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The Meaning and Strategic Use of Factor Analysis

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Handbook of Multivariate Experimental Psychology

Part of the book series: Perspectives on Individual Differences ((PIDF))

Abstract

The general surveys of multivariate analysis methods in other chapters in this and the first edition give some idea of the relation of factor analysis to other methods in a mathematical sense. However, factor analysis differs also in a wide, experimental, strategic sense, from, for example, both multiple-correlation linear equations, and discriminant functions, in not arbitrarily choosing a criterion variable or criterion group, but in arriving at a reduced number of abstract variables and a weighting of observed variables according to structural indications in the data itself. It is thus a means of creating concepts, not merely of employing them or checking their fit to new data, though the new methods of Maxwell, Lawley, and Jöreskog also fit it for hypothesis testing.

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References

  • Ahmavaara, Y. Transformation analysis of factorial data. Annales Academiae Scientiarum Fennicae Series B, 1985, 88, 2.

    Google Scholar 

  • Apport, G. W. Personality, New York: Holt, 1937.

    Google Scholar 

  • Baggaley, A. R., and Cattell, R. B. A comparison of exact and approximate linear function estimates of oblique factor scores. British Journal of Statistical Psychology, 1956, 9, 83–86.

    Google Scholar 

  • Bargmann, R. A comparison of new analytic methods for the determination of simple structure. Frankfurt am Main: Hochschule fuer Internationale Paedagogische Forschung, 1953a (mimeographed).

    Google Scholar 

  • Bargmann, R. The statistical significance of simple structure in factor analysis. Frankfurt am Main: Hochschule fuer Internationale Paedagogische Forschung, 1953b (mimeographed).

    Google Scholar 

  • Bartlett, M. Internal and external factor analysis. British Journal of Psychology, 1948, 1, 73–81.

    Google Scholar 

  • Bechtoldt, H. P. An empirical study of the factor analysis stability hypothesis. Psychometrika, 1961, 26, 405–432.

    Google Scholar 

  • Bechtoldt, H. P. Factor analysis and the investigation of hypotheses. Perceptual Motor Skills, 1962, 14, 319–342.

    Google Scholar 

  • Bechtoldt, H. P., Benton, A. L., and Fogel, M. L. An application of factor analysis in neuropsychology. Psychological Record, 1962, 12, 147–156.

    Google Scholar 

  • Becker, W. C. A comparison of the factor structure and other properties of the 16 P.F. and the Guilford–Martin personality inventories. Educational and Psychological Measurement, 1961, 21, 383–404.

    Google Scholar 

  • Broverman, D. M. Effects of score transformations in Q and R factor analysis techniques. Psychological Review, 1961, 68, 68–80.

    Google Scholar 

  • Broverman, D. M. Normative and ipsative measurement in psychology. Psychological Review, 1962, 69, 295–305.

    Google Scholar 

  • Brunswik, E. Perception and the representative design of psychological experiments. Berkeley: University of California Press, 1956.

    Google Scholar 

  • Burt, C. L. Correlations between persons. British Journal of Psychology, 1937, 28, 59–96.

    Google Scholar 

  • Burt, C. L. The factors of the mind: An introduction to factor analysis in psychology. New York: Macmillan Co., 1941.

    Google Scholar 

  • Burt, C. L. Tests of significance in factor studies. British Journal of Psychology, 1952, 5, 109–133.

    Google Scholar 

  • Campbell, D. T., and Fiske, D. W. Convergent and discriminant validation by the multitrait–multimethod matrix. Psychological Bulletin, 1959, 56, 81–105.

    PubMed  Google Scholar 

  • Carroll, J. B. Oblimin rotation solution in factor analysis. Computing program for the IBM 704. Harvard University, 1958.

    Google Scholar 

  • Cattell, R. B. “Parallel proportional profiles” and other principles for determining the choice of factors by rotation. Psychometrika, 1944, 9, 267–283.

    Google Scholar 

  • Cattell, R. B. The diagnosis and classification of neurotic states: A reinterpretation of Eysenck’s factors. Journal of Nervous and Mental Disease, 1945, 102, 576–589.

    PubMed  Google Scholar 

  • Cattell, R. B. The description and measurement of personality. New York: World Book, 1946.

    Google Scholar 

  • Cattell, R. B. A note on factor invariance and the identification of factors. British Journal of Psychology, 1949, 2, 134–138.

    Google Scholar 

  • Cattell, R. B. Personality: A systematical, theoretical, and factual study. New York: McGraw–Hlll, 1950.

    Google Scholar 

  • Cattell, R. B. Factor analysis. New York: Harper, 1952a.

    Google Scholar 

  • Cattell, R. B. The three basic factor analytic research designs—Their interrelationships and derivatives. Psychological Bulletin, 1952b, 49, 499–520.

    PubMed  Google Scholar 

  • Cattell, R. B. Growing points in factor analysis, Australian Journal of Psychology, 1954, 6, 105–140.

    Google Scholar 

  • Cattell, R. B. Validation and intensification of the Sixteen Personality Factor Questionnaire Journal of Clinical Psychology, 1956, 12, 205–214.

    PubMed  Google Scholar 

  • Cattell, R. B. Personality and motivation structure and measurement. New York: World Book, 1957.

    Google Scholar 

  • Cattell, R. B. The dynamic calculus: A system of concepts derived from objective motivation measurement. In G. Lindzey (Ed.), The assessment of human motives. New York: Reinehart, 1958a.

    Google Scholar 

  • Cattell, R. B. Extracting the correct number of factors in factor analysis. Educational Psychological Measurement, 1958b, 18, 791–838.

    Google Scholar 

  • Cattell, R. B. The dynamic calculus: Concepts and crucial experiments. In M. R. Jones (Ed.), Nebraska symposium of motivation. Lincoln: University of Nebraska Press, 1959.

    Google Scholar 

  • Cattell, R. B. Theory of situational, instrument, second order, and refraction factors in personality structure research. Psychological Bulletin, 1961, 58, 160–174.

    PubMed  Google Scholar 

  • Cattell, R. B. The basis of recognition and interpretation of factors. Educational and Psychological Measurement, 1962, 22, 667–697.

    Google Scholar 

  • Cattell, R. B. Personality, role, mood, and situation-perception: A unifying theory of modulators. Psychological Review, 1963a, 70, 1–18.

    PubMed  Google Scholar 

  • Cattell, R. B. Theory of fluid and crystallized intelligence: A critical experiment. Journal of Educational Psychology, 1963b, 54, 1–22.

    Google Scholar 

  • Cattell, R. B. The configurative method for surer identification of personality dimensions, notably in child study. Psychological Reports, 1965a, 16, 269–270.

    PubMed  Google Scholar 

  • Cattell, R. B. Higher order structures: Reticular vs. hierarchical formulae for their interpretation. In C. Banks and P. L. Broadhurst (Eds.), Studies in psychology. London: University of London Press, 1965h.

    Google Scholar 

  • Cattell, R. B. Cultural and political-economic psychology. In R. B. Cattell (Ed.), Handbook of multivariate experimental psychology. Chicago: Rand McNally, 1966a.

    Google Scholar 

  • Cattell, R. B. The scree test of the number of significant factors. Multivariate Behavioral Research, 1966b, 1, 140–161.

    Google Scholar 

  • Cattell, R. B. The scientific use of factor analysis. New York: Praeger, 1978.

    Google Scholar 

  • Cattell, R. B. Personality and learning theory. Vol. 1. New York: Springer, 1979.

    Google Scholar 

  • Cattell, R. B. Personality and learning theory. Vol. 2, New York: Springer, 1980.

    Google Scholar 

  • Cattell, R. B., and Baggaley, A. R. The salient variable similarity index for factor matching. British Journal of Statistical Psychology, 1960, 13, 33–46.

    Google Scholar 

  • Cattell, R. B., and Brennan, J. The confactor approximation to an oblique solution. Multivariate Behavioral Research, 1977, 3, 103–110.

    Google Scholar 

  • Cattell, R. B., and Brennan, J. The effects of factoring ipsatzed scores, 1987 (in press).

    Google Scholar 

  • Cattell, R. B., and Cattell, A. K. S. Factor rotation for proportional profiles: Analytical solution and an example. British Journal of Statistical Psychology, 1955, 8, 83–92.

    Google Scholar 

  • Cattell, R. B., and Coulter, M. A. Principles of behavioral taxonomy and the taxonome program. British Journal of Mathematical and Statistical Psychology, 1966, 19, 237–269.

    PubMed  Google Scholar 

  • Cattell, R. B., and Dickman, K. A dynamic model of physical influences demonstrating the necessity of oblique simple structure. Psychological Bulletin, 1962, 59, 389–400.

    PubMed  Google Scholar 

  • Cattell, R. B., and Digman, J. A theory of the structure of perturbations in observer ratings and questionnaire data in personality research. Behavioral Science, 1964, 9, 341–358.

    PubMed  Google Scholar 

  • Cattell, R. B., and Foster, M. J. The rotoplot program for multiple single-plane, visually-guided rotation. Behavioral Science, 1963, 8, 156–165.

    Google Scholar 

  • Cattell, R. B., and Gorsuch, R. L. The uniqueness and significance of simple structure demonstrated by contrasting organic “natural structure” and “random structure” data. Psychometrika, 1963, 28, 55–67.

    Google Scholar 

  • Cattell, R. B., and Jaspars, J. A general plasmode (No. 30-10-5-2) for factor analytic exercises and researches. Monograph of the Society of Multivariate Experimental Psychology (Whole No. 3), 1967.

    Google Scholar 

  • Cattell, R. B., and Muerle, J. L. The “maxplane” program for factor rotation to oblique simple structure. Educational and Psychological Meausrement, 1960, 20, 569–590.

    Google Scholar 

  • Cattell, R. B., and Nesselroade, J. R. The “fidelity” plasmode, with known higher order structure and error. Multivariate Behavioral Research, 1987 (in press).

    Google Scholar 

  • Cattell, R. B., and Raymond, J. S. The spectrad model for attribution research: An extension of trait view theory. Interdisciplinaria, 1982, 3, 135–154.

    Google Scholar 

  • Cattell, R. B., and Scheier, I. H. Factors in personality change: A discussion of the condition—response incremental design and application to 69 personality response measures and three stimulus conditions. Urbana: University of Illinois, Laboratory for Personality Assessment and Group Behavior, 1958.

    Google Scholar 

  • Cattell, R. B., and Scheier, I. H. The meaning and measurement of neuroticism and anxiety. New York: Ronald Press, 1961.

    Google Scholar 

  • Cattell, R. B., and Sullivan, W. The scientific nature of factors: A demonstration by cups of coffee. Behavioral Science, 1962, 7, 184–193.

    Google Scholar 

  • Cattell, R. B., Stice, G. F., and Eber, M. The 16 Personality Factor Questionnaire. Champaign, Ill.: Institute for Personality and Ability Testing, 1949.

    Google Scholar 

  • Coombs, C. M., and Kao, R. C. Nonmetric factor analysis. Bulletin of the Department of Engineering Research, No. 38. Ann Arbor: University of Michigan, 1955.

    Google Scholar 

  • Cronbach, L. J. Coefficient alpha and the internal structure of tests. Psychometrika, 1951, 16, 297–334.

    Google Scholar 

  • Eber, H. W. Toward oblique simple structure: A new version of Cattell’s Maxplane Rotation Program for the 7094. Multivariate Behavioral Research, 1966, 1, 112–125.

    Google Scholar 

  • Eysenck, H. J. Dimensions of personality. London: Kegan Paul, 1947.

    Google Scholar 

  • Eysenck, H. J. Experiments in personality. London: Routledge & Kegan Paul, 1960.

    Google Scholar 

  • Gibson, W. A. Non-linear factors in two dimensions. Psychometrika, 1960, 25, 381–392.

    Google Scholar 

  • Gorsuch, R. L. Factor analysis. Philadelphia: Saunders, 1984.

    Google Scholar 

  • Guttman, L. Image theory for the structure of quantitative variates. Psychometrika, 1953, 18, 277–296.

    Google Scholar 

  • Harman, H. Modern factor analysis. Chicago: University of Chicago Press, 1960.

    Google Scholar 

  • Harris, C. W. Some Rao—Guttman relationships. Psychometrika, 1962, 27, 247–263.

    Google Scholar 

  • Harris, C. W., and Kaiser, H. F. Oblique factor analysis solutions by orthogonal transformations. Psychometrika, 1964, 29, 347–362.

    Google Scholar 

  • Hakstian, R., Rogers, W., and Cattell, R. B. The behavior of number of factor rules with simulated data. Multivariate Behavioral Research, 1982, 17, 193–219.

    Google Scholar 

  • Hendrickson, A. F., and White, P. O. PROMAX: A quick method for rotation to oblique simple structure. British Journal of Statistical Psychology, 1964, 17, 65–70.

    Google Scholar 

  • Henrysson, S. Applicability of factor analysis in the behavioral sciences. Stockholm: Almqvist & Wiksells, 1957.

    Google Scholar 

  • Horn, J. L. On the estimation of factor scores. Educational and Psychological Measurement,1964, 24, 525–527.

    Google Scholar 

  • Horn, J. F. Summing up: Evaluation of the evolution of a psychological theory. Multivariate Behavioral Research, 1984, 19, 337–343.

    Google Scholar 

  • Horst, P. Matrix algebra for social scientists. New York: Holt, Rinehart & Winston, 1963.

    Google Scholar 

  • Horst, P. Factor analysis of data matrices. New York: Holt, 1965.

    Google Scholar 

  • Humphreys, L. G. Characteristics of type concepts with special reference to Sheldon’s typology. Psychological Bulletin, 1957, 54, 218–228.

    PubMed  Google Scholar 

  • Humphreys, L. G. The organization of human abilities. American Psychologist, 1962, 17, 475–483.

    Google Scholar 

  • Hundleby, J. D., Pawlik, K., and Cattell, R. B. Personality factors in objective test devices. San Diego: Knapp, 1965.

    Google Scholar 

  • Hurley, J. R., and Cattell, R. B. The Procrustes Program: Producing direct rotation to test a hypothesized factor structure. Behavioral Science, 1962, 7, 258–262.

    Google Scholar 

  • Jöreskog, K. G. Some contributions to maximum likelihood factor analysis. Psychometrika, 1967, 32, 443–482.

    Google Scholar 

  • Jöreskog, K. G., and Sörbom, D. Advances in factor analysis and structural equation models. Cambridge, Mass.: ABT Books, 1970.

    Google Scholar 

  • Kaiser, H. F. The varimax criterion for analytic rotation in factor analysis. Psychometrika, 1958, 23, 187–200.

    Google Scholar 

  • Kaiser, H. F. Relating factors between studies based upon different individuals. Unpublished manuscript, 1960.

    Google Scholar 

  • Kaiser, H. F. Image analysis. In C. W. Harris (Ed.), Problems in measuring change. Madison: University of Wisconsin Press, 1963.

    Google Scholar 

  • Kaiser, H. F., and Caffrey, J. Alpha factor analysis. Psychometrika, 1965, 30, 1–14.

    PubMed  Google Scholar 

  • Kaiser, H. F., and Dickman, K. W. Analytic determination of common factors. American Psychologist, 1959, 14, 425.

    Google Scholar 

  • Kline, P. The use of the Cattell 16PF and Eysenck’s EPI in Ghana. British Journal of Social and Clinical Psychology, 1984, 6, 97–107.

    Google Scholar 

  • Landahi, H. D. Centroid orthogonal transformations. Psychometrika, 1938, 3, 219–223.

    Google Scholar 

  • Lawley, D. N. The estimation of factor loadings by the method of maximum likelihood. Proceedings of the Royal Society of Edinburgh, 1940, 60, 64–82.

    Google Scholar 

  • Lawley, D. N. Tests of significance for the latent roots of covariance and correlation matrices. Biometrika, 1956, 43, 128–136.

    Google Scholar 

  • Lawley, D. N., and Maxwell, A. E. Factor analysis as a statistical method. London: Butterworths, 1963.

    Google Scholar 

  • McNemar, Q. On the sampling errors of factor loadings. Psychometrika, 1941, 6, 141–152.

    Google Scholar 

  • Overall, J. E. A common solution for transposed factor analyses. Privately circulated manuscript, 1964.

    Google Scholar 

  • Peterson, D. R. The scope and generality of verbally defined personality factors. Psychological Review, 1965, 72, 48–59.

    PubMed  Google Scholar 

  • Pinzka, C., and Saunders, D. R. Analytic rotation to simple structure. II. Extension to an oblique solution (RB-54–31). Princeton, N.J.: Educational Testing Service, 1954 (multilithed).

    Google Scholar 

  • Rao, C. R. Estimation and test of significance in factor analysis. Psychometrika, 1955, 20, 93–111.

    Google Scholar 

  • Ross, J. Informational coverage and correlational analysis. Psychometrika, 1962, 27, 297–306.

    Google Scholar 

  • Ross, J. The relation between test and person factors. Psychological Review, 1963, 70, 432–443.

    PubMed  Google Scholar 

  • Rummel, R. J. Dimensions of nations. Beverly Hills, Calif.: Sage Publications, 1972.

    Google Scholar 

  • Saunders, D. R. Factor analysis. I. Some effects of chance error. Psychometrika, 1948, 13, 251–257.

    PubMed  Google Scholar 

  • Saunders, D. R. Practical methods in the direct factor analysis of psychological score matrices. Unpublished doctoral dissertation, University of Illinois, 1950.

    Google Scholar 

  • Saunders, D. R. Moderator variables in prediction. Educational and Psychological Measurement, 1956, 16, 209–222.

    Google Scholar 

  • Schmid, J., and Leiman, J. M. The development of hierarchical factor solutions. Psychometrika, 1957, 22, 53–61.

    Google Scholar 

  • Schoenemann, P. M. A solution with applications to orthogonal and oblique rotation. Unpublished doctoral dissertation, University of Illinois, 1964.

    Google Scholar 

  • Sokal, R. R. A comparison of five tests for completeness of factor extraction. Transactions of the Kansas Academy of Sciences, 1959, 62, 141–152.

    Google Scholar 

  • Stephenson, W. The study of behavior: Q-technique and its methodology. Chicago: University of Chicago Press, 1953.

    Google Scholar 

  • Thomson, G. M. The factorial analysis of human ability. Boston: Houghton—Mifflin, 1939.

    Google Scholar 

  • Thurstone, L. L. Primary mental abilities. Psychometric Monographs, 1938, No. 1.

    Google Scholar 

  • Thurstone, L. L. Multiple factor analysis. Chicago: University of Chicago Press, 1947.

    Google Scholar 

  • Tryon, R. C. Cluster analysis: Correlation profile and orthometric (factor) analysis for the isolation of unities in mind and personality. Ann Arbor, Mich.: Edwards, 1939.

    Google Scholar 

  • Tucker, L. R. A method for synthesis of factor analysis study. Department Army A.G.O., Personnel Research, Section Report No. 984, 1955.

    Google Scholar 

  • Tucker, L. R. Factor analysis of double centered score matrices. Paper read at the annual meeting of the American Psychological Association, September 1956.

    Google Scholar 

  • Tucker, L. R. An inter-battery method of factor analysis. Psychometrika, 1958, 23, 111–137.

    Google Scholar 

  • Whittle, P. On principle components and least square methods of factor analysis. Skandinavisk Aktvar, 1952, 35, 223–239.

    Google Scholar 

  • Wrigley, C., Saunders, D. R., and Neuhaus, J. O. Application of the Quartimax method of rotation to Thurstone’s primary mental abilities study. Psychometrika, 1958, 23, 151–170.

    Google Scholar 

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Cattell, R.B. (1988). The Meaning and Strategic Use of Factor Analysis. In: Nesselroade, J.R., Cattell, R.B. (eds) Handbook of Multivariate Experimental Psychology. Perspectives on Individual Differences. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0893-5_4

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