks as manifest variables (see text for the explanation of the models) Model Model Model Model Model Model Model Model Model

0 I 2 3 4 5 6 7

XT

d.f.

P

3962.70 894.32 1605.38 2031.41 896.28 902.23 I41 1.48 1162.41

990 879 939 942 879 879 913 885

0.00 0.35 0.00 0.00 0.34 0.29 0.00 0.00

AGFI

RMSR

0.21 0.74 0.65 0.56 0.74 0.74 0.71 0.76

0.26 0.09 0.08 0.09 0.19 0.14 0.08 0.07

NFI

0.94 0.59 0.49 0.94 0.94 0.64 0.71

NNFI

1.00 0.76 0.61 1.00 1.00 0.82 0.90

X1ld.f. 4.00 I .02 I.71 2.16 I .02 I .a3 1.55 I.31

&VI’ 22.39 6.66 9.93 12.25 6.68 6.71 9.15 8.08

d.f., degrees of freedom; P. probability of error in rejecting the model; AGFI. adjusted goodness-of-fit index; RMSR, root means square residual; NFI. normed fit index; NNFI nonormed fit index: X2,/d.f., the ratio between XI and degrees of freedom; eCV1, expected cross-validation index. * CVI for saturated model = Il.44

4 and 5, that each variable should reflect exactly two factors, is therefore not implemented in this model (see Appendix A for factor loadings used). Model 7: Similarly to the relation between the Models 4 and 5, this model differs from Model 6 only with respect to factor rotation (Oblimin). The loadings over 0.35 were set to be free (see Appendix B). For estimating the overall fit of alternative models to our data, different indices were used, namely x2 and its statistical significance and the X’/d.f. ratio (the closer to one the better, Bollen, 1989), adjusted goodness of fit index (AGFI) and root mean square residual (RMSR) (Jdreskog & Siirbom, 1993), the normed fit index (NFI) and non-normed fit index (NNFI) (Bentler & Bonett, 1980; Tucker & Lewis, 1973) and expected cross-validation index (eCVI), where the best of the alternative models is the one that has the lowest eCV1, relative to other models, including the null model and the fully saturated model (Brown & Cudeck, 1989, 1992). For the purposes of calculation of some indices based on ratio between the fit indices (usually x2) in the target and an initial model (NFI and NNFI), the latter model (called ‘null model’ in which the fitted population covariance matrix is diagonal, Bentler & Bonett, 1980) was also estimated. In our null model each variable represented an independent factor, no relations between observed variables or between latent variables were set free, and no correlation between errors of measurement were allowed. The summary of overall goodness of fit statistics in the alternative models is presented in Table 7. Regarding the indices shown in Table 7 the fit of Model 1 to the data is good, so the theoretically proposed BIS model can be accepted as appropriate with reasonably high confidence. All indices of overall fit show that relations between manifest and latent variables explain the variability in the analysed structure, hypothesized as the BIS model, in a sufficient way. The estimates of fit of the models where the structure of intelligence would encompass only four operations (Model 2) or three contents (Model 3) show that both solutions must clearly be rejected. The possibility of making an error by rejecting the model is less than 1% according to x2 statistics and degrees of freedom. Other indices lead to the same conclusion. Although the RMSR is low, which means that not much variability has been left unexplained in the models, AGFI, NFI and NNFI are not suficiently high. In Model 3 the eCVI is even greater than the CVI in the saturated model (cf. Table 7). The rejection of Models 2 and 3 is in strong accordance with our results in the exploratory analysis and also with results from Jager’s (1982, 1984) and Schmidt’s (1984) analyses, where the BIS model showed significantly better fit, too. However, an important difference between Models 2 and 3 must be distinctly pointed out: Regardless of the poor fit of both models to the data it can be said that the ‘operations’ Model 2 did not perform as ‘badly’ as the ‘contents’ Model 3. One should recall that Jager, too, did not obtain the distinct content based components of the structure until he aggregated tasks over operations (Jager, 1984). The goodness of fit of Model 4 is almost the same as that of Model 1. Interestingly, Schmidt ( 1984) obtained a surprisingly similar outcome. As was mentioned in the above discussion, it is very difficult to interpret the relations between the tasks and factors in the exploratory factor analysis of the unimodal seven-factor model, where each of the manifest variables reflects two factors. The reader can get an impression of these difficulties by looking at the factor loadings matrix in Appendix

Bimodality Table 8. Overall goodness-of-fit with 12 BIS-4 parcels aggregated

Model Model Model Model Model

0

I 2 3 4

d.f.

P

1058.77 21.32 220.50 303.10 25.44

66 21 48 51 21

0.00 0.44 0.00 0.00 0.23

* CVI for saturated

999

indices of four alternative confirmatory factor analytic models, and the null model, from tasks. as manifest variables (see text for the explanatton of the models and Table 7 for the description of indices)

X2

Model

in the BIS

AGFI

RMSR

0.23 0.94 0.69 0.65 0.91

0.38 0.02 0.08 0.09 0.02

NFI

0.98 0.79 0.71 0.99

NNFI

X’/d.f.

eCVI*

I .oo 0.76 0.69 0.99

16.04 I.01 4.59 5.94 I.21

5.98 0.75 1.55 I .97 0.77

model = 0.86.

A. In spite of the fact that the model represents a solution as statistically acceptable as the BIS model, the inadequacy of the model to distinguish the contents on one side and unequivocal structure of Model 1 on the other side favours the theoretically grounded descriptive BIS model as proposed by Jager. In Table 7 only one meaningful difference in the goodness of fit between Model 1 and Model 4 can be observed, namely the difference in RMSR. It is reasonable to conclude that a larger residual in the variability of the latter model could be attributed to some artificial paths in the model-note that the model required the relation of each variable to two components regardless of the actual height of the two highest loadings in the factor matrix on the exploratory factor-analysis. Overall goodness of fit statistics in Models, 5,6, and 7 shows that neither different rotation methods in exploratory analyses nor the more exact establishment of the connections between the manifest and latent variables obtained with exploratory factor analysis help improve the goodness of fit of the model to the available data. Summarizing, these analyses demonstrated that different approaches involving unimodal structures do not contribute to the explanation of the covariance structure. Therefore, the bimodal structure as proposed in the BIS seems to be the most appropriate solution. Finally, we performed similar confirmatory analyses of the structure of intelligence with aggregated scores. We used 12 standardized scores instead of 45 tasks as the observed variables in the model. Each of these scores represented the average of the results on three, four or five tasks in the particular cell in the two-dimensional matrix of operations and contents with 12 cells (cf. Figure 1 and Table 1). Each of the manifest variables was therefore an aggregate of tasks representing a particular operation in a particular content (e.g. the aggregate BV delineated the standardized averaged scores in tasks measuring processing speed in verbal material). There were two major reasons for this decision. First, the psychometric shortcomings of some BIS4 tasks (departures of distributions from normality. Mostly because of the small numbers of items in some tasks, cf. Table 2) resulted in lower reliability and consequently in difficulties in regarding them as members of particular structural components in different models. We presumed that aggregation of the results of the tasks in each of the 12 BIS cells would overcome these shortcomings. Second, the number of Ss included in our analysis seemed to be rather small regarding the number of input variables and the number of parameters that had to be estimated in the models. Studies evaluating the problem of sample size in covariance structures analysis (Bollen, 1989; Cudeck & Henly, 199 1; Marsh, Balla & McDonald, 1988; Tanaka, 1987) claim that overall goodness of fit indices, with few exceptions, are generally affected by the sample size. It is not easy, however, to determine the proper sample size for a certain model. This is especially true for more complex models, where stricter researchers advocate the classical rules in the multivariate analysis, in which the sample size should equal 10 times the number of input variables or five times the number of free parameters in the model, if the distributions of input variables do not depart significantly from normality. The outcome of the additional confirmatory analysis of alternative models is presented in Table 8. It should be noted that the principles of building the models were exactly the same as in the confirmatory analysis shown in Table 7, with the only exception being that here 12 cells, aggregated from three to five tasks in each cell, instead of 45 initial tasks, were used as observed variables. We estimated only the first four target models (and a null model), and decided from the outcome of this analysis that no further substantial information would be gained by testing the additional exploratory based Models 5, 6 and 7. Descriptive statistics of the 12 aggregated scores as input variables showed no significant departures from normality. The results are almost identical to those in Table 7 in all four models. The structure in Model 1

Valentin Bucik and Aljoscha C. Neubauer

Fig. 4. Parameter

estimates

and associations among the constructs in the BIS model. The diagram Model 1 (see text for explanation).

from

was even more definitely confirmed, presumably because of more stable psychometric properties of the aggregated observed variables. The parameter estimates and associations among the latent variable in Model 1, let us call it the final model, are presented in Fig. 4. As has been confirmed in previous steps, here also the parameter estimates show stronger relations of the manifest variables with operations than with contents. The present models all include only the first-order latent factors. In addition, some other models were being tested, particularly hierarchical models with factors of higher order, but still in the framework of the BIS model. In the present context it is, however, difficult to present them in extensa, so we will shortly comment only on the three most relevant ones. In the first model, manifest variables, 12 cells in BIS, reflected seven constructs (operations and contents) as the first-order factors, as in Model 1. An additional, second-order g factor was added to account for the intercorrelations among the first-order factors. The overall fit of the model was not very good (x2 = 59.68, d.f. = 28, P < 0.00). In the second model two second-order factors (operations and contents) were introduced to account for the intercorrelations among two groups of seven first-order factors (B, M, E, K, and F, V, N). The goodness-of-fit test for this model showed better fit (x2 = 32.41, d.f. = 27, P -c0.22; the difference in x2 was 27.27, which is highly significant). But the difference in overall fit statistics between this model and Model 1 shows that the latter still fits the data better (x2 = 11.09, d.f. = 6, P < 0.07). The third model was the modification of the second model in the way that a third-order g factor was added to explain the intercorrelations among the second-order factors. The model did not perform as well as the previous one, but was still acceptable according to its overall fit statistics (x2 = 43.47, d.f. = 3 1, P < 0.07, the difference in x2 regarding the second model was 11.06, d.f. = 4, P < 0.05, the difference compared to Model 1 was 22.15, d.f. = 10, P < 0.05). These results show that the hierarchical structure of intelligence as proposed by BIS and as expressed in additional three models was adequately confirmed according to overall fit statistics.

Bimodality in the BIS

1001

But they also declare that the bimodal hierarchical model with each manifest variable loaded on each of two modalities seems to remain the most appropriate way to describe the structure of intelligence as being measured by BE-4 test and that more complex hierarchical models do not contribute significantly to the explanation of the structure.

CONCLUSIONS The data in our study show that the modified version of the test for the BIS (BIS-4) confirms the bimodal structure of intelligence as proposed by Jager and his co-workers, at least as well as the original version of the test. Again, it was shown in the exploratory analysis that the unimodal sevenfactor solution fails to simultaneously explain the structure. The solution was shown to be unclear and difficult to interpret. Only aggregation of the scores over operations gave information of three content based components (figural, verbal and numerical ability), and the aggregation over contents gave the four factor solution with operations processing speed, memory, creativity and processing capacity. On this basis it can be concluded that the structure of intellect as measured by the BE-4 consists of two dimensions, operations and contents, and that both dimensions should be analysed simultaneously. Models with only three content based or only four operation based latent variables left too much unexplained variance and therefore could not be accepted. The confirmatory analysis also showed that the bimodal BIS is an appropriate model of the structure of intelligence, regardless of the fact that both the BIS model and a model based on exploratory analysis can be accepted with a similar (and very low) percentage of risk. The reason is that the alternative seven-factor models, as in the exploratory analysis, give no grounds for a theoretically meaningful interpretation of the obtained structure, which is in accordance with Jager’s and Schmidt’s conclusions (Jager, 1982, 1984; Schmidt, 1984). The only distinction is that we obtained greater differences between the importance of the operation and the content components. However, it should be noted here, that the operative factors were not always shown to be stronger in explaining the variance than the content factors. In studies including apprentices as Ss Schmidt (1986) ascertained that factors N and V were similarly strong in explaining the variance as operations. Therefore at least one part of the difference in the power of explanation of total variance between operations and contents should be attributed to the educational level of the particular (sub) populations, resulting in a reduced N and V variance in highly educated Ss. The concurrent validity of the AI factor in the BIS as the final aggregate of standardized results on all tasks is satisfactory. Its correlation with the score in the APM is high. It is clear from the results, however, that the processing capacity (K) among operations and figural ability (F) among contents share the largest amount of common variance with the APM, which seems logical considering the nature of the tasks in this test. Small differences in correlations between particular operations and contents mean that specific contents do not radically influence the performance of different Ss on different operations and that there is a certain amount of generality in the processes (operations) regardless of different contents. This is in accordance with the results in a study examining the generality of the mental speed-intelligence relationship (Neubauer & Bucik, 1996). The authors of the BIS do not consider it simply one of the many alternative structural models of intelligence. Jager (1984) pointed out the following important principles of construction and application of the BIS model, which demonstrate its universality, generality and temporal stability: it tries to include a diversity of intellectual abilities; it provides good methodological tests of reliability of the structure through parallel use of different analytical procedures on sets of manifest variables and on different representative samples; it assumes the differentiation between levels of generality, the concept of hierarchy, on one side and between empirically confirmed modalities on the other side; it is open to theoretically inspired and empirically founded modifications and extensions. The present study could be placed in the row of successful attempts to confirm the stability of the structure in this model. Research evidence also shows that cognitive abilities measured by tests that appertain to some other theoretical models can be classified according to the BIS. Schmidt (1993) cross-classified Thurstone’s original tests of primary mental abilities into the operative and content components of the BIS, aggregated them accordingly to Jager’s technique, and formed several bundles of either

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Valentin Bucik and Aljoscha C. Neubauer

operative or content homogeneous subscales. Factor analysis of these subscales revealed the components postulated by the BIS in Thurstone’s data. Regarding Thurstone’s model of primary mental abilities the BIS was shown to be the model with the higher degree of generality. In another study, a reanalysis of the data collected with the Kit of Reference Tests for Cognitive Factors was made by Jager and Tesch-Romer (1988) to verify the generality and universality of the BIS model. Results demonstrated that the BIS model could adequately describe the data obtained from the test batteries developed on the basis of other models. Regarding these promising results for the Berlin model of intelligence structure, future research efforts towards a further validation of the structure of intellect according to the BIS model seem worthwhile. These should include a comparative investigation of its convergent validity regarding other well-known and established theoretical models of the structure of intelligence. Acknorvledgements-This research was partially supported by the Slovenian Ministry of Science and Technology for the project ‘Speed of information processing as the basis of the hierarchical structure of intelligence’ (no. 55-6261-0581-94). by a fellowship granted to the first author by the Rector’s Conference of the ARGE Alps-Adria, and by the help of the Austrian Institute for Eastern and Southern Europe. We are grateful to Adolf 0. Jager and an anonymous reviewer for their insightful comments and suggestions in an earlier version of this report. We also wish to thank Petra Eppich, Gerda Klopf and Elsbeth Sitzwohl for their help in collecting the data. Portions of this paper were presented at the 3rd European Conference on Psychological Assessment, Trier, Germany, August 27-30, 1995.

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(For Appendices see ocerleaf)

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Valentin Bucik and Aljoscha C. Neubauer APPENDIX A Factor matrix of the BIS-4 tasks as the basis for Models 4 and 6 (PC extraction, Varimax rotation). Two highest loadings for each mamfest variable are highlighted. loadings used in Model 6 are italicised (see Table I for the explanation of abbreviattons of the names of tasks)

ZS OE BD OG FM WE ZF ZK OJ LO CH FA BG AN AW KW TG UW ST WM PS EF AM MA IT SL TM sv WA ws XG SI RZ ZP zz zw ZR DR ZG TN ZN BR TL RD SC

FI

F2

F3

F4

F5

F6

Fl

0.32 0.19 0.19 0.34 0.39 0.38 -0.01 0.22 0.21 0.26 0.75 0.68 0.61 0.72 0.78 -0.18 0.21 0.07 0.03 0.01 -0.13 0.03 0.17 -0.14 0.03 0.39 0.25 0.22 0.42 0.22 0.14 - 0.06 0.60 0.10 -0.16 0.05 0.37 0.23 0.18 0.39 0.32 0.54 0.38 0.34 0.51

-0.22 0.08 0.04 0.23 0.02 0.30 0.01 0.45 0.07 0.05 0.01 0.05 0.07 0.03 0.04 -0.11 0.02 0.11 0.20 -0.32 -0.17 0.06 -0.18 0.23 0.03 0.05 0.09 -0.02 -0.02 -0.12 0.15 -0.04 0.04 0.06 0.43 -0.14 0.47 0.04 0.39 0.16 0.39 0.09 0.05 0.01 -0.05

0.14 0.13 0.14 -0.07 0.06 0.09 0.56 0.51 0.68 0.70 0.06 0.02 0.06 0.18 0.16 0.26 0.22 0.17 0.00 0.19 0.20 0.71 0.69 0.48 0.62 0.14 0.20 0.00 0.28 0.25 -0.05 -0.02 0.14 0.04 0.04 0.24 0.21 0.30 0.28 0.50 0.09 0.13 0.10 0.09 0.14

0.18 0.06 0.08 - 0.08 - 0.09 -0.13 -0.11 0.06 0.05 0.01 0.18 0.12 -0.02 0.06 -0.07 0.29 0.18 0.39 0.13 0.1 I 0.17 0.06 0.15 0.06 -0.04 0.20 0.19 0.20 0.03 0.06 0.69 0.67 0.28 0.18 0.09 0.31 0.32 0.54 0.35 0.15 0.36 0.19 0.49 0.45 0.4 I

0.43 0.75 0.76 0.18 0.23 0.10 0.19 0.36 0.15 0.1 I 0.13 0.09 0.07 0.1 I 0.08 0.56 0.55 0.30 0.22 -0.02 0.13 0.04 0.10 0.18 0.16 0.17 0.24 0.12 0.16 0.21 0.29 0.18 0.26 0.05 -0.02 -0.02 0.04 0.09 0.13 - 0.03 -0.10 0.05 0.02 -0.15 0.00

0.09 0.07 0.03 0.43 0.58 0.50 0.00 -0.03 0.18 -0.01 0.07 -0.04 0.12 0.07 -0.00 0.14 0.28 0.17 0.58 0.52 0.58 0.14 0.03 0.22 0.19 0.40 0.04 0.06 0.15 0.23 0.11 0.22 0.18 0.73 0.50 0.62 -0.03 0.19 0.08 -0.00 0.16 0.20 0.04 0.06 -0.00

0.16 0.14 0.03 0.21 0.07 -0.10 -0.12 0.03 0.03 0.08 0.18 - 0.03 0.14 0.22 -0.01 0.15 0.13 0.16 0.33 0.34 0.31 0.23 0.02 0.38 0.23 0.66 0.51 0.55 0.52 0.36 0.12 0.09 0.27 0.00 0.16 -0.23 0.03 0.11 0.06 -0.10 0.37 0.39 0.28 0.18 0.15

Bimodality

in the BIS

1005

APPENDIX B Factor matrix of the BIS-4 tasks as the basis for Models 5 and 7 (PC extraction, Oblimin rotation). Two highest loadings for each manifest variable are highlighted, loadings used in Model 7 are italicised (see Table I for the explanation of abbreviations of the names of tasks)

zs OE BD OG FM WE ZF ZK OJ LO CH FA BG AN AW KW TG uw ST WM PS EF AM MA IT SL TM sv WA ws XG Sl RZ ZP zz zw ZR DR ZG TN ZN BR TL RD SC

Fl

F2

F3

0.29 0.29 0.19 0.32 0.20 0.04 -0.06 0.23 0.18 0.22 0.42 0.19 0.32 0.45 0.21 0.20 0.29 0.28 0.39 0.31 0.29 0.31 0.14 0.41 0.30 0.79 0.63 0.62 0.65 0.44 0.30 0.18 0.51 0.07 0.17 -0.14 0.25 0.29 0.24 0.09 0.53 0.51 0.45 0.32 0.34

-0.33 -0.20 -0.20 -0.31 -0.38 -0.36 -0.01 -0.22 -0.24 -0.28 -0.74 -0.67 -0.60 0.71 -0.78 0.16 -0.22 -0.07 -0.01 -0.02 0.12 -0.05 -0.21 0 I4 -0.04 -0.37 - 0.23 -0.20 - 0.42 -0.23 -0.13 0.05 -0.60 -0.10 0.19 -0.08 -0.35 -0.24 -0.17 -0.40 -0.29 -0.52 -0.37 -0.33 -0.52

-0.25 -0.27 -0.27 -0.07 -0.22 -0.22 - 0.56 -0.61 -0.75 -0.74 -0.21 -0.13 -0.19 -0.32 -0.28 -0.32 -0.36 -0.27 -0.14 -0.24 -0.27 -0.74 -0.71 -0.54 -0.67 - 0.28 -0.31 -0.10 -0.41 -0.34 -0.06 -0.03 -0.31 -0.16 -0.12 -0.30 -0.32 -0.39 -0.37 -0.55 -0.21 -0.28 -0.20 -0.16 -0.24

F4 0.08 0.22 0.16 0.57 0.60 0.63 0.03 0.27 0.27 0.09 0.21 0.09 0.26 0.23 0.15 0.1 I 0.36 0.26 0.65 0.34 0.45 0.21 0.00 0.36 0.25 0.22 0.21 0.15 0.27 0.25 0.22 0.17 0.33 0.68 0.62 0.44 0.26 0.24 0.30 0.13 0.41 0.35 0.15 0.1 I 0.06

F5

F6

F7

0.53 -0.78 -0.79 -0.25 -0.34 -0.17 -0.02 -0.43 -0.30 -0.24 -0.26 -0.17 -0.17 -0.25 -0.17 -0.63 -0.65 -4.31 -0.33 -0.13 -0.27 -0.20 -0.25 -0.30 -0.29 -0.32 -0.36 -0.23 -0.32 -0.35 -0.39 -0.28 -0.42 -0.18 -0.03 -0.12 -0.13 -0.26 -0.22 - 0.08 -0.02 -0.20 -0.16 0.01 -0.14

- 0.22 0.03 0.04 -0.04 0.27 0.01 0.24 0.39 -0.05 0.04 0.01 0.14 0.03 0.01 0.12 -0.22 -0.14 -0.04 -0.22 -0.63 -0.55 - 0.09 -0.17 -0.03 -0.14 -0.07 -0.02 -0 I4 -0.15 - 0.28 0.01 -0.21 -0.06 -0.36 0.00 -0.44 0.40 -0.10 0.24 0.17 0.16 -0.06 -0.02 -0.05 - 0.03

0.27 0.16 0.16 0.10 0.10 0.06 -0.04 0.21 0.22 0.15 0.36 0.24 0.14 0.25 0.09 0.31 0.31 0.47 0.30 0.22 0.28 0.21 0.25 0 I9 0.10 0.37 0.33 0.30 0.23 0.20 0.73 0.67 0.47 0.34 0.21 0.41 0.45 0.65 0.46 0.28 0.52 0.39 0.59 0.53 0.51