Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-07T16:27:31.125Z Has data issue: false hasContentIssue false
  • English
  • Français

Factor Analysis and Psychometrika: Major Developments

Published online by Cambridge University Press:  01 January 2025

Stanley A. Mulaik
Stanley A. Mulaik*
Affiliation:
Georgia Institute of Technology
*
Requests for reprints should be sent to Stanley A. Mulaik, School of Psychology, Georgia Institute of Technology, Atlanta, GA 30332.
Get access Rights & Permissions [Opens in a new window]

Abstract

Papers on factor analysis appearing in Psychometrika reflect the initial efforts of the Thurstonians to reformulate psychology as a quantitative science. The Thurstonians' emphasis on the development of factor analysis as an exploratory methodology was not new with them but was taken from British statisticians and psychologists who preceded them, whose literature the Thurstonians otherwise tended to ignore. The Thurstonians' rejection of general factors and focus on rotation to simple structure reflected an attempt to avoid statistical artifact and to identify factors with psychological substance. Much of the literature on factor analysis in Psychometrika concerned solving technical problems in the exploratory factor analysis method. Factor analysis took a major shift in direction in the 1970's with the development of confirmatory methodologies, many of which now receive greater attention than the method of exploratory factor analysis, most of the problems of which are now resolved.

Keywords

factor analysishistoryPsychometrikamultivariate statistics
Type
50th Anniversary Section
Information
Psychometrika , Volume 51 , Issue 1 , March 1986 , pp. 23 - 33
Copyright
Copyright © 1986 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aune, B. (1970). Rationalism, empiricism, and pragmatism, New York: Random House.Google Scholar
Bargmann, R. E. (1971). Matrices and determinants. In Selby, S. M. (Eds.), Standard mathematical tables, Cleveland, OH: The Chemical Rubber Co..Google Scholar
Bentler, P. M., Weeks, D. G. (1980). Linear structural equations with latent variables. Psychometrika, 45, 289–308.CrossRefGoogle Scholar
Bock, R. D., Bargmann, R. E. (1966). Analysis of covariance structures. Psychometrika, 31, 507–534.CrossRefGoogle ScholarPubMed
Browne, M. W. (1967). On oblique procrustes rotation. Psychometrika, 32, 375–394.CrossRefGoogle ScholarPubMed
Browne, M. W. (1969). Fitting the factor analysis model. Psychometrika, 34, 375–394.CrossRefGoogle Scholar
Carroll, J. B. (1941). A factor analysis of verbal abilities. Psychometrika, 6, 279–307.CrossRefGoogle Scholar
Carroll, J. B. (1953). An analytic solution for approximating simple structure in factor analysis. Psychometrika, 18, 23–38.CrossRefGoogle Scholar
Carroll, J. B. (1957). Biquartimin criterion for rotation to oblique simple structure in factor analysis. Science, 126, 1114–1115.CrossRefGoogle ScholarPubMed
Dwyer, Paul S. (1937). The determination of the known factor loadings of other tests. Psychometrika, 2, 173–178.CrossRefGoogle Scholar
Eckart, C., Young, G. (1936). The approximation of one matrix by another of lower rank. Psychometrika, 1, 211–218.CrossRefGoogle Scholar
Engelhart, M. D. (1936). The technique of path coefficients. Psychometrika, 1, 287–293.CrossRefGoogle Scholar
Ferguson, G. A. (1954). The concept of parsimony in factor analysis. Psychometrika, 19, 281–290.CrossRefGoogle Scholar
Feyerabend, P. K. (1965). Problems of empiricism. In Colodny, R. G. (Eds.), Beyond the edge of certainty, Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Feyerabend, P. K. (1970). Classical empiricism. In Butts, R. E., Davis, J. W. (Eds.), The methodological heritage of Newton, Toronto: The University of Toronto Press.Google Scholar
Fletcher, R., Powell, M. J. D. (1963). A rapidly convergent descent method for minimization. The Computer Journal, 2, 163–168.CrossRefGoogle Scholar
Garnett, J. C. M. (1919). On certain independent factors in mental measurements. Proceedings of the Royal Society of London, 96 A91–111.Google Scholar
Garnett, J. C. M. (1919). General ability, cleverness and purpose. British Journal of Psychology, 9, 345–366.Google Scholar
Goldstine, H. H., Murray, F. J., von Neuman, J. (1959). The Jacobi method for real symmetric matrices. Journal of the Association for Computing Machinery, 6, 59–96.CrossRefGoogle Scholar
Green, B. F. (1952). The orthogonal approximation of an oblique structure in factor analysis. Psychometrika, 27, 429–440.CrossRefGoogle Scholar
Guttman, L. (1940). Multiple rectilinear prediction and the resolution into components. Psychometrika, 5, 75–99.CrossRefGoogle Scholar
Guttman, L. (1944). General theory and methods for matric factoring. Psychometrika, 9, 1–16.CrossRefGoogle Scholar
Guttman, L. (1952). Multiple group methods for common-factor analysis: Their basis, computation, and interpretation. Psychometrika, 17, 209–222.CrossRefGoogle Scholar
Guttman, L. (1953). Image theory for the structure of quantitative variates. Psychometrika, 18, 277–296.CrossRefGoogle Scholar
Guttman, L. (1954). Some necessary conditions for common-factor analysis. Psychometrika, 19, 149–161.CrossRefGoogle Scholar
Guttman, L. (1955). The determinacy of factor score matrices, with implications for five other basic problems of common-factor theory. British Journal of Statistical Psychology, 8, 65–81.CrossRefGoogle Scholar
Guttman, L. (1956). “Best possible” systematic estimates of communalities. Psychometrika, 21, 65–81.CrossRefGoogle Scholar
Harrell, W. (1940). A factor analysis of mechanical ability tests. Psychometrika, 5, 17–33.CrossRefGoogle Scholar
Harris, C. W. (1962). Some Rao-Guttman relationships. Psychometrika, 27, 247–263.CrossRefGoogle Scholar
Hendrickson, A. E., White, P. O. (1964). PROMAX: A quick method for rotation to oblique simple structure. British Journal of Statistical Psychology, 17, 65–70.CrossRefGoogle Scholar
Holzinger, K. J., Swineford, F. (1937). The bi-factor method. Psychometrika, 2, 41–54.CrossRefGoogle Scholar
Horst, P. (1941). A non-graphical method for transforming an arbitrary factor matrix into a simple structure factor matrix. Psychometrika, 6, 79–99.CrossRefGoogle Scholar
Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24, 417–441.CrossRefGoogle Scholar
Hotelling, H. (1936). Simplified calculation of principal components. Psychometrika, 1, 27–35.CrossRefGoogle Scholar
Howe, W. G. (1955). Some contributions to factor analysis (Report No. ONRL-1919), Oak Ridge, TN: Oak Ridge National Laboratory.CrossRefGoogle Scholar
James, L. R., Mulaik, S. A., Brett, J. M. (1982). Causal analysis: Assumptions, models, and data, Beverly Hills, CA: Sage Publications.Google Scholar
Jennrich, R. I., Sampson, P. F. (1966). Rotation for simple loadings. Psychometrika, 31, 313–323.CrossRefGoogle ScholarPubMed
Jöreskog, K. G. (1966). Testing a simple structure hypothesis in factor analysis. Psychometrika, 31, 165–178.CrossRefGoogle ScholarPubMed
Jöreskog, K. G. (1967). Some contributions to maximum likelihood factor analysis. Psychometrika, 31, 443–482.CrossRefGoogle Scholar
Jöreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 182–202.CrossRefGoogle Scholar
Jöreskog, K. G. (1970). A general method for the analysis of covariance structures. Biometrika, 57, 239–251.CrossRefGoogle Scholar
Jöreskog, K. G. (1973). A general method for estimating a linear structural equation system. In Goldberger, A. S., Duncan, O. D. (Eds.), Structural equation models for the social sciences, New York: Seminar Press.Google Scholar
Jöreskog, K. G. (1978). Structural analysis of covariance and correlation matrices. Psychometrika, 43, 443–477.CrossRefGoogle Scholar
Jöreskog, K. G. (1979). Statistical models and methods for analysis of longitudinal data. In Jöreskog, K. G., Sörbom, D. (Eds.), Advances in factor analysis and structural equation models, Cambridge, MA: Abt. Books.Google Scholar
Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Educational and Psychological Measurement, 23, 770–773.Google Scholar
Kaiser, H. F., Caffrey, J. (1965). Alpha factor analysis. Psychometrika, 30, 1–14.CrossRefGoogle ScholarPubMed
Karlin, J. E. (1941). Music ability. Psychometrika, 6, 61–65.CrossRefGoogle Scholar
Karlin, J. E. (1942). A factorial study of auditory function. Psychometrika, 7, 251–279.CrossRefGoogle Scholar
Lawley, D. N. (1940). The estimation of factor loadings by the method of maximum likelihood. Proceedings of the Royal Society of Edinburgh, 60, 64–82.CrossRefGoogle Scholar
Ledermann, W. (1937). On the rank of the reduced correlational matrix in multiple factor analysis. Psychometrika, 2, 85–93.CrossRefGoogle Scholar
Lord, F. M. (1958). Some relations between Guttman's principal components of scale analysis and other psychometric theory. Psychometrika, 23, 291–296.CrossRefGoogle Scholar
McArdle, J. J. (1979). The development of general multivariate software. In Hirschbuhl, (Eds.), Proceedings of the Association for the Development of Computer Based Instructional Systems, Akron, OH: University of Akron Press.Google Scholar
McArdle, J. J., McDonald, R. P. (1984). Some algebraic properties of the reticular action model for moment structures. British Journal of Mathematical and Statistical Psychology, 37, 234–251.CrossRefGoogle ScholarPubMed
McDonald, R. P. (1974). The measurement of factor indeterminacy. Psychometrika, 30, 203–222.CrossRefGoogle Scholar
McDonald, R. P. (1978). A simple comprehensive model for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 31, 59–72.CrossRefGoogle Scholar
McDonald, R. P. (1980). A simple comprehensive model for the analysis of covariance structures. Some remarks on applications. British Journal of Mathematical and Statistical Psychology, 33, 161–183.CrossRefGoogle Scholar
Mosier, C. I. (1937). A factor analysis of certain neurotic symptoms. Psychometrika, 2, 263–286.CrossRefGoogle Scholar
Mosier, C. I. (1938). A note on Dwyer: The determination of the factor loadings of a given test. Psychometrika, 3, 297–299.CrossRefGoogle Scholar
Mosier, C. I. (1939). Determining a simple structure when loadings for certain tests are known. Psychometrika, 4, 149–162.CrossRefGoogle Scholar
Mulaik, S. A. (1972). The foundations of factor analysis, New York: McGraw-Hill.Google Scholar
Mulaik, S. A. (1976). Comments on “The measurement of factorial indeterminacy.”. Psychometrika, 49, 249–262.CrossRefGoogle Scholar
Mulaik, S. A. (1985). Exploratory statistics and empiricism. Philosophy of Science, 52, 410–430.CrossRefGoogle Scholar
Mulaik, S. A. (in press). Toward a synthesis of deterministic and probabilistic formulations of causal relations by the functional relation concept. Philosophy of Science.Google Scholar
Mulaik, S. A., McDonald, R. P. (1978). The effect of additional variables on factor indeterminacy in models with a single common factor. Psychometrika, 43, 177–192.CrossRefGoogle Scholar
Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49, 115–132.CrossRefGoogle Scholar
Neuhaus, J. O., Wrigley, C. (1954). The quartimax method: An analytic approach to orthogonal simple structure. British Journal of Statistical Psychology, 7, 81–91.CrossRefGoogle Scholar
Peterson, P. L. (1984). Semantic indeterminacy and scientific undetermination. Philosophy of Science, 51, 464–487.CrossRefGoogle Scholar
Piaggio, H. T. (1931). The general factor in Spearman's theory of intelligence. Nature, 127, 56–57.CrossRefGoogle Scholar
Piaggio, H. T. (1933). Three sets of conditions necessary for the existence of ag that is real and unique except in sign. British Journal of Psychology, 24, 88–105.Google Scholar
Rao, C. R. (1955). Estimation and tests of significance in factor analysis. Psychometrika, 20, 93–111.CrossRefGoogle Scholar
Roff, M. (1936). Some properties of the communality in multiple-factor theory. Psychometrika, 1, 1–6.CrossRefGoogle Scholar
Saunders, D. R. (1953). An analytic method for rotation to orthogonal simple structure, Princeton, NJ: Educational Testing Service.CrossRefGoogle Scholar
Saunders, D. R. (1961). The rationale for an “oblimax” method of transformation in factor analysis. Psychometrika, 26, 317–324.CrossRefGoogle Scholar
Schönemann, P. H. (1965). On the formal differentiation of traces and determinants, Chapel Hill, NC: The Psychometric Laboratory.Google Scholar
Schönemann, P. H. (1966). The generalized solution for the orthogonal procrustes problem. Psychometrika, 31, 1–16.CrossRefGoogle Scholar
Schönemann, P. H. (1971). The minimum average correlation between equivalent sets of uncorrelated factors. Psychometrika, 36, 21–30.CrossRefGoogle Scholar
Schönemann, P. H. (1973). Erratum. Psychometrika, 38, 149–149.CrossRefGoogle Scholar
Schönemann, P. H. (1985). On the formal differentiation of traces and determinants. Multivariate Behavioral Research, 20, 113–139.CrossRefGoogle ScholarPubMed
Schönemann, P. H., Steiger, J. H. (1976). Regression component analysis. British Journal of Statistical Psychology, 29, 175–189.Google Scholar
Schönemann, P. H., Wang, M. M. (1972). Some new results on factor indeterminacy. Psychometrika, 37, 61–91.CrossRefGoogle Scholar
Soles, D. H. (1984). On the indeterminacy of action. Philosophy of Social Science, 14, 457–488.CrossRefGoogle Scholar
Spearman, C. (1903). General intelligence, objectivity determined and measured. American Journal of Psychology, 15, 201–293.CrossRefGoogle Scholar
Spearman, C. (1927). The abilities of man, New York: MacMillan.Google Scholar
Spearman, C. (1929). The uniqueness of “g”. Journal of Educational, Psychology, 20, 212–216.CrossRefGoogle Scholar
Spearman, C. (1933). The uniqueness and exactness ofg. British Journal of Psychology, 24, 106–108.Google Scholar
Steiger, J. (1979). Factor indeterminacy in the 1930's and 1970's: Some interesting parallels. Psychometrika, 44, 157–167.CrossRefGoogle Scholar
Steiger, J. H., Schönemann, P. H. (1978). A history of the factor indeterminacy. In Shye, S. (Eds.), Theory construction and data analysis in the behavioral sciences, San Francisco: Jossey-Bass.Google Scholar
Stephenson, W. (1936). The foundations of psychometry: Four factor systems. Psychometrika, 1, 195–209.CrossRefGoogle Scholar
Thomson, G. H. (1934). On measuringg ands by tests which break theg-hierarchy. Journal of Educational Psychology, 25, 204–210.Google Scholar
Thomson, G. L. H. (1935). The definition and measurement ofg (general intelligence). Journal of Educational Psychology, 26, 241–262.CrossRefGoogle Scholar
Thurstone, L. L. (1936). The factorial isolation of primary abilities. Psychometrika, 1, 175–182.CrossRefGoogle Scholar
Thurstone, L. L. (1937). Current misuse of the factorial methods. Psychometrika, 2, 73–76.CrossRefGoogle Scholar
Thurstone, L. L. (1944). A multiple group method of factoring the correlation matrix. Psychometrika, 10, 73–78.CrossRefGoogle Scholar
Tucker, L. R. (1940). The role of correlated factors in factor analysis. Psychometrika, 5, 141–152.CrossRefGoogle Scholar
Wilson, E. B. (1928). Review of “The abilities of man, their nature and measurement”. Science, 67, 244–248.CrossRefGoogle Scholar
Wilson, E. B. (1928). On hierarchical correlation systems. Proceedings of the National Academy of Sciences, 14, 283–291.CrossRefGoogle ScholarPubMed
Wilson, E. B. (1929). Comments on Professor Spearman's note. Journal of Educational Psychology, 20, 217–223.CrossRefGoogle Scholar
Wilson, E. B., Worcester, J. (1939). Note on factor analysis. Psychometrika, 4, 133–148.CrossRefGoogle Scholar
Wolfle, D. (1940). Factor analysis to 1940. Psychometrika Monograph No. 3, 5(4, Pt. 2).Google Scholar