Latent partition analysis

Latent partition analysis has been formulated to study the relationships between two or more partitions of the same set of items. The major structural hypothesis is that a latent partition underlies the manifest partitions; that is, it is assumed that each item belongs to a latent category and that the manifest categories are derived by dividing and combining the latent categories. We have found that by examining manifest categories it is possible to reconstruct information about the latent partition and about its relation to the manifest partitions.The research reported herein was originally supported through the U. S. O. E. Cooperative Research Project 5-1005-2-12-1, directed by Donald M. Miller, at the Instructional Research Laboratory, University of Wisconsin. Further work has been supported by the National Science Foundation Grant No. GS-1025 at The University of Chicago. The author wishes to acknowledge the invaluable assistance of Richard G. Wolfe in the final statement of the theory and the assistance of Robert M. Pruzek in certain early formulations.     

Some models for individual-group comparisons and group behavior

In problem solving situations, it has been suggested the superiority of groups over individuals is due simply to the fact that groups consist of several individuals. In this paper, the Lorge and Solomon [1955] approach to such situations is reexamined using the method of maximum likelihood. Extensions to trichotomous response situations are also presented, and the resulting models are applied to data gathered by Staub [1970]. The partitioning of the likelihood ratio goodness-of-fit statistic is then discussed in order that the effects of additional variables on the response variate can be assessed. Finally, the small sample behavior of the likelihood ratio statistic is examined.This research was supported in part by Research Contract No. NSF GS-2818 from the Division of Social Sciences of the National Science Foundation to the Department of Statistics, The University of Chicago.Now at the University of Minnesota.     

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.     

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.     

Women,men, and aggression in an egalitarian society

Vanatinai, a small island society off New Guinea, is egalitarian, with no indigenous formal systems of rank or authority. Assertiveness and autonomy are highly valued as personal qualities and equivalent for males and females. Overt aggression is condemned and violence is rare. Women were the aggressors in four out of five incidents over ten years. Sexual jealousy was the dominant motif in all five cases. This article considers, in historical contexts, indigenous concepts of the gendered person and their relations to anger, violence, and the supernatural aggression of sorcery and witchcraft. The Vanatinai case is evidence that the rarity of intragroup violence, especially of attacks by men on women, is a characteristic of egalitarian societies.An earlier version of this paper was read at the Session on Female Aggression at the American Anthropological Association Annual Meeting, Chicago, in November 1991. I would like to thank session participants, Douglas Fry, Victoria Burbank, Robert Lepowsky, Florence Lepowsky, and the anonymous reviewers forSex Roles for their helpful comments at various points. The fieldwork in Papua New Guinea on which this paper is based was carried out over a total of eighteen months in 1977–1979, 1981, and 1987. I gratefully acknowledge the financial support of the National Science Foundation, Chancellor's Patent Fund and Department of Anthropology of the University of California, Berkeley, the Papua New Guinea Institute of Applied Social and Economic Research, the National Institute of Child Health and Human Development of the National Institutes of Health, the Wenner-Gren Foundation, and the Graduate School of the University of Wisconsin, Madison.     

An individual differences model for multidimensional scaling

A quantitative system is presented to permit the determination of separate multidimensional perceptual spaces for individuals having different viewpoints about stimulus interrelationships. The structure of individual differences in the perception of stimulus relationships is also determined to provide a framework for ascertaining the varieties of consistent individual viewpoints and their relationships with other variables.This research was supported in part by the National Institute of Mental Health, United States Public Health Service, under Research Grants M-2878 and M-4186 to Educational Testing Service, in part by Educational Testing Service, and in part by the Office of Naval Research under Contract Nonr-1834(39) and the University of Illinois. The authors wish to thank Drs. Harold Gulliksen and Douglas N. Jackson for their helpful comments and Miss Henrietta Gallagher for supervising the computations. Portions of this paper were presented at the American Psychological Association meetings in Chicago, September 1960.This paper was written while Dr. Messick was a Fellow at the Center for Advanced Study in the Behavioral Sciences.     

Evaluation of the diagnostic interview for children and adolescents for use in general population samples

This article presents evaluative data on the use of the Diagnostic Interview for Children and AdolescentsRevised (DICAR) to classify DSM-IIIR disorders in the general population. Data for the analyses came from a probability sample (N=251) of parentchild/adolescent dyads aged 6 to 16 separately administered the DICAR on two occasions, 10 to 20 days apart, by trained lay interviewers and child psychiatrists. Data are presented on prevalence,testretest reliability, parentchild/adolescent agreement, and trained lay interviewerchild psychiatrist agreement. High prevalences of oppositional defiant disorder derived from parent assessments and overanxious disorder and dysthymia derived from adolescent assessments suggest that these disorders may be overidentified. Interview data provided by 6 to 11year olds to classify the internalizing disorders were too unreliable to be useful. Agreement between parentchild/adolescent dyads was generally low while agreement between trained lay interviewerschild psychiatrists was generally high.This work was supported by funds from the National Health Research and Development Program (grant number 6606-3760-42) and the Ontario Ministry of Community and Social Services, and was carried out by the Child Epidemiology Unit, Department of Psychiatry, McMaster University and the Child and Family Centre, Chedoke-McMaster Hospitals, Hamilton, Ontario. Dr. Boyle is supported by a William T. Grant Foundation Faculty Scholar Award; Dr. Offord by a National Health Scientist Award, Health and Welfare Canada; Dr. Szatmari by a Research Fellowship, Ontario Mental Health Foundation; and Dr. Fleming by a NARSAD Young Investigator Award. The authors wish to thank the Hamilton Board of Education, particularly Mr. Keith Reilly and Mr. Owen Jackson; principals and teachers of the Board; and parents and students for their help on this project. Our appreciation also extends to Ms. Barb Hall who assisted in the analysis of the data.     

An inter-battery method of factor analysis

The inter-battery method of factor analysis was devised to provide information relevant to the stability of factors over different selections of tests. Two batteries of tests, postulated to depend on the same common factors, but not parallel tests, are given to one sample of individuals. Factors are determined from the correlation of the tests in one battery with the tests in the other battery. These factors are only those that are common to the two batteries. No communality estimates are required. A statistical test is provided for judging the minimum number of factors involved. Rotation of axes is carried out independently for the two batteries. A final step provides the correlation between factors determined by scores on the tests in the two batteries. The correlations between corresponding factors are taken as factor reliability coefficients.This research was jointly supported by Princeton University and the Office of Naval Research under contract N6onr-270-20 and the National Science Foundation under grant NSF G-642; Harold Gulliksen, principal investigator. The preparation of this paper and the accompanying material has been aided by the Educational Testing Service. The author is grateful to Professors Harold Gulliksen and Samuel S. Wilks for their many most helpful comments and suggestions.     

History of a historian of psychology in the United States

This article focuses on the author's activities in the United States relating to the history of psychology. It does not deal with his involvement in applied psychology in Europe (1937-1939), and it only touches on research on malnutrition and behavior, illumination and performance, and aging carried out in the Laboratory of Physiological Hygiene at the University of Minnesota (1941-1958). Activities bearing on the history of psychology dominated the years spent at Lehigh University (1959-1979) and the years of retirement (1979-present). The principal events include organizing the first scientific meeting of the American Psychological Association's Division 26, History of Psychology (1966); two summer institutes on the history of psychology (1968, 1971); the editing of a historically oriented volume on psychology in the USSR (1972) and of R.I. Watson's papers on the history of psychology (1977); organizing and editing a volume containing 6 monographs on the history of psychology in the United States (1984); and editing a volume concerned with international research during the years 1919-1981 on malnutrition and behavior.     

Multidimensional analysis of complex structure: Mixtures of class and quantitative variation

For certain kinds of structure consisting of quantitative dimensions superimposed on a discrete class structure, spatial representations can be viewed as being composed of two subspaces, the first of which reveals the discrete classes as isolated clusters and the second of which contains variation along the quantitative attributes. A numerical method is presented for rotating a multi-dimensional configuration or factor solution so that the first few axes span the space of classes and the remaining axes span the space of quantitative variation. The use of this method is then illustrated in the analysis of some experimental data.The author is particulary indebted to Dr. W. S. Torgerson for many valuable suggestions. In addition, Mr. M. David Todd and Mr. Joseph Young provided technical assistance in developing several assembly language routines, and Dr. James E. Deese made a number of helpful comments. This research was undertaken in partial fulfillment of the doctoral requirements at Johns Hopkins University, and was financed in part by the National Science Foundation.     

An empirical study of the factor analysis stability hypothesis

Note is taken of four related sources of confusion as to the usefulness of Thurstone's factor analysis model and of their resolutions. One resolution uses Tucker's distinction between exploratory and confirmatory analyses. Eight analyses of two sets of data demonstrate the procedures and results of a confirmatory study with statistical tests of some, but not all, relevant hypotheses in an investigation of the stability (invariance) hypothesis. The empirical results provide estimates, as substitutes for unavailable sampling formulations, of effects of variation in diagonal values, in method of factoring, and in samples of cases. Implications of these results are discussed.The computational costs of this study were defrayed, in part, by a research small grant M-1922 from the National Institute of Health, and, in part, by support under project 176-0002 by the University of Iowa Computing Center, Dr. J. P. Dolch, Director. The assistance of Dr. Kern Dickman and Mr. Leonard Wevrick of the University of Illinois and of Mr. Norman Luther of the University of Iowa in handling the computing problems is gratefully acknowledged.     

The guttman-harris uniqueness estimates

It is shown that, under very general conditions, uniqueness estimates proposed independently by Guttman [1957] and by Harris [1963] provide tighter upper bounds on the unknown uniqueness values of factor analysis than do existing estimates.The Illinois Department of Mental Health Drug Abuse Program is co-sponsored by the State of Illinois and the Department of Psychiatry, Division of the Biological Sciences and Pritzker School of Medicine, University of Chicago. Send reprint requests to Drug Abuse Programs—Research, East Pavilion, Museum of Science and Industry, 57th Street and South Lake Shore Drive, Chicago, Illinois 60637.     

A general least squares solution for successive intervals

A general least squares solution for successive intervals is presented, along with iterative procedures for obtaining stimulus scale values, discriminal dispersions, and category boundaries. Because provisions for weighting were incorporated into the derivation, the solution may be applied without loss of rigor to the typical experimental matrix of incomplete data, i.e., to a data matrix with missing entries, as well as to the rarely occurring matrix of complete data. The use of weights also permits adjustments for variations in the reliability of estimates obtained from the data. The computational steps involved in the solution are enumerated, the amount of labor required comparing favorably with other procedures. A quick, yet accurate, graphical approximation suggested by the least squares derivation is also described.This research was jointly supported in part by Princeton University, the Office of Naval Research under contract N6onr-270-20, and the National Science Foundation under grant NSF G-642, and in part by Educational Testing Service.     

Sex differences in nonverbal behavior

A variety of nonverbal behaviors was coded from videotapes of 88 dyadic conversations. The 44 male and 44 female subjects were paired so that each participated in one conversation with a stranger of the same sex and one conversation with a stranger of the opposite sex. It was found that sex of subject, but not sex of partner, had a significant effect on many of the nonverbal behaviors displayed during the conversations. Subjects' scores on the behavioral measures were correlated with their scores on several personality measures and on a post-conversation questionnaire. Sex differences in these correlations were used to generate hypotheses linking specific behavioral differences between the sexes to more general differences between the masculine and feminine interpersonal styles.This study was supported in part by NSF grant GS-3033, awarded to Starkey Duncan, University of Chicago; by NSF grant GS-3127, awarded to Donald Fiske, University of Chicago; by a grant awarded to Starkey Duncan and Donald Fiske by the Social Science Divisional Research Committee of the University of Chicago; and by a University of Chicago Humanities Fellowship awarded to the author. The author is grateful to Starkey Duncan and Donald Fiske for the extensive assistance they provided with this study. The author also wishes to express her appreciation to Jeanine Carlson, George Niederehe, Bruno Repp, Thomas Shanks, and Cathy Stepanek, who assisted in coding the videotaped data and in the statistical analysis. This article is based on the author's doctoral dissertation (Beekman, 1973), which may be consulted for further details.Previous drafts of this article have been circulated under the author's former name, Susan J. Beekman.     

Format effects in two teacher rating scales of hyperactivity

The object of this study was to investigate the effect of differences in format on the precision of teacher ratings and thus on the reliability and validity of two teacher rating scales of children's hyperactive behavior. Teachers (N=242) rated a sample of children in their classrooms using rating scales assessing similar attributes with different formats. For a sub-sample the rating scales were readministered after 2 weeks. The results indicated that improvement can be made in the precision of teacher ratings that may be reflected in improved reliability and validity.This research was supported by grants from the Spencer Foundation and the National Institute of Mental Health (MH 29495). A somewhat different version of this paper was presented at the annual convention of the American Educational Research Association, Toronto, Canada, March 1978. The author thanks Nadine Lambert and Leonard Marascuilo for their assistance in the preparation of this paper.     

Accuracy of maximum-likelihood estimates of correlation for a biserial model

Tables are given for the calculation of variances of maximum-likelihood estimates in a multiple biserial model. For the estimates of individual correlations between the dichotomized variable and each of the graduated variables additional calculation is necessary; variances for estimates of the multiple correlation and the point of dichotomy are available directly. The required formulas and notation are those of a recent paper by Hannan and Tate.Research sponsored by the National Science Foundation under grant NSF-GP219.Aero-Space Division (Applied Mathematics), Seattle, Washington.     

Estimation of latent ability and item parameters when there are omitted responses

Omitted items cannot properly be treated as wrong when estimating ability and item parameters. A convenient method for utilizing the information provided by omissions is presented. Theoretical and empirical justifications are presented for the estimates obtained by the new method.Research reported in this paper has been supported by grant GB-32781X from National Science Foundation.     

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.     

Probability matching

The class of symmetric path-independent models with experimenter-controlled events is considered in conjunction with two-choice probability learning experiments. Various refinements of the notion of probability matching are defined, and the incidence of these properties within this class is studied. It is shown that the linear models are the only models of this class that predict a certain phenomenon that we call stationary probability matching. It is also shown that models within this class that possess an additional property called marginal constancy predict approximate probability matching.This research grew out of questions posed by William K. Estes. We are also indebted to Professor Estes for his encouragement and assistance at all stages of this research. During the course of this research J. I. Y. received support from the U. S. Public Health Service (N. I. M. H.). M. F. N.'s present address is the University of Pennsylvania. J. I. Y.'s present address is the University of Minnesota.     

Some contributions to maximum likelihood factor analysis

A new computational method for the maximum likelihood solution in factor analysis is presented. This method takes into account the fact that the likelihood function may not have a maximum in a point of the parameter space where all unique variances are positive. Instead, the maximum may be attained on the boundary of the parameter space where one or more of the unique variances are zero. It is demonstrated that suchimproper (Heywood) solutions occur more often than is usually expected. A general procedure to deal with such improper solutions is proposed. The proposed methods are illustrated using two small sets of empirical data, and results obtained from the analyses of many other sets of data are reported. These analyses verify that the new computational method converges rapidly and that the maximum likelihood solution can be determined very accurately. A by-product obtained by the method is a large sample estimate of the variance-covariance matrix of the estimated unique variances. This can be used to set up approximate confidence intervals for communalities and unique variances.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 National Science Foundation to Educational Testing Service.The author is deeply indebted to Dr. D. N. Lawley whose contributions amounted nearly to coauthorship. The author also wishes to thank Mr. G. Gruvaeus for much valuable assistance in constructing the computer program.