@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},
volume = {41},
year = {1993},
pages = {45-72},
mrnumber = {1255292},
zbl = {0972.62525},
language = {fr},
url = {http://dml.mathdoc.fr/item/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) pp. 45-72. http://gdmltest.u-ga.fr/item/RSA_1993__41_4_45_0/
(1) , 1985, Comments on D.J. Bartholomew, Foundations of Factor Analysis : some practical implications, Brit. J. Math. Statist. Psych., 38, 127-128.
(2) , 1963, Asymptotic theory for Principal Component Analysis. Ann. Math. Statist., 34, 122-148. | MR 145620 | Zbl 0202.49504
(3) , 1984a, Estimating linear statistical relationships, Ann. Statist., 12, 1-45. | MR 733497 | Zbl 0542.62039
(4) , 1984b, 2ème éd., An introduction to Multivariate statistical analysis, Wiley.
(5) et , 1956, Statistical inference in Factor Analysis. Proceed. 3rd Berkeley Symp. Math. Statist. Probab, 5, 11-150. | Zbl 0070.14703
(6) , 1981, Posterior analysis of Factor Model, Brit. J. Math. Statist. Psych., 34, 92- 99. | MR 649325 | Zbl 0462.62084
(7) , 1984, The Foundations of Factor Analysis, Biometrika, 71, 221-232. | MR 767150 | Zbl 0575.62055
(8) , 1985a, Foundations of Factor Analysis : some practical implications, Brit. J. Math. Statist. Psych., 38, 1-10. | Zbl 0595.62052
(9) , 1985b, Reply to discussion on Foundations of Factor Analysis, Brit. J. Math. Statist. Psych., 38, 138-140.
(10) , 1987, Latent variable models and Factor Analysis, Griffin. | Zbl 0664.62057
(11) , 1937, The statistical conception of mental factors, Brit. J. Psych., 28, 97-104.
(12) , 1938, Methods of estimating mental factors, Nature, 141, 609-610.
(13) et , 1987, The rank of reduced dispersion matrices, Psychometrika, 52, 125- 135. | MR 903651 | Zbl 0615.62069
(14) , 1985, On the implications of Bartholomew's approach to Factor Analysis, Brit. J. Math. Statist. Psych., 38, 129-131.
(15) et , 1990, On the equivalence of Factors and Components, Mult. Behav. research, 25, 67- 74.
(16) , 1992, PCA stability and choice of dimensionality, Statist. Probab. Letters, 13, 405-410. | MR 1175167 | Zbl 0743.62046
(17) , , , , 1988, Principal Component Analysis and optimization of graphical displays, Statistics, 19, 301-312. | MR 945387 | Zbl 0643.62046
(18) et , 1966, Analysis of covariance structures, Psychometrika, 31,507- 534. | MR 205389
(19) , et , 1986, A cautionary note on the use of PCA, Sociol. Meth. Research, 15, 160 -168.
(20) , 1967, On oblique procrustes rotation, Psychometrika, 32, 375- 394. | MR 215511
(21) , 1974, Generalized least squares estimators in the analysis of covariance structures, South Afric. J., 8, 1- 24. | MR 370949 | Zbl 0281.62071
(22) , 1982, Covariances structures, In Topics in Applied Multivariate Analysis, D.M. Hawkins (ed), Cambridge Univ. Press, 72-141.
(23) , 1984, Asymptotically distribution-free methods for the analysis of covariance structures, Brit. J. Math. Statist. Psych., 37, 62-83. | MR 783499 | Zbl 0561.62054
(24) , 1985, Comments on D.J. Bartholomew, Foundations of Factor Analysis : some practical implications, Brit. J. Math. Statist. Psych., 38, 132-133.
(25) , 1987, Robustness of statistical inference in Factor Analysis and related models, Biometrika, 74, 2, 375-384. | MR 903138 | Zbl 0633.62052
(26) et , 1976, Introduction à l'Analyse des Données, SMASH, Paris.
(27) , 1932, The converse of Pearson's two factor theorem, Biometrika, 24, 418-427. | JFM 58.1173.03 | Zbl 0005.40505
(28) , 1934, Spearman's factor again, Biometrika, 26, 260-261. | JFM 60.1198.22
(29) , 1953, An analytic solution for approximating simple structure in factor analysis, Psychometrika, 18, 23-38. | Zbl 0053.27604
(30) , 1957, Biquartimin criterion for rotation to oblique simple structure in factor analysis, Science, 126, 1114-1115.
(31) , 1986, Models and uses of Principal Component Analysis, in Mult. Data Analysis, J. de Leeuw et al (eds), DSWO Press, Leiden, 149- 170.
(32) et I., 1988, Quartic rotation criteria and algorithms, Psychometrika, 53, 251-259. | MR 955469 | Zbl 0718.62134
(33) , , et , 1982, Asymptotic theory for the Principal Component Analysis of a random vector function. J. Mult. Analysis, 12, 136-154. | MR 650934 | Zbl 0539.62064
(34) , 1977, Asymptotic theory for Principal Component Analysis : non normal case, Austr. J. Statist., 19, 206 -212. | MR 501590 | Zbl 0417.62046
(35) , 1969, Elements of continuous multivariate analysis, Addison-Wisley Publishing Co. | Zbl 0197.44904
(36) , 1976, Stuctural relations and Factor Analysis, The Math. Scientist, Supp.1, 25-29.
(37) et , 1991, Applied Multivariate Data Analysis, Arnold, E., (ed), London. | Zbl 0788.62001
(38) , 1990, A mean square error criterion to determine the number of components in generalized Principal Component Analysis, Preprint, Lab. Statist. Prob., Toulouse.
(39) , 1993, Asymptotic study of the functional models in the case of a random number of observations for each mean, Proposé pour publication.
(40) et , 1992, Asymptotic study of the multivariate functional model. Application to the metric choice in Principal Component Analysis, Statistics, 23, 63-83. | MR 1245709 | Zbl 0809.62052
(41) et ROMAIN Y, 1984, Reduced Principal Component Analysis, Statistics, 15, 493-512. | MR 767736 | Zbl 0616.62080
(42) , 1971, The biplot graphic display of matrices with application to PCA, Biometrika, 58, 453- 467. | MR 312645 | Zbl 0228.62034
(43) , 1919, General ability, cleverness and purpose, Brit. J. Psych., 9, 345-366.
(44) , 1952, The orthogonal approximation of an oblique structure in factor analysis, Psychometrika, 27, 429 -440. | MR 53057 | Zbl 0049.37601
(45) , 1976, On the factor score controversy, Psychometrika, 41, 263-266.
(46) et , 1948, Approaches to univocal factor scores, Psychometrika, 13, 1- 22.
(47) , 1953, Image theory for the structure of quantitative variates, Psychometrika, 18, 277- 296. | MR 59514 | Zbl 0053.27703
(48) , 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) , 1986, The indeterminacy problem in factor analysis and its consequences for prediction, Osterr. Zeit. Statist. Inform., 15, 197-205.
(50) , 1991, Necessary and sufficient conditions for vanishing the arbitrariness in a common-factor model, The Statist., 40, 401-408.
(51) , , , , 1976, Sur les traces de Spearman, I. Le problème des communautés, II. Le problème des rangs, Cahiers du BURO, 25.
(52) et , 1912, General ability, its existence and nature, Brit. J. Psych., 51- 84.
(53) , 1964, The geometry of factorial indeterminacy, Psychometrika, 29, 371-381. | MR 174152 | Zbl 0134.19802
(54) , 1966, The algebra of factorial indeterminacy, Psychometrika, 31, 531-543. | MR 210242
(55) et , 1964, Promax : a quick method for rotation to oblique simple structure, Brit. J. Statist. Psych., 17, 65-70.
(56) , 1933, Analysis of a complex of statistical variables into Principal Components, J. Educ. Psych., 24, 417-441, 498-520. | JFM 59.1183.01
(57) et , 1987, A Cautionary note on the use of PCA; supportive empirical evidence, Sociol. Meth. Research, 16, 301-308.
(58) , 1991, A user's guide to Principal Components, Wiley. | Zbl 0743.62047
(59) et , 1966, Rotation for simple loadings, Psychometrika, 31, 313-323. | MR 203869
(60) , 1986, Principal Component Analysis, Springer-Verlag, New-York | MR 841268
(61) , 1962, On the statistical treatment of residuals in Factor Analysis, Psychometrika, 27, 335- 345. | MR 165630 | Zbl 0113.13805
(62) , 1970, A general method for the analysis of covariance stuctures, Biometrika, 57, 239- 251. | MR 269024 | Zbl 0195.48801
(63) , 1978, Structural analysis of covariance and correlation matrices, Psychometrika, 43, 443- 477. | MR 521901 | Zbl 0392.62043
(64) , 1981, Analysis of covariance structures, Scand. J. Statist., 8, 65-92. | MR 623585 | Zbl 0498.62060
(65) et , 1984, LISREL VI. A user's guide., 3°ed, Mooresville, In Scientific Software, Inc.
(66) , 1958, The varimax criterion for analytic rotation in Factor Analysis, Psychometrika, 23, 187- 200. | Zbl 0095.33603
(67) , 1984, Construction of additional variables conforming to a common factor model, Statist. Prob. Letters, 2, 241-244. | MR 764927 | Zbl 0551.62040
(68) , 1952, The fundamental equation of factor analysis, Brit. J. Psych. Statist., 5, 1- 6.
(69) , 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 549668 | Zbl 0443.62043
(70) , 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) , 1988, Principles of Multivariate Analysis, Clarendon Press, Oxford. | MR 969370 | Zbl 0678.62001
(72) , et , 1984, Multivariate Descriptive Statistical Analysis, Wiley, New-York. | MR 744990 | Zbl 0658.62069
(73) , 1938, The orthogonal transformation of a factorial matrix into itself, Psychometrika, 3, 181- 187. | JFM 64.0946.03
(74) , et 1979, Multivariate Analysis, Academic Press, London. | MR 560319 | Zbl 0432.62029
(75) , 1979, The development of general multivariate software, Proceed. Ass. Dev. Computer Based Instruct. Syst., Hirschbuhl (Ed), Univ. Akron, OH.
(76) et , 1984, Some algebraic properties of the Reticular Action Model for moment structures, Brit. J. Math. Statist. Psych., 37, 234-251. | Zbl 0556.62099
(77) , 1974, The measurement of factor indeterminacy, Psychometrika, 39, 203-222. | MR 350973 | Zbl 0295.62065
(78) , 1977, The indeterminacy of components and the definition of common factors, Brit. J. Math. Statist. Psych., 30, 165-176. | MR 474634 | Zbl 0375.92020
(79) , 1978, A simple comprehensive model for the analysis of covariance structures, Brit. J. Math. Statist. Psych., 31, 59-72. | MR 633690 | Zbl 0411.62048
(80) , 1980, A simple comprehensive model for the analysis of covariance structures; some remarks and applications, Brit. J. Math. Statist. Psych., 33, 161-183. | MR 604072 | Zbl 0439.62054
(81) McDONALD R.P., 1985a, Factor Analysis and related methods, Lawrence Erlbaum Associates Publishers, London.
(82) , 1985b, Comments on D.J. Bartholomew, Foundations of Factor Analysis : some practical implications, Brit. J. Math. Statist. Psych., 38, 134-37.
(83) et , 1967, A comparaison of four methods of constructing factor scores, Psychometrika, 32, 381- 401. | MR 216664 | Zbl 0183.24602
(84) et , 1979, Determinacy of common factors : a non technical review, Psych. Bull., 86, 297- 306.
(85) et , 1985, On component analyses, Psychometrika, 50, 495-507. | MR 818934 | Zbl 0609.62097
(86) , 1973, On the relationship between ratio of number of variables to number of factors and factorial indeterminacy, Psychometrika, 38, 375-378. | MR 400547 | Zbl 0291.62140
(87) , 1939, Determining a simple structure when loadings for certain tests are known, Psychometrika, 4, 149-162. | JFM 65.0604.03
(88) , 1972, The foundations of factor analysis, McGraw-Hill, New-York. | Zbl pre05675897
(89) , 1976, Comments on "The measurement of factorial indeterminacy", Psychometrika, 41, 249- 262. | MR 483189 | Zbl 0331.92012
(90) , 1981, A note on sufficient conditions that common factor will be determinate in an infinite domain of variables, Psychometrika, 46, 105-107. | MR 655011 | Zbl 0452.62044
(91) , 1986, Factor Analysis and Psychometrika : major developments, Psychometrika, 51, 23-33.
(92) et P., 1978, The effect of additional variables on factor indeterminacy in models with a single common factor, Psychometrika, 43, 177-192. | MR 514728 | Zbl 0404.92019
(93) , 1901, On lines and planes of closest fit to systems of points in space, Philos. Mag., 2, 559- 572. | JFM 32.0710.04
(94) , 1931, The general factor in Spearman's theory of intelligence, Nature, 127, 56-57. | JFM 57.0639.06
(95) , 1933, Approximate general and specific factors without indeterminate parts, Brit. J. Psych., 25, 485 -489.
(96) , 1964, The use and interpretation of Principal Component Analysis in applied research, Sankhya, A, 26, 329-358. | MR 184375 | Zbl 0137.37207
(97) , 1982, The determinacy of common factors in large item domains, Psychometrika, 47, 281- 295. | MR 678063 | Zbl 0521.62052
(98) , 1988, Factor indeterminacy : the saga continues, Brit. J. Math. Statist. Psych., 41, 209- 226. | MR 985134 | Zbl 0718.62131
(99) , 1990, Probabilités, Analyse des Données et Statistique, Ed. Technip, Paris. | MR 1674525 | Zbl 0703.62003
(100) , 1961, The rationale for an oblimax method of transformation in factor analysis, Psychometrika, 26, 317 -324.
(101) , 1966, The generalized solution for the orthogonal procrustes problem, Psychometrika, 31, 1- 16. | MR 215870 | Zbl 0147.19401
(102) , 1971, The minimum average correlation between equivalent sets of uncorrelated factors, Psychometrika, 36, 21-30. | MR 311047 | Zbl 0218.62121
(103) , 1990, Facts, fictions, and common sense about Factors and Components, Mult. Behav. Research, 25, 47-51.
(104) et , 1987, On the use of factor scores for prediction, Biometrical J., 29, 835-847. | Zbl 0718.62130
(105) et H., 1976, Regression Component Analysis, Brit. J. Math. Statist. Psych., 29, 175- 189. | MR 443274 | Zbl 0356.92026
(106) et , 1978, On the validity of indeterminate factor scores, Bull. Psych. Society, 12, 287-290.
(107) et , 1972, Some new results on factor indeterminacy, Psychometrika, 37, 61-91. | MR 314202 | Zbl 0236.92005
(108) et , 1989, Principal Component Analysis versus Factor Analysis, a Monte Carlo study, Psych. Bull., 106, 148-154.
(109) , 1904, General intelligence, objectively determined and measures, Amer. J. Psych., 15, 201- 293.
(110) , 1927, The abilities of man; their nature and measurement, MacMillan, New-York. | JFM 53.0521.13
(111) , 1933, The uniqueness of «g», J. Educ. Psych., 24, 106-108.
(112) , 1934, The factor theory and its trouble, IV Uniqueness of g, J. Educ. Psych., 25, 142- 153.
(113) et , 1983, An introduction to Applied Multivariate Statistics, North-Holland. | MR 686273 | Zbl 0554.62041
(114) , 1979a, The relationships between external variables and indeterminate factors, Psychometrika, 44, 93-97. | MR 529393 | Zbl 0419.62051
(115) , 1979b, Factor indeterminacy in the 1930's and the 1970's. Some interesting parallels. Psychometrika, 44, 157-167.
(116) et , 1978, A history of factor score indeterminacy, In Theory Construction and Data Analysis in the Behavioural Sciences, Skye (ed), San Francisco, Jossey-Bass.
(117) , 1934, On measuring g and s by tests which break the g-hierarchy, J. Educ. Psych., 25, 204- 210.
(118) , 1935, The meaning of « i» in the measurement of «g» (general intelligence, J. Educ. Psych., 26, 241-262.
(119) , 1939, 5° éd 1951, The Factorial Analysis of human ability, Houghton Mifflin, Boston.
(120) , 1935, The vectors of mind : multiple factor analysis for the isolation of primary traits, Univ. Chicago Press, Chicago. | JFM 62.1380.06
(121) , 1947, Multiple Factor Analysis, Univ. Chicago Press, Chicago. | MR 21272 | Zbl 0029.22203
(122) , et , 1990, Component Analysis versus Common Factor Analysis : some issues in selecting an appropriate procedure, Mult. Behav. Research, 25, 1-28.
(123) , 1989, Indetermination problems in the LISREL model, Mult. Behav. Research, 24, 4, 397-414.
(124) , 1976, Asymptotic distribution of the sample roots for a non normal population, Biometrika, 63, 639 -646. | MR 501582 | Zbl 0352.62076
(125) , 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) , 1978, A definition for the common factor model and the elimination of problems of factor score indeterminacy, Psychometrika, 43, 293-306. | MR 514723 | Zbl 0392.62042
(127) , 1928, Review of «The abilities of man, their nature and measurement» by C. Spearman, Science, 67, 244 -248.
(128) , 1929, Comments on Professor Spearman's note, J. Educ. Psych., 20, 217-223.
(129) , 1940, Factor Analysis to 1940, Psychometric Monographs, 3, Univ. Chicago Press, Chicago. | JFM 66.0653.02 | Zbl 0025.19906