The determination of successive principal components without computation of tables of residual correlation coefficients

A procedure is presented for determining the successive principal components of a correlation matrix where it is not necessary to compute the successive tables of residual correlations. The original correlation matrix is bordered with a new row and column for each principal component that is determined.This paper is one of a series of reports on the development of multiple factor analysis in the study of primary human abilities which have been supported by research grants from the Carnegie Corporation of New York and the facilities of the Psychometric Laboratory, which have been provided by the Social Science Research Committee of The University of Chicago.     

Review of family treatment studies in israel

Much of the culturally specific knowledge about helping families in Israel is not readily available; either it is not in English and often appears in local circulation publications or is interwoven in the larger fabric of family treatment literature. This paper attempts to present the knowledge about helping families that has emerged in Israel based on an extensive literature review of all known work in Hebrew and English since 1980 that is related to studying and treating family problems in Israel. Major works, particularly research findings are highlighted. Recommendations for future research in this broad area are given.Revised on October 13, 1994 forContemporary Family Therapy. The author wishes to thank Nomi Mey-Ami for her vital assistance in compling the source material. The complete bibliographic listing is available in Hebrew from the Information Retrieval Center for Research in Social Sciences Henrietta Szold Institute in Jerusalem.     

A factorial study of the reasoning and closure factors

A battery of 46 tests was given to 237 college men. A factor analysis using the Thurstone technique revealed eight clearly interpretable first-order factors, one dubious factor, and a residual factor. The factors were interpreted as induction, deduction, flexibility of closure, speed of closure, space, verbal comprehension, word fluency, and number. Four second-order factors were abstracted from the matrix of first-order correlations. The presence of induction, deduction, and flexibility of closure on the first second-order factor, interpreted as an analytic factor, confirmed previous indications of relationships between the reasoning and closure factors. A second bipolar factor is interpreted as a speed of association factor. The third factor is interpreted as facility in handling meaningful verbal materials—perhaps an ability to do abstract thinking. The fourth factor is possibly a second-order closure factor—perhaps an ability to do concrete thinking.The author is grateful to Professor L. L. Thurstone for his encouragement and invaluable advice and for permission to use many tests originally prepared in the Psychometric Laboratory of the University of Chicago, to Mr. James Degan for assistance in rotations, and to the Social Science Research Committee of the University of Chicago for a grant to this study.     

A multiple group method of factoring the correlation matrix

There are a number of methods of factoring the correlation matrix which require the calculation of a table of residual correlations after each factor has been extracted. This is perhaps the most laborious part of factoring. The method to be described here avoids the computation of residuals after each factor has been computed. Since the method turns on the selection of a set of constellations or clusters of test vectors, it will be calleda multiple group method of factoring. The method can be used for extracting one factor at a time if that is desired but it will be considered here for the more interesting case in which a number of constellations are selected from the correlation matrix at the start. The result of this method of factoring is a factor matrixF which satisfies the fundamental relationFF'=R.This study is one of a series of investigations in the development of multiple factor analysis and application to the study of primary mental abilities. We wish to acknowledge the financial assistance from the Social Science Research Committee of The University of Chicago which has made possible the work of the Psychometric Laboratory.     

“Best possible” systematic estimates of communalities

At least four approaches have been used to estimate communalities that will leave an observed correlation matrixR Gramian and with minimum rank. It has long been known that the square of the observed multiple-correlation coefficient is a lower bound to any communality of a variable ofR. This lower bound actually provides a best possible estimate in several senses. Furthermore, under certain conditions basic to the Spearman-Thurstone common-factor theory, the bound must equal the communality in the limit as the number of observed variables increases. Otherwise, this type of theory cannot hold forR.This research was facilitated by a grant from the Lucius N. Littauer Foundation to the American Committee for Social Research in Israel in order to promote methodological work of the Israel Institute of Applied Social Research.     

Factor analysis of the social performance survey schedule

There are several studies suggesting that the Social Performance Survey Schedule (SPSS) is a reliable and valid measure of social skill. However, the factorial structure of the SPSS has never been examined. In the present study, SPSSs taken by 652 college students were factor analyzed by the method of principal components and the resulting factors were rotated according to the varimax criterion. Separate factor analyses were conducted for men and women. Seven factors, which accounted for a little over a third of the total variance, were retained for each sex. A large general factor labeled Prosocial Competence emerged for both sexes. Beyond this, the factorial solutions for the two sexes tended to diverge, with males showing a large negative factor (Social Offensiveness) and three smaller negative factors and females showing five relatively small negative factors. Suggestions were made concerning additional factor analytic studies of the SPSS and the ways in which derived factors might be used in research and clinical work.This research was supported by funds from the Rutgers University Research Council. Thanks are due to Leona Aiken for her statistical consultation.     

The effect of sex differences on sociometric data generated by a roster-rating scale instrument

Sociometric data generated by roster-rating scale instruments are being used for assessment and evaluation purposes. Little information exists, however, on the influence of peer gender on this particular type of sociometric data. In a sample of 441 male and 455 female fourth, fifth, and sixth grade children, this study found same-sex ratings to be significantly higher than opposite-sex ratings. Opposite-sex ratings, while significantly lower, were slightly correlated with the higher same-sex ratings. Differing methods for interpreting roster-rating scale data are discussed in light of the above results.The author is Assistant Professor at the School of Social Welfare, State University of New York at Albany currently on leave at the Baerwald School of Social Work, Hebrew University, Jerusalem, Israel. This project was completed under the auspices of the Interpersonal Skill Training and Research Project of the School of Social Work, University of Wisconsin-Madison, Madison, Wisconsin.     

Intrinsic-extrinsic factors in sport motivation

Participants were 83 students (36 men and 47 women). 10 intrinsic-extrinsic factors involved in sport motivation were obtained. The factors were generated from items obtained from the participants rather than items from the experimenter. This was done to avoid the possible influence of preconceptions on the part of the experimenter regarding what the final dimensions may be. Obtained motivational factors were Social Reinforcement, Fringe Benefits, Fame and Fortune, External Forces, Proving Oneself, Social Benefits, Mental Enrichment, Expression of Self, Sense of Accomplishment, and Self-enhancement. Each factor was referred to an intrinsic-extrinsic dimension to describe its relative position on that dimension. The order of the factors as listed indicates increasing intrinsic motivation. i.e., the first four factors were rated in the extrinsic range, whereas the remaining six were rated to be in the intrinsic range. Next, the participants rated the extent to which each of the various factors was involved in their decision to participate in sport activities. The pattern of use of the motivational factors was the same for both sexes except that men indicated greater use of the Fringe Benefits factor. Overall, the more intrinsic a sport motivation factor was rated, the more likely it was to be rated as a factor in actual sport participation.     

Constrained least squares estimators of oblique common factors

An expression is given for weighted least squares estimators of oblique common factors, constrained to have the same covariance matrix as the factors they estimate. It is shown that if as in exploratory factor analysis, the common factors are obtained by oblique transformation from the Lawley-Rao basis, the constrained estimators are given by the same transformation. Finally a proof of uniqueness is given.The research reported in this paper was partly supported by Natural Sciences and Engineering Research Council Grant No. A6346.     

A single plane method of rotation

The method of rotation described here is applied to one hyperplane at a time. The method seems to be simple and quite effective and it can be applied by a relatively inexperienced computer. The method does not postulate a positive manifold, and hence it is applicable also to bipolar factors.The author wishes to express his indebtedness to the Social Science Research Committee of The University of Chicago for support of the Psychometric Laboratory and these factorial investigations.     

Student-teacher concordance on dimensions of student social competence: A multitrait-multimethod analysis

Teacher and self-ratings of social competence were obtained for 669 (341 males, 328 females) grades 3–6 students using the Social Behavior Assessment—Revised (SBA-R) and a self-report scale consisting of the identical items reworded in first person. Factor analysis and multitrait-multimethod matrix analysis were used to validate construct interpretations. The previous four-factor structure of the SBA-R was not replicated. However, the three-factor structure that did emerge was better defined. Although student-teacher concordance was moderate for the Self-Control/Social Convention and Academic Responsibility factors, it was minimal for the Social Participation factor. Evidence of discriminant validity was weak. As with other studies using rating scales, method bias was in evidence. Sex differences were found in terms of variance explained by each factor and convergent validity. Discussion focuses on problems associated with construct validation in general and validation of school-related social competence in particular.     

Relation of the Big Five and Factor V subcomponents to social intelligence

Factor analysis of trait terms defining Factor V yielded five oblique subcomponents (Creativity, Intellect, Reflectiveness, Conservatism, and Closed Minded), the last of which seems to be an artifact due to social desirability. Factor analysis of Sternberg's laymen's and experts' implicit conceptions of intelligence yielded seven oblique factors. These seven factors (Social Competence, Reading, Planning, Objectivity, Inquiring Intellect, Nonjudgmental, and Problem Solving) describe dimensions of what could be termed Social Intelligence. Hierarchical regression analysis revealed that the Social Intelligence factors were quite predictable from Factor V subcomponents and other Big Five traits. Several Social Intelligence factors were predicted in a large part primarily by other Big Five Traits. Higher order factor analysis followed by regression revealed that a general Social Intelligence factor was predicted primarily by a higher order Factor V. Addition of the other Big Five traits to prediction increased Rmodestly but did not diminish the influence of Factor V. These results suggest that at a low level of the factor hierarchy specific aspects of Social Intelligence are broader than the subcomponents of Factor V and involve other personality traits. However, at the highest level of the factor hierarchy Factor V is the primary predictor of Social Intelligence; while other traits aid in prediction, they do not diminish the relation between the two. The results provide some support for the lexical hypothesis prediction that Factor V trait terms summarize behaviors that shape implicit conceptions of intelligence, which is more social and practical than IQ assessed as g Copyright © 1999 John Wiley & Sons, Ltd.     

Factor analysis of the army air forces sheppard field battery of experimental aptitude tests

A factor analysis was made of 39 experimental printed aptitude tests and seven reference tests selected from the Army Air Forces Aircrew Classification Battery. Thirteen factors were extracted and two independent orthogonal rotational solutions were completed. Twelve factors were interpreted. Of these, seven were clearly identifiable with previously known factors: numerical, perceptual-speed, spatial-relations, visualization, visual-memory, paired-associates-memory, and length-estimation factors. A planning factor was not as clearly identifiable. A reasoning factor was probably a composite of two or more factors that failed to separate. A new factor possibly has to do with orientation with respect to the points of the compass. Two factors were doublets, each apparently specific to one kind of test. Better conceptions were gained of the spatial-relations and visualization factors and of the kinds of tests that measure them best. Efforts to improve measures of unique factors were not uniformly successful. The attempt to duplicate a psychomotor test rather directly by analogy in printed form failed almost completely.For support of a large part of the investigation the senior author is indebted to the Social Sciences Research Council for a grant-in-aid. Dr. Fruchter supervised the computational work in the extraction of factors and in one of the rotational solutions. Much of the work was done while he was employed by the Air Training Command Human Resources Research Center. While the opinions and conclusions are those of the authors, they wish to express their appreciation to that organization and especially to Dr. John T. Dailey for making the facilities possible and to Mr. William B. Lecznar for technical and computational assistance.     

A factor analysis of mental abilities and personality traits

The relationship between measures of verbal fluency and certain personality traits is examined by factor techniques. From a matrix of eight factor scores derived from mental tests plus five personality scores, six factors were obtained. An oblique solution lends limited support to the hypothesized relationship between the two domains.This study was supported by a grant from the Research Foundation of the University of Utah.Currently on leave of absence with the National Research Council.     

社会预警系统与心理学

首先探讨了对社会不稳定因素预警的需要,以及社会预警系统对国家公共政策制定和行政决策的意义。社会预警系统是一种系统的社会态度调查网络,通过对公众对社会事物的态度调查,预见其可能的行为反应,将不稳定事件化解于未然。然后,介绍了国外承担社会预警职能的研究机构的研究实践。最后,讨论了社会预警研究两个重要的方法论问题：态度与行为反应的关系,调查抽样问题。     

Psychopathology and response styles in the SCL-90 responses of acutely distressed persons

Using the responses of 197 suicidal and nonsuicidal patients of a crisis and short-term intervention unit, the item factor structure of the SCL-90 was examined. Results suggested a reduced dimensionality for the checklist rather than supporting the nine scales associated with the instrument's scoring key. The influence of various response styles on the SCL-90's dimensionality was also explored. Although a social desirability response style was strongly related to all SCL-90 subscales and factors, it did not offer a complete explanation for the checklist's apparent unidimensionality. Other explanations relating to methods of test construction and to patients' inability to differentiate symptoms were also preferred. Finally, although subscale scores may facilitate clinical interpretation, it was suggested that the SCL-90 might best be scored as a single index of general symptomatology.We wish to thank G. C. Fekken and R. N. MacLennan for their assistance with this project.This work was supported in part by Social Sciences and Humanities Research Council of Canada Grant 410-85-1043 and by an Ontario Ministry of Health Research Personnel Award.     

Sex and cultural differences in the factorial structure of the self-directed search

Holland's Self-Directed Search was administered to 247 male and 252 female high school students, aged 16 to 18 years, attending state schools in New Zealand. Principal factor analysis was used in an attempt to identify six orthogonal factors analogous to Holland's six personality types. The Social and Enterprising scales could not be split into two factors in either sample, and the Investigative and Realistic scales defined a single factor for the female students. Computed distances between pairs of the six personality types in five dimensional factorial space were compared with the relative ordering of the distances expected from Holland's hexagonal model. The positions of the types in space corresponded more closely with the model for the males than they did for the females. The results, in conjunction with those of similar studies in Israel and the United States, imply that the correspondence between some summary codes on the SDS and existing occupational classifications based on Holland's types may be less than perfect, particularly for females. Also, care should be taken when using codes on the SDS to calculate Holland's indices of “consistency,” especially for females.     

A rational-emotive group intervention for preventing and coping with stress among safety officers

A stress management and prevention workshop for nonclinical industrial workers using rational-emotive principles with 18 months followup is reported. Twenty-two senior safety officers participated in an intervention program of five weekly meetings aimed at improving cognitive skills and assertiveness mainly by decreasing irrational thought processes. We hypothesized an increase in assertiveness, and a decrease in irrational beliefs, and emotional and cognitive stress symptoms (manifested in somatic complaints and cognitive weariness). Assertiveness improved and somatic complaints and irrationality decreased in the short term. Eighteen months later, cognitive weariness was also reduced. The other improvements were still evident, but not to the same extent as short-term effects. Although the workshop improved rationality, further practice would be needed in the behavioral aspect of stress prevention to achieve long-term improvements in assertiveness.Talma Kushnir, Ph.D., is a social and medical psychologist at the Occupational Health and Rehabilitation Institute, Raanana, Israel, and teaches psychology and health promotion at the Tel-Aviv University Medical School.Ruth Malkinson, Ph.D., fellow and RET trainer and supervisor of the Institute for RET, and teaches at the School of Social Work and Medical School at Tel-Aviv University, Israel. Both authors contributed equally to this studyThis study was supported by the Committee for Preventive Action and Research in Occupational Health, The Ministry of Labor and Social Affairs, Jerusalem, Israel.The authors thank Estie Weisberg for her administrative assistance in organizing the workshops.     

Efficient estimation in image factor analysis

The image factor analytic model (IFA), as related to Guttman's image theory, is considered as an alternative to the traditional factor analytic model (TFA). One advantage with IFA, as compared with TFA, is that more factors can be extracted without yielding a perfect fit to the observed data. Several theorems concerning the structural properties of IFA are proved and an iterative procedure for finding the maximum likelihood estimates of the parameters of the IFA-model is given. Substantial experience with this method verifies that Heywood cases never occur. Results of an artificial experiment suggest that IFA may be more factorially invariant than TFA under selection of tests from a large battery. The first part of this work was done at the University of Uppsala, Sweden and supported by the Swedish Council for Social Science Research. The second part was done at Educational Testing Service and supported by a grant (NSF-GB-1985) from the National Science Foundation to Educational Testing Service. The author is indebted to Mr. G. Gruvaeus, who wrote many of the computer programs, checked the mathematical derivations and gave other invaluable assistance throughout the work.     

Orthogonal rotation to congruence

Two problems are considered. The first is that of rotating two factor solutions orthogonally to a position where corresponding factors are as similar as possible. A least-squares solution for transformations of the two factor matrices is developed. The second problem is that of rotating a factor matrix orthogonally to a specified target matrix. The solution to the second problem is related to the first. Applications are discussed.This research was supported in part by contract Nonr 228 (22) between the office of Naval Research and the University of Southern California. Portions of this paper were presented at the American Psychological Association Convention, Los Angeles, September, 1964.