Construct Explication through Factor or Component Analysis: A Review and Evaluation of Alternative Procedures for Determining the Number of Factors or Components
 Wayne F. Velicer,
 Cheryl A. Eaton,
 Joseph L. Fava
 … show all 3 hide
Abstract
The concept of a construct is central to many of the advances in the behavioral sciences during the second half of this century. Constructs serve to summarize, organize, and facilitate the interpretation of data. The concept of a construct also permits us to move directly from data analysis to theory development and testing. Factor analysis and component analysis are two very similar methods that facilitate the transition from dealing with a large number of observed variables to a smaller number of constructed or latent variables. Douglas Jackson employed factor or component analysis as an integral part of his sequential approach to the development of psychological measures (Jackson, 1970, 1971). It has become a standard part of measure development and is one of the most employed statistical procedures in the behavioral sciences.
 Allen, S. J & Hubbard, R. (1986). Regression equations for the latent roots of random data correlation matrices with unities on the diagonal. Multivariate Behavioral Research, 21, 393–398. CrossRef
 Anderson, R. D., Acito, F. & Lee, H. (1982). A simulation study of three methods for determining the number of image components. Multivariate Behavioral Research, 17, 493–502. CrossRef
 Bartlett, M. S. (1950). Tests of significance in factor analysis. British Journal of Psychology, Statistical Section, 3, 77–85. CrossRef
 Bartlett, M. S. (1951). A further note on tests of significance in factor analysis. British Journal of Psychology, Statistical Section, 4, 1–2. CrossRef
 Bentler, P. M. (1980). Multivariate analysis with latent variables: Causal modeling. In M. R. Rosenzweig & L. W. Porter (eds.), Annual Review of Psychology, (pp. 419–454). Stanford, CA Annual Reviews, Inc.
 Bentler, P.M. & Kano, Y, (1990). On the equivalence of factors and components. Multivariate Behavioral Research, 51, 67–74. CrossRef
 Bookstein, F. L. (1990). Least squares and latent variables. Multivariate Behavioral Research, 25, 75–80. CrossRef
 Boomsma, A. (1983). On the robustness of LJSREL (maximum likelihood) estimates against small sample sizes and nonnormality. Unpublished doctoral dissertation, kijksuniversiteit Gronigen, the Netherlands.
 Cattell, R. B. (1966). The scree test for the number of fastors. Multivariate Behavioral Research, 1, 245–276. CrossRef
 Cattell, R. B. & Jaspers, J. (1967). A general plasmode for factor analytic exercises and research. Multivariate Behavioral Research Monographs, 3, 1–212.
 Cattell, R. B. & Vogelmann, S. A (1977). A comprehensive trial of the scree and KaiserGuttman criteria for determining the number of factors. Multivariate Behavioral Research, 12, 289–325. CrossRef
 Cliff, N. (1970). The relation between sample and population characteristic vectors. Psychometrika, 35, 163–178. CrossRef
 Cliff, N. (1988). The eigenvalue greater than one rule and the reliability of components. Psychological Bulletin, 103, 276–279. CrossRef
 Cliff, N. & Hamburger, C. (1967). Study of sampling errors in factor analysis by means of artificial experiments. Psychological Bulletin, 68, 430–445. CrossRef
 Crawford, C. B. & Koopman, P. (1973). A note on Horn’s test for the number of factors in factor analysis. Multivariate Behavioral Research, 8, 117–125. CrossRef
 Eaton, C. A., Velicer, W. F., & Fava, J. L. (1999). Determining the Number of Components: An Evaluation of Parallel Analysis and the Minimum Average Partial Correlation Procedures. Manuscript under review.
 Fava, J. L., & Velicer, W.F. (1992a). An empirical comparison of factor, image, component, and scale scores. Multivariate Behavioral Research, 27, 301–322. CrossRef
 Fava, J. L., & Velicer, W.F. (1992b). The effects of overextraction on factor and component analysis. Multivariate Behavioral Research, 27, 387–415. CrossRef
 Fava, J. L., & Velicer, W.F. (1996). The effects of underextraction in factor and component analysis. Educational and Psychological Measurement, 56, 907–929. CrossRef
 Gorsuch, R. L. (1973). Using Bartlett’s significance test to determine the number of factors to extract. Educational and Psychological Measurement, 33, 361–364. CrossRef
 Gorsuch, R. L. (1983). Factor Analysis. (2nd ed.) Hillsdale, N. J.: Lawrence Erlbaum.
 Gorsuch, R.L. (1991). UniMult Guide. Altadena, CA: UniMult
 Guttman, L. (1990). Common factor analysis versus component analysis Some well and little known facts. Multivariate Behavioral Research, 25, 33–39. CrossRef
 Guttman, L. (1954). Some necessary conditions for common factor analysis. Psychometrika, 19, 149–162. CrossRef
 Guadagnoli, E. & Velicer, W. F. (1988). Relation of sample size to the stability of component patterns. Psychological Bulletin, 103, 265–275. CrossRef
 Guadagnoli, E. & Velicer, W. (1991). A comparison of pattern matching indices. Multivariate Behavioral Research, 26, 323–343. CrossRef
 Hakstian, A R., Rogers, W. T., & Cattell, R. B. (1982). The behavior of numberoffactors rules with simulated data. Multivariate Behavioral Research, 17, 193–219. CrossRef
 Hays, RD. (1987). PARALLEL: A program for performing parallel analysis. Applied Psychological Measurement, 11, 58. CrossRef
 Holden, R. R., Longman, R. S., Cota, A. A., & Fekken, G. C. (1989). PAR: Parallel analysis routine for random data eigenvalue estimation. Applied PsychologicalMeasurement, 13, 192. CrossRef
 Horn, J.L. (1965). A Rationale and test for the number of factors in factor analysis. Psychometrika, 30, 179–185. CrossRef
 Horn, J.L & Engstrom, R. (1979). Cattell’s scree test in relation to Bartlett’s chisquare test and other observations on the number of factors problem. Multivariate Behavioral Research, 14, 283–300. CrossRef
 Howe, H. G. (1955). Some contributions to factor analysis. Oak Ridge, TH: Oak Ridge National Laboratory. CrossRef
 Hubbard, R. & Allen, S. J. (1987). An empirical comparison of alternate methods for principal components extractioa. Journal of Business Research, 15, 173–190. CrossRef
 Jackson, D.N. (1970). A sequential system for personality scale development. In CD. Spielberger (Ed.), Current Topics in Clinical and Community Psychology, (Vol. 2, pp. 61–96). New York: Academic Press.
 Jackson, D. N. (1971). The dynamics of structured personality tests. Psychological Review, 78, 229–248. CrossRef
 Jackson, D. N., & Chan, D. W. (1980). Maximumlikelihood estimation in common factor analysisA cautionary note. Psychological Bulletin, 88, 502–508. CrossRef
 Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20, 141–151. CrossRef
 Lautenschlager, G. J. (1989a). A comparison of alternatives to conducting Monte Carlo analyses for determining parallel analysis criteria. Multivariate Behavioral Research, 24, 365–395. CrossRef
 Lautenschlager, G. J. (1989b). PARANALTOK: A program for developing parallel analysis criteria. Applied Psychological Measurement, 13, 176. CrossRef
 Lautenschlager, G. J., Lance, C. E., & Flaherty, V. L. (1989). Parallel analysis criteria: Revised equations for estimating the latent roots of random data correlation matrices. Educational and Psychological Measurement, 49, 339–345. CrossRef
 Lee, H. B. & Comrey, A. L. (1979). Distortions in a commonly used factor analytic procedure. Multivariate Behavioral Research, 14, 301–321. CrossRef
 Linn, R. L. (1968). A Monte Carlo approach to the number of factors problem. Psychometrika, 33, 37–71. CrossRef
 Loehlin, J.C. (1990). Component analysis versus common factor analysis: A case of disputed authorship. Multivariate Behavioral Research, 25, 29–31. CrossRef
 Longman, R. S., Cota, A. A., Holden, R. R., & Fekken, G. C. (1989a). A regressionequation for the parallel analysis criterion in principal components analysis: Mean and 95th percentile eigenvalues. Multivariate Behavioral Research, 24, 59–69. CrossRef
 Longman, R. S., Cota, A. A., Holden, R. R., & Fekken, G. C. (1989b). PAM: A double precision FORTRAN routine for the parallel analysis method in principal components analysis. Behavior Research Methods, Instruments, and Computers, 21, 477–480. CrossRef
 Longman, R. S., Cota, A. A., Holden, R. R., & Fekken, G. C. (1991). Implementing parallel analysis for principal components analysis: A comparison of six methods. Unpublished manuscript
 Longman, R. S., Holden, R. R., & Fekken, G. C. (1991). Anomalies in the Allen and Hubbard parallel analysis procedure. Applied Psychological Measurement, 15, 95–97. CrossRef
 MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S. (1999). Sample size in factor analysis. Psychological Methods, 4, 84–99. CrossRef
 Marsh, H.W., Balla, J. R., & McDonald, R. P. (1988). Goodness of fit indices in confirmatory factor analysis: The effect of sample size. Psychological Bulletin, 103, 391–410. CrossRef
 McArdle, J.J. (1990). Principles versus principals of structural factor analysis. Multivariate Behavioral Research, 25, 81–87. CrossRef
 Montanelli, Jr., R. G. (1975). A computer program to generate sample correlation and covariance matrices. Educational and Psychological Measurement, 35, 195–197. CrossRef
 Montanelli, Jr., R. G. & Humphreys, L. G. (1976). Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A Monte Carlo study. Psychometrika, 41, 341–348. CrossRef
 Morrison, D. F. (1976). Multivariate Statistical Methods. (2^{nd} ed). New York: McGrawHill
 Mulaik, S.A (1990). Blurring the distinctions between component analysisand common factor analysis. Multivariate Behavioral Research, 25, 53–59. CrossRef
 Odell, P. L. & Feiveson, A. H. (1966). A numerical procedure to generate a sample covariance matrix. Journal of the American Statistical Association, 61, 199–203. CrossRef
 Reddon, J. R (1985). MAPF and MAPS: Subroutines for the number of principal components. Applied Psychological Measurement, 9, 97. CrossRef
 Revelle, W. & Rocklin, T. (1979). Very simple structure: An alternative procedure for estimating the optimal number of interpretable factors. Multivariate Behavioral Research, 14, 403–414. CrossRef
 Rozeboom, W.W. (1990). Whatever happened to broad perspective? Multivariate Behavioral Research, 25, 61–65. CrossRef
 Schonemann, P. H. (1990). Facts, fictions, and common sense about factors and components. Multivariate Behavioral Research, 25, 47–51. CrossRef
 Steiger, J.H. (1990). Some additional thoughts on components, factors, and factor indeterminacy. Multivariate Behavioral Research, 25, 47–51. CrossRef
 Tucker, L. R., Koopman, R. F., & Linn, R. L. (1969). Evaluation of factor analytic research procedures by means of simulated correlation matrices. Psychometrika, 34, 421–459. CrossRef
 Tucker, L.R., & Lewis, C. (1973). A reliability coefficient for maximum likelihoodfactor analysis. Psychometrika, 38, 1–10. CrossRef
 Velicer, W. F. (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 31, 321–327. CrossRef
 Velicer, W. F. & Fava, J. L. (1987). An evaluation of the effects of variable sampling on component, image, and factor analysis. Multivariate Behavioral Research, 22, 193–209. CrossRef
 Velicer, W. F. & Fava, J. S. (1998). The effects of variable and subject sampling on factor pattern recovery. Psychological Methods, 3, 231–251. CrossRef
 Velicer, W. F., Fava, J. L., Zwick, W. R., & Harrop, J. W. (1990). CAX (Computer program). Kingston, RI: University of Rhode Island
 Velicer, W. F., & Jackson, D. N. (1990a). Component analysis versus common factor analysis: Some issues in selecting an appropriate procedure. Multivariate Behavioral Research, 25, 1–28. CrossRef
 Velicer, W. F., & Jackson, D. N. (1990b). Component analysis versus common factor analysissome further observations. Multivariate Behavioral Research, 25, 97–114. CrossRef
 Velicer, W. F., Peacock, A. C., & Jackson, D. N. (1982). A comparison of component and factor patterns: A Monte Carlo approach. Multivariate Behavioral Research, 17, 371–388. CrossRef
 Widaman, K. F. (1990). Bias in pattern loadings represented by common factor analysis and component analysis. Multivariate Behavioral Research, 25, 89–95. CrossRef
 Wood, J.M., Tataryn, D. J., & Gorsuch, R. L. (1996). Effects of Underand overextraction on principal axis factor analysis with varimax rotation. Psychological Methods, 1, 254–365. CrossRef
 Yeomans, K. A. & Golder, P. A. (1982). The GuttmanKaiser criterion as a predictor of the number of common factors. The Statistician, 31, 221–229. CrossRef
 Zwick, W. R. & Velicer W. F. (1982). Factors influencing four rules for determining the number of components to retain. Multivariate Behavioral Research, 17, 253–269. CrossRef
 Zwick, W. R. & Velicer W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432–442. CrossRef
 Title
 Construct Explication through Factor or Component Analysis: A Review and Evaluation of Alternative Procedures for Determining the Number of Factors or Components
 Book Title
 Problems and Solutions in Human Assessment
 Book Subtitle
 Honoring Douglas N. Jackson at Seventy
 Book Part
 Section I
 Pages
 pp 4171
 Copyright
 2000
 DOI
 10.1007/9781461543978_3
 Print ISBN
 9781461369783
 Online ISBN
 9781461543978
 Publisher
 Springer US
 Copyright Holder
 Springer Science+Business Media Dordrecht
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors

 Richard D. Goffin ^{(1)}
 Edward Helmes ^{(2)}
 Editor Affiliations

 1. University of Western Ontario
 2. Edith Cowan University
 Authors
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