A factor analysis of the most frequently used Korean personality trait adjectives

We tested the cross‐cultural generalizability of personality structure by factor‐analysing self‐ratings of 435 Korean university students on the 406 most frequently used Korean personality trait adjectives. A plot of eigenvalues and a test of factor replicability both suggested a four‐factor solution. The four varimax‐rotated factors showed strong correlations with the first four factors of the Big Five (Extraversion, Agreeableness, Conscientiousness, and Emotional Stability), as measured by markers selected a priori from the pool of 406 adjectives. We also investigated a five‐factor solution, in an attempt to recover an Intellect factor. The five varimax‐rotated factors corresponded closely to the classic Big Five, but with a minor difference in the rotation of the Conscientiousness and Intellect factors. Solutions involving six and seven factors were also investigated, and these solutions produced a Truthfulness factor similar to some previously discovered lexical factors. The results of the study were discussed in relation to the lexical hypothesis and to previous studies of personality structure in East Asian languages. Copyright © 1999 John Wiley & Sons, Ltd.     

Tandem criteria for analytic rotation in factor analysis

Two related orthogonal analytic rotation criteria for factor analysis are proposed. Criterion I is based upon the principle that variables which appear on the same factor should be correlated. Criterion II is based upon the principle that variables which are uncorrelated should not appear on the same factor. The recommended procedure is to rotate first by criterion I, eliminate the minor factors, and then rerotate the remaining major factors by criterion II. An example is presented in which this procedure produced a rotational solution very close to expectations whereas a varimax solution exhibited certain distortions. A computer program is provided.     

A note on the discovery of ag factor by means of Thurstone's centroid method of analysis

A fictitious factor matrix including 16 tests and 3 factors, one of which was ag factor, was prescribed. From it two typical factor problems, including errors of sampling, were derived. Students in training, without awareness of the factor patterns, arrived at essentially correct solutions by the use of Thurstone's centroid method with rotation of axes. Errors in the calculated factor matrix were very close in size to the sampling errors in the correlation coefficients. It is concluded that ag factor need not escape detection by Thurstone's procedures if the criteria of complete simple structure are not demanded.     

Application of the quartimax method of rotation to Thurstone's primary mental abilities study

This study compares a quartimax rotation of the centroid factor loadings for Thurstone's Primary Mental Abilities Test Battery with factorings of the same correlation matrix by Thurstone (simple structure), Zimmerman (revised simple structure), Holzinger and Harman (bi-factor analysis), and Eysenck (group factor analysis). The quartimax results agree very closely with the solutions of Holzinger and Harman and of Eysenck, and reasonably well with the two simple structure analyses. The principal difference is the general factor provided by the quartimax solution. Reproduction of the factorial structure is sufficiently good to justify its use at least as the first stage of rotation. More extensive trial of the method will be needed with more varied data before it will be possible to decide whether quartimax factors meet psychological requirements sufficiently well without further rotation.We wish to thank Professor L. G. Henyey and the University of California Computer Center for making the IBM 701 electronic computer available for this study, and the National Science Foundation for its support of the work of the Computer Center. Professor H. F. Kaiser of the University of Illinois has made helpful criticisms of the paper, and Mr. Louis S. Davis of the University of California has assisted with preparation of the tables. The research was supported in part by the United States Air Force under Contract No. AF 33 (038)-25726 monitored by the Air Force Personnel and Training Research Center. Permission is granted for reproduction, translation, publication, use and disposal in whole and in part by or for the United States Government.A 701 program for calculation of the quartimax and varimax loadings, prepared by Professor H. F. Kaiser, is available in the library of computer programs held by the Computer Center at the University of California (Program No. 464). Mr. J. O. Neuhaus and Mr. K. W. Dickman have prepared a quartimax program for Illiac at the University of Illinois. This Illiac program will be usable on three other computers recently built or under construction: Mistic (Michigan State University), Silliac (University of Sydney), and the machine being constructed by Iowa State College.     

Comparison Of Oblique And Orthogonal Simple Structure Solutions For Personality And Interest Factors

The study was directed to the need to structure in a few variables the domain measured by personality and interest measures commonly employed in educational counseling: Strong, Kuder, EPPS and the Study of Values. Despite initial uncertainty regarding number of factors to be employed, effects of ipsative scores and of mixing test formats, both an oblique and orthogonal rotation yielded nearly identical results. Of the twenty factors identified by both the biquartimin and varimax solutions, Seven linked vocational interest clusters with personality. Two of the remaining factors had only interest loadings, while of the eleven personality factors, only four were scale specific. Definition of the 16 common factors required that extraction proceed beyond the unit latent root criterion. The results offer evidence that over- extracting factors does not confuse the results of rotation. Further, psycho- metric differences between tests had essentially no effect on the factors found. Of three oblimin rotations attempted, only the biquartimin was successful, yielding results essentially like those of the varimax solution. Because of the vast difference in computation time for these two solutions (computer time 20 times greater for biquartimin), however, the orthogonal varimax remains the method of choice.     

Factorial analysis of Thurstone's seven primary abilities

Intercorrelation coefficients among Thurstone's seven primary mental abilities scores were obtained from scores of 170 freshmen engineering students on the experimental edition of thePrimary Mental Abilities Tests. These correlation coefficients were factored to four factors, interpreted as a general factor, a reasoning factor, a verbal factor, and, tentatively, a specific memory factor. The finding of a general factor for a college population corroborates the Thurstones' finding of a general factor for eighth-grade children.     

The Cognitive Failures Questionnaire Revisited: Dimensions and Correlates

The authors reexamined the factor structure of the Cognitive Failures Questionnaire (D. E. Broadbent, P. F. Cooper, P. Fitzgerald, & K. R. Parkes, 1982) and its correlates. The Cognitive Failures Questionnaire was designed to assess a person's likelihood of committing an error in the completion of an everyday task. A principal components factor analysis with varimax rotation yielded 4 internally consistent, interpretable factors. These factors were labeled Memory, Distractibility, Blunders, and (memory for) Names. This study lends partial support for the factor analytic solution proposed by L. K. Pollina, A. L. Greene, R. H. Tunick, and J. M. Puckett (1992). In addition, it extends previous findings by providing initial evidence for the construct validity of the factors established by correlating factor scores with measures of other related constructs (i.e., boredom proneness, attention deficit/hyperactivity disorder. Type A behavior pattern).     

The cognitive failures questionnaire revisited: dimensions and correlates

The authors reexamined the factor structure of the Cognitive Failures Questionnaire (D. E. Broadbent, P. F. Cooper, P. Fitzgerald, & K. R. Parkes, 1982) and its correlates. The Cognitive Failures Questionnaire was designed to assess a person's likelihood of committing an error in the completion of an everyday task. A principal components factor analysis with varimax rotation yielded 4 internally consistent, interpretable factors. These factors were labeled Memory, Distractibility, Blunders, and (memory for) Names. This study lends partial support for the factor analytic solution proposed by L. K. Pollina, A. L. Greene, R. H. Tunick, and J. M. Puckett (1992). In addition, it extends previous findings by providing initial evidence for the construct validity of the factors established by correlating factor scores with measures of other related constructs (i.e., boredom proneness, attention deficit/hyperactivity disorder, Type A behavior pattern).     

Validity and reliability for the Bruininks-Oseretsky Test of Motor Proficiency-Short Form as applied in the United Arab Emirates culture

Validity and reliability of the Bruininks-Oseretsky Test of Motor Proficiency-Short Form were examined through factor analysis, differences in motor proficiency among age groups, and internal consistency. The sample was comprised of 194 children (96 boys and 98 girls) of ages 6 to 11 years. A principal factor analysis solution with varimax rotation produced four factors: Gross and Fine Motor Skills, Eye-Hand Coordination, Balance-Coordination and Speed, and Visual-motor Coordination. The loadings of these factors partially supported the theoretical work of Bruininks. Univariate analysis of variance showed significant differences between age groups either for each single item or for the total score. Correlation coefficients between single-item and total short form were all significant, although some values were relatively small. These results provided positive support for the construction and reliability of the test.     

Dimensions of adolescent psychopathology

A factor-analytic study of parent ratings of 253 male and female adolescents between the ages of 13 and 17 referred for psychiatric and delinquent problems is reported. Parents rated their children on the Adolescent Form of the Louisville Behavior Checklist. One hundred thirty-seven items were intercorrelated and subjected to a principal component factor analysis and nine factors were rotated to varimax solution. The nine factors were named: Egocentric-Exploitive, Destructive-Assaultive, Social Delinquency, Academic Disability, Adolescent Turmoil, Apathetic Isolation, Neuroticism, Dependent-Inhibited, and Neurological or Psychotic Abnormality. A second-order analysis revealed two broad-band Internalizing and Externalizing dimensions. The factors were shown to be similar to but different from DSM III categories as well as from other factor-analytic studies of adolescents. This study indicates that much research will be required before a consensus can be reached on the basic dimensions of psychopathology of adolescence.     

Reexamination of the Bem Sex-Role Inventory: The Interpersonal BSRI

The 40 masculine and feminine items of 746 Bern Sex-Role Inventory (BSRI; Bern, 1974) were subjected to a principal axis factor analysis with varimax rotation. Results revealed a four-factor solution, indicating that the original BSRI items do not provide two unidimensional ratings of femininity and masculinity. However, some support is given to Bern's initial two-factor thesis in that two principal factors emerged: one consisting of items that were originally identified as feminine, the other consisting of items that were originally identified as masculine. Content examination of the two principal factors resulted in an interpretation of the factors as Interpersonal Sensitivity and Interpersonal Potency. Internal consistency and validity of these two scales were examined and found to be adequate.     

Is the state-trait anxiety inventory multidimensional?

The factor structure of the State-Trait Anxiety Inventory (STAI) was investigated to determine whether the STAI State and Trait Anxiety scales were multidimensional. The STAI (Form Y) was administered to a heterogeneous sample of Air Force recruits (N = 1728); the scores for all 40 STAI items were factor-analyzed together, using the principal axis method and varimax rotation. Two- and four-factor solutions were found to be equally good in simple structure and psychological meaningfulness. Clearly defined state and trait anxiety factors were found in the more parsimonious two-factor solution. In the four-factor solution, the factors were: State Anxiety-Present, State Anxiety-Absent, Trait Anxiety-Present and Trait Anxiety-Absent. Using Cattell's (1966) confactor method, these factors were found to be congruent with similar factors previously identified for high school students by Spielberger et al. (1980). The anxiety-present and anxiety-absent factors were interpreted as reflecting either ‘item method’ variance or ‘item-intensity specificity’. There was no evidence in the present study that the STAI scales were multidimensional in terms of item content.     

The varimax criterion for analytic rotation in factor analysis

An analytic criterion for rotation is defined. The scientific advantage of analytic criteria over subjective (graphical) rotational procedures is discussed. Carroll's criterion and the quartimax criterion are briefly reviewed; the varimax criterion is outlined in detail and contrasted both logically and numerically with the quartimax criterion. It is shown that thenormal varimax solution probably coincides closely to the application of the principle of simple structure. However, it is proposed that the ultimate criterion of a rotational procedure is factorial invariance, not simple structure—although the two notions appear to be highly related. The normal varimax criterion is shown to be a two-dimensional generalization of the classic Spearman case, i.e., it shows perfect factorial invariance for two pure clusters. An example is given of the invariance of a normal varimax solution for more than two factors. The oblique normal varimax criterion is stated. A computational outline for the orthogonal normal varimax is appended.Part of the material in this paper is from the writer's Ph.D. thesis. I am indebted to my committee, Professors F. T. Tyler, R. C. Tryon, and H. D. Carter, chairman, for many helpful suggestions and criticisms. Dr. John Caffrey suggested the namevarimax, and wrote the original IBM 602A computer program for this criterion.I am also indebted to the staff of the University of California Computer Center for help in programming the procedures described in the paper for their IBM 701 electronic computer. Since their installation is partially supported by a grant from the National Science Foundation, the assistance of this agency is acknowledged.     

A counterexample to two-dimensional varimax-rotation

Usually, an iterative procedure based on two-dimensional rotations is employed to find the varimax solution in factor analysis. A matrix is given where this procedure does not yield the maximum value of the varimax criterion. However, random orthogonal transformations of some matrices and subsequent varimax-rotation using the iterative procedure seem to indicate that usually no local maxima exist.     

Factorial invariance and significance

It is shown that invariance requirements remove the indeterminacy in factor determination and lead to an integration of factorial studies with promise of considerable reduction in computational labor. The selection of significant primary factors is discussed, with special reference to Thurstone's simple structure criterion.     

On equivariance and invariance of standard errors in three exploratory factor models

Current practice in factor analysis typically involves analysis of correlation rather than covariance matrices. We study whether the standardz-statistic that evaluates whether a factor loading is statistically necessary is correctly applied in such situations and more generally when the variables being analyzed are arbitrarily rescaled. Effects of rescaling on estimated standard errors of factor loading estimates, and the consequent effect onz-statistics, are studied in three variants of the classical exploratory factor model under canonical, raw varimax, and normal varimax solutions. For models with analytical solutions we find that some of the standard errors as well as their estimates are scale equivariant, while others are invariant. For a model in which an analytical solution does not exist, we use an example to illustrate that neither the factor loading estimates nor the standard error estimates possess scale equivariance or invariance, implying that different conclusions could be obtained with different scalings. Together with the prior findings on parameter estimates, these results provide new guidance for a key statistical aspect of factor analysis.We gratefully acknowledge the help of the Associate Editor and three referees whose constructive comments lead to an improved version of the paper. This work was supported by National Institute on Drug Abuse Grants DA01070 and DA00017 and by the University of North Texas Faculty Research Grant Program.     

On the identifiability of Parameters in Thurstone's multiple factor analysis

In econometric literature a parameter in a theoretical model has been called identifiable if it can be uniquely determined in terms of the joint probability distribution of the observed variables. In this paper the identifiability of parameters in four different factor analysis models is considered. The last of these four models corresponds to Thurstone's factor analysis. In Sections 7 and 11, the possibility of a statistical testing of the models is discussed. Section 10 deals with the problem of actually determining the parameterr (the number of common factors) in terms of the probability distribution of the observed variables.This article will be included in Cowles Commission Paper, New Series, No. 39.     

The common factors in fifty-two mental tests

An analysis by Thurstone's centroid method of the intercorrelations of fifty-two tests was carried to ten factors. Included were tests of social intelligence, Philip's attention tests, and Seashore's tests of musical ability. After rotation of axes, the most important factors appeared to pertain to operations conventionally alluded to by the following terms: verbal facility; spatial ability; numerical ability; attention; musical ability; and memory (or memory span). The social intelligence tests proved to be mainly tests of the verbal factor. A factorial sex difference was indicated by the superiority of men in tests of spatial ability.     

A solution for case iii of the law of comparative judgment

A solution for Case III of the Law of Comparative Judgment, modeled after Thurstone's solution for Case IV but eliminating the restrictive assumption of relatively equal discriminal dispersions, is developed.