Problèmes d'indétermination en analyse en facteurs et analyse en composantes principales optimale

Fine, J.

Fine, J.

Revue de Statistique Appliquée, Tome 41 (1993) no. 4, pp. 45-72.

EuDML MR Zbl

@article{RSA_1993__41_4_45_0,
     author = {Fine, J.},
     title = {Probl\`emes d'ind\'etermination en analyse en facteurs et analyse en composantes principales optimale},
     journal = {Revue de Statistique Appliqu\'ee},
     pages = {45--72},
     publisher = {Soci\'et\'e de Statistique de France},
     volume = {41},
     number = {4},
     year = {1993},
     mrnumber = {1255292},
     zbl = {0972.62525},
     language = {fr},
     url = {http://www.numdam.org/item/RSA_1993__41_4_45_0/}
}

TY  - JOUR
AU  - Fine, J.
TI  - Problèmes d'indétermination en analyse en facteurs et analyse en composantes principales optimale
JO  - Revue de Statistique Appliquée
PY  - 1993
SP  - 45
EP  - 72
VL  - 41
IS  - 4
PB  - Société de Statistique de France
UR  - http://www.numdam.org/item/RSA_1993__41_4_45_0/
LA  - fr
ID  - RSA_1993__41_4_45_0
ER  -

%0 Journal Article
%A Fine, J.
%T Problèmes d'indétermination en analyse en facteurs et analyse en composantes principales optimale
%J Revue de Statistique Appliquée
%D 1993
%P 45-72
%V 41
%N 4
%I Société de Statistique de France
%U http://www.numdam.org/item/RSA_1993__41_4_45_0/
%G fr
%F RSA_1993__41_4_45_0

Fine, J. Problèmes d'indétermination en analyse en facteurs et analyse en composantes principales optimale. Revue de Statistique Appliquée, Tome 41 (1993) no. 4, pp. 45-72. http://www.numdam.org/item/RSA_1993__41_4_45_0/

Bibliographie
Cité par

(1) Aitkin M., 1985, Comments on D.J. Bartholomew, Foundations of Factor Analysis : some practical implications, Brit. J. Math. Statist. Psych., 38, 127-128.

(2) Anderson T.W., 1963, Asymptotic theory for Principal Component Analysis. Ann. Math. Statist., 34, 122-148. | MR | Zbl

(3) Anderson T.W., 1984a, Estimating linear statistical relationships, Ann. Statist., 12, 1-45. | MR | Zbl

(4) Anderson T.W., 1984b, 2ème éd., An introduction to Multivariate statistical analysis, Wiley.

(5) Anderson T.W. et Rubin M., 1956, Statistical inference in Factor Analysis. Proceed. 3rd Berkeley Symp. Math. Statist. Probab, 5, 11-150. | Zbl

(6) Bartholomew D.J., 1981, Posterior analysis of Factor Model, Brit. J. Math. Statist. Psych., 34, 92- 99. | MR | Zbl

(7) Bartholomew D.J., 1984, The Foundations of Factor Analysis, Biometrika, 71, 221-232. | MR | Zbl

(8) Bartholomew D.J., 1985a, Foundations of Factor Analysis : some practical implications, Brit. J. Math. Statist. Psych., 38, 1-10. | Zbl

(9) Bartholomew D.J., 1985b, Reply to discussion on Foundations of Factor Analysis, Brit. J. Math. Statist. Psych., 38, 138-140.

(10) Bartholomew D.J., 1987, Latent variable models and Factor Analysis, Griffin. | Zbl

(11) Bartlett M.S., 1937, The statistical conception of mental factors, Brit. J. Psych., 28, 97-104.

(12) Bartlett M.S., 1938, Methods of estimating mental factors, Nature, 141, 609-610.

(13) Bekker P.A. et De Leeuw, J., 1987, The rank of reduced dispersion matrices, Psychometrika, 52, 125- 135. | MR | Zbl

(14) Bentler P.M., 1985, On the implications of Bartholomew's approach to Factor Analysis, Brit. J. Math. Statist. Psych., 38, 129-131.

(15) Bentler P.M. et Kano, Y., 1990, On the equivalence of Factors and Components, Mult. Behav. research, 25, 67- 74.

(16) Besse P., 1992, PCA stability and choice of dimensionality, Statist. Probab. Letters, 13, 405-410. | MR | Zbl

(17) Besse P., Caussinus, H., Ferré, L., Fine, J., 1988, Principal Component Analysis and optimization of graphical displays, Statistics, 19, 301-312. | MR | Zbl

(18) Bock R.D. et Bargmann, R.E., 1966, Analysis of covariance structures, Psychometrika, 31,507- 534. | MR

(19) Borgotta E.F., Kercher, K. et Stull, D.E., 1986, A cautionary note on the use of PCA, Sociol. Meth. Research, 15, 160 -168.

(20) Browne M.W., 1967, On oblique procrustes rotation, Psychometrika, 32, 375- 394. | MR

(21) Browne M.W., 1974, Generalized least squares estimators in the analysis of covariance structures, South Afric. J., 8, 1- 24. | MR | Zbl

(22) Browne M.W., 1982, Covariances structures, In Topics in Applied Multivariate Analysis, D.M. Hawkins (ed), Cambridge Univ. Press, 72-141.

(23) Browne M.W., 1984, Asymptotically distribution-free methods for the analysis of covariance structures, Brit. J. Math. Statist. Psych., 37, 62-83. | MR | Zbl

(24) Browne M.W., 1985, Comments on D.J. Bartholomew, Foundations of Factor Analysis : some practical implications, Brit. J. Math. Statist. Psych., 38, 132-133.

(25) Browne M.W., 1987, Robustness of statistical inference in Factor Analysis and related models, Biometrika, 74, 2, 375-384. | MR | Zbl

(26) Cailliez F. et Pagès J.P., 1976, Introduction à l'Analyse des Données, SMASH, Paris.

(27) Camp B.H., 1932, The converse of Pearson's two factor theorem, Biometrika, 24, 418-427. | JFM | Zbl

(28) Camp B.H., 1934, Spearman's factor again, Biometrika, 26, 260-261. | JFM

(29) Carroll J.B., 1953, An analytic solution for approximating simple structure in factor analysis, Psychometrika, 18, 23-38. | Zbl

(30) Carroll J.B., 1957, Biquartimin criterion for rotation to oblique simple structure in factor analysis, Science, 126, 1114-1115.

(31) Caussinus H., 1986, Models and uses of Principal Component Analysis, in Mult. Data Analysis, J. de Leeuw et al (eds), DSWO Press, Leiden, 149- 170.

(32) Clarkson D.B. et Jennrich, R.I., 1988, Quartic rotation criteria and algorithms, Psychometrika, 53, 251-259. | MR | Zbl

(33) Dauxois J., Pousse, A., et Romain, Y., 1982, Asymptotic theory for the Principal Component Analysis of a random vector function. J. Mult. Analysis, 12, 136-154. | MR | Zbl

(34) Davis A.W., 1977, Asymptotic theory for Principal Component Analysis : non normal case, Austr. J. Statist., 19, 206 -212. | MR | Zbl

(35) Dempster A.P., 1969, Elements of continuous multivariate analysis, Addison-Wisley Publishing Co. | Zbl

(36) Dolby G.R., 1976, Stuctural relations and Factor Analysis, The Math. Scientist, Supp.1, 25-29.

(37) Everitt B.S. et Dunn G., 1991, Applied Multivariate Data Analysis, Arnold, E., (ed), London. | Zbl

(38) Ferré L., 1990, A mean square error criterion to determine the number of components in generalized Principal Component Analysis, Preprint, Lab. Statist. Prob., Toulouse.

(39) Fine J., 1993, Asymptotic study of the functional models in the case of a random number of observations for each mean, Proposé pour publication.

(40) Fine J. et Pousse A., 1992, Asymptotic study of the multivariate functional model. Application to the metric choice in Principal Component Analysis, Statistics, 23, 63-83. | MR | Zbl

(41) Fine J. et ROMAIN Y, 1984, Reduced Principal Component Analysis, Statistics, 15, 493-512. | MR | Zbl

(42) Gabriel K.R., 1971, The biplot graphic display of matrices with application to PCA, Biometrika, 58, 453- 467. | MR | Zbl

(43) Garnett J.C., 1919, General ability, cleverness and purpose, Brit. J. Psych., 9, 345-366.

(44) Green B.F., 1952, The orthogonal approximation of an oblique structure in factor analysis, Psychometrika, 27, 429 -440. | MR | Zbl

(45) Green B.F., 1976, On the factor score controversy, Psychometrika, 41, 263-266.

(46) Guilford J.P. et Michael W.B., 1948, Approaches to univocal factor scores, Psychometrika, 13, 1- 22.

(47) Guttman L., 1953, Image theory for the structure of quantitative variates, Psychometrika, 18, 277- 296. | MR | Zbl

(48) Guttman L., 1955, The determinacy of factor score matrices with implications for five other basic problems of common factor theory, Brit. J. Statist. Psych., 8, 65-81.

(49) Haagen K., 1986, The indeterminacy problem in factor analysis and its consequences for prediction, Osterr. Zeit. Statist. Inform., 15, 197-205.

(50) Haagen K., 1991, Necessary and sufficient conditions for vanishing the arbitrariness in a common-factor model, The Statist., 40, 401-408.

(51) Hakim M., Lochard E.Q., Olivier J.P., Terouanne E., 1976, Sur les traces de Spearman, I. Le problème des communautés, II. Le problème des rangs, Cahiers du BURO, 25.

(52) Hart B. et Spearman C., 1912, General ability, its existence and nature, Brit. J. Psych., 51- 84.

(53) Heerman E.F., 1964, The geometry of factorial indeterminacy, Psychometrika, 29, 371-381. | MR | Zbl

(54) Heerman E.F., 1966, The algebra of factorial indeterminacy, Psychometrika, 31, 531-543. | MR

(55) Hendrickson, A.E. et White P.O., 1964, Promax : a quick method for rotation to oblique simple structure, Brit. J. Statist. Psych., 17, 65-70.

(56) Hotelling H., 1933, Analysis of a complex of statistical variables into Principal Components, J. Educ. Psych., 24, 417-441, 498-520. | JFM

(57) Hubbard R. et Allenn S.J., 1987, A Cautionary note on the use of PCA; supportive empirical evidence, Sociol. Meth. Research, 16, 301-308.

(58) Jackson J.E., 1991, A user's guide to Principal Components, Wiley. | Zbl

(59) Jennrich R.I. et Sampson, P.F., 1966, Rotation for simple loadings, Psychometrika, 31, 313-323. | MR

(60) Jolliffe I., 1986, Principal Component Analysis, Springer-Verlag, New-York | MR

(61) Jöreskog K.G., 1962, On the statistical treatment of residuals in Factor Analysis, Psychometrika, 27, 335- 345. | MR | Zbl

(62) Jöreskog K.G., 1970, A general method for the analysis of covariance stuctures, Biometrika, 57, 239- 251. | MR | Zbl

(63) Jöreskog K.G., 1978, Structural analysis of covariance and correlation matrices, Psychometrika, 43, 443- 477. | MR | Zbl

(64) Jöreskog K.G., 1981, Analysis of covariance structures, Scand. J. Statist., 8, 65-92. | MR | Zbl

(65) Jöreskog K.G. et Sorbom, D., 1984, LISREL VI. A user's guide., 3°ed, Mooresville, In Scientific Software, Inc.

(66) Kaiser H.F., 1958, The varimax criterion for analytic rotation in Factor Analysis, Psychometrika, 23, 187- 200. | Zbl

(67) Kano Y., 1984, Construction of additional variables conforming to a common factor model, Statist. Prob. Letters, 2, 241-244. | MR | Zbl

(68) Kestelman H., 1952, The fundamental equation of factor analysis, Brit. J. Psych. Statist., 5, 1- 6.

(69) Konishi S., 1979, Asymptotic expansions for the distributions of statistics based on the sample correlation matrix in Principal Component Analysis, Hiroshima Math. J., 9, 647- 700. | MR | Zbl

(70) Kruskal J.B., 1978, Factor Analysis and Principal Components : Bilinear Methods, Intern. Ency. Statist. Kruskal, W.H. and Tanur, J.M. (eds), The Free Press, MacMillan, London.

(71) Krzanowski W.J., 1988, Principles of Multivariate Analysis, Clarendon Press, Oxford. | MR | Zbl

(72) Lebart L., Morineau A. et Warwick K.M., 1984, Multivariate Descriptive Statistical Analysis, Wiley, New-York. | MR | Zbl

(73) Ledermann W., 1938, The orthogonal transformation of a factorial matrix into itself, Psychometrika, 3, 181- 187. | JFM

(74) Mardia K.V., Kent J.T. et Bibby J.M. 1979, Multivariate Analysis, Academic Press, London. | MR | Zbl

(75) Mcardle J.J., 1979, The development of general multivariate software, Proceed. Ass. Dev. Computer Based Instruct. Syst., Hirschbuhl (Ed), Univ. Akron, OH.

(76) Mcardle J.J. et Mcdonald R.P., 1984, Some algebraic properties of the Reticular Action Model for moment structures, Brit. J. Math. Statist. Psych., 37, 234-251. | Zbl

(77) Mcdonald R.P., 1974, The measurement of factor indeterminacy, Psychometrika, 39, 203-222. | MR | Zbl

(78) Mcdonald R.P., 1977, The indeterminacy of components and the definition of common factors, Brit. J. Math. Statist. Psych., 30, 165-176. | MR | Zbl

(79) Mcdonald, R.P., 1978, A simple comprehensive model for the analysis of covariance structures, Brit. J. Math. Statist. Psych., 31, 59-72. | MR | Zbl

(80) Mcdonald R.P., 1980, A simple comprehensive model for the analysis of covariance structures; some remarks and applications, Brit. J. Math. Statist. Psych., 33, 161-183. | MR | Zbl

(81) McDONALD R.P., 1985a, Factor Analysis and related methods, Lawrence Erlbaum Associates Publishers, London.

(82) Mcdonald R.P., 1985b, Comments on D.J. Bartholomew, Foundations of Factor Analysis : some practical implications, Brit. J. Math. Statist. Psych., 38, 134-37.

(83) Mcdonald R.P. et Burr E.J., 1967, A comparaison of four methods of constructing factor scores, Psychometrika, 32, 381- 401. | MR | Zbl

(84) Mcdonald R.P. et Mulaik, S.A., 1979, Determinacy of common factors : a non technical review, Psych. Bull., 86, 297- 306.

(85) Meredith W. et Millsap R.E., 1985, On component analyses, Psychometrika, 50, 495-507. | MR | Zbl

(86) Meyer E.P., 1973, On the relationship between ratio of number of variables to number of factors and factorial indeterminacy, Psychometrika, 38, 375-378. | MR | Zbl

(87) Mosier C.I., 1939, Determining a simple structure when loadings for certain tests are known, Psychometrika, 4, 149-162. | JFM

(88) Mulaik S.A., 1972, The foundations of factor analysis, McGraw-Hill, New-York.

(89) Mulaik S.A., 1976, Comments on "The measurement of factorial indeterminacy", Psychometrika, 41, 249- 262. | MR | Zbl

(90) Mulaik S.A., 1981, A note on sufficient conditions that common factor will be determinate in an infinite domain of variables, Psychometrika, 46, 105-107. | MR | Zbl

(91) Mulaik S.A., 1986, Factor Analysis and Psychometrika : major developments, Psychometrika, 51, 23-33.

(92) Mulaik S.A. et Mcdonald, R.P., 1978, The effect of additional variables on factor indeterminacy in models with a single common factor, Psychometrika, 43, 177-192. | MR | Zbl

(93) Pearson K., 1901, On lines and planes of closest fit to systems of points in space, Philos. Mag., 2, 559- 572. | JFM

(94) Piaggio H.T.H., 1931, The general factor in Spearman's theory of intelligence, Nature, 127, 56-57. | JFM

(95) Piaggio H.T.H., 1933, Approximate general and specific factors without indeterminate parts, Brit. J. Psych., 25, 485 -489.

(96) Rao C.R., 1964, The use and interpretation of Principal Component Analysis in applied research, Sankhya, A, 26, 329-358. | MR | Zbl

(97) Rozeboom W.W., 1982, The determinacy of common factors in large item domains, Psychometrika, 47, 281- 295. | MR | Zbl

(98) Rozeboom W.W., 1988, Factor indeterminacy : the saga continues, Brit. J. Math. Statist. Psych., 41, 209- 226. | MR | Zbl

(99) Saporta G., 1990, Probabilités, Analyse des Données et Statistique, Ed. Technip, Paris. | MR | Zbl

(100) Saunders D.R., 1961, The rationale for an oblimax method of transformation in factor analysis, Psychometrika, 26, 317 -324.

(101) Schönemann P.H., 1966, The generalized solution for the orthogonal procrustes problem, Psychometrika, 31, 1- 16. | MR | Zbl

(102) Schönemann P.H., 1971, The minimum average correlation between equivalent sets of uncorrelated factors, Psychometrika, 36, 21-30. | MR | Zbl

(103) Schönemann P.H., 1990, Facts, fictions, and common sense about Factors and Components, Mult. Behav. Research, 25, 47-51.

(104) Schönemann P.H. et Haagen K., 1987, On the use of factor scores for prediction, Biometrical J., 29, 835-847. | Zbl

(105) Schönemann P.H. et Steiger, J.H., 1976, Regression Component Analysis, Brit. J. Math. Statist. Psych., 29, 175- 189. | MR | Zbl

(106) Schönemann P.H. et Steiger J.H., 1978, On the validity of indeterminate factor scores, Bull. Psych. Society, 12, 287-290.

(107) Schönemann P.H. et Wang M.M., 1972, Some new results on factor indeterminacy, Psychometrika, 37, 61-91. | MR | Zbl

(108) Snook S.C. et Gorsuch R.L., 1989, Principal Component Analysis versus Factor Analysis, a Monte Carlo study, Psych. Bull., 106, 148-154.

(109) Spearman C., 1904, General intelligence, objectively determined and measures, Amer. J. Psych., 15, 201- 293.

(110) Spearman C., 1927, The abilities of man; their nature and measurement, MacMillan, New-York. | JFM

(111) Spearman C., 1933, The uniqueness of «g», J. Educ. Psych., 24, 106-108.

(112) Spearman C., 1934, The factor theory and its trouble, IV Uniqueness of g, J. Educ. Psych., 25, 142- 153.

(113) Srivastava M.S. et Carter, E.M., 1983, An introduction to Applied Multivariate Statistics, North-Holland. | MR | Zbl

(114) Steiger J.H., 1979a, The relationships between external variables and indeterminate factors, Psychometrika, 44, 93-97. | MR | Zbl

(115) Steiger J.H., 1979b, Factor indeterminacy in the 1930's and the 1970's. Some interesting parallels. Psychometrika, 44, 157-167.

(116) Steiger J.H. et Schönemann P.H., 1978, A history of factor score indeterminacy, In Theory Construction and Data Analysis in the Behavioural Sciences, Skye (ed), San Francisco, Jossey-Bass.

(117) Thompson G.H., 1934, On measuring g and s by tests which break the g-hierarchy, J. Educ. Psych., 25, 204- 210.

(118) Thompson G.H., 1935, The meaning of « i» in the measurement of «g» (general intelligence, J. Educ. Psych., 26, 241-262.

(119) Thompson G.H., 1939, 5° éd 1951, The Factorial Analysis of human ability, Houghton Mifflin, Boston.

(120) Thurstone L.L., 1935, The vectors of mind : multiple factor analysis for the isolation of primary traits, Univ. Chicago Press, Chicago. | JFM

(121) Thurstone L.L., 1947, Multiple Factor Analysis, Univ. Chicago Press, Chicago. | MR | Zbl

(122) Velicer W.F., et Jackson D.N., 1990, Component Analysis versus Common Factor Analysis : some issues in selecting an appropriate procedure, Mult. Behav. Research, 25, 1-28.

(123) Vittadini G., 1989, Indetermination problems in the LISREL model, Mult. Behav. Research, 24, 4, 397-414.

(124) Waternaux C.M., 1976, Asymptotic distribution of the sample roots for a non normal population, Biometrika, 63, 639 -646. | MR | Zbl

(125) Wilkinson L., 1989, A cautionary note on the use of FA; a response to Borgotta, Kercher and Stull and Hubbard and Allen, Sociol. Meth. Research, 17, 449-459.

(126) Williams J.S., 1978, A definition for the common factor model and the elimination of problems of factor score indeterminacy, Psychometrika, 43, 293-306. | MR | Zbl

(127) Wilson E.B., 1928, Review of «The abilities of man, their nature and measurement» by C. Spearman, Science, 67, 244 -248.

(128) Wilson E.B., 1929, Comments on Professor Spearman's note, J. Educ. Psych., 20, 217-223.

(129) Wolfe D., 1940, Factor Analysis to 1940, Psychometric Monographs, 3, Univ. Chicago Press, Chicago. | JFM | Zbl