The minimum average correlation between equivalent sets of uncorrelated factors

A simplified proof of a lemma by Ledermann [1938], which lies at the core of the factor indeterminacy issue, is presented. It leads to a representation of an orthogonal matrixT, relating equivalent factor solutions, which is different from Ledermann's [1938] and Guttman's [1955].T is used to evaluate bounds on the average correlation between equivalent sets of uncorrelated factors. It is found that the minimum average correlation is independent of the data.

[1]  Raymond B. Cattell,et al.  Factor Analysis. An Introduction and Manual for the Psychologist and Social Scientist. , 1953 .

[2]  E. Heermann.  The algebra of factorial indeterminancy , 1966, Psychometrika.

[3]  K. Dunlap.  THE HIPP CHRONOSCOPE WITHOUT ARMATURE SPRINGS , 1912 .

[4]  B. H. Camp.  THE CONVERSE OF SPEARMAN'S TWO-FACTOR THEOREM , 1932 .

[5]  H. Piaggio.  THREE SETS OF CONDITIONS NECESSARY FOR THE EXISTENCE OF A g THAT IS REAL AND UNIQUE EXCEPT IN SIGN , 1933 .

[6]  A. E. Maxwell,et al.  Factor Analysis as a Statistical Method. , 1964 .

[7]  H. Harman.  Modern factor analysis , 1961 .

[8]  Godfrey H. Thomson,et al.  THE MEANING OF ‘i’ IN THE ESTIMATE OF ‘g’ , 1934 .

[9]  R. Cattell,et al.  Factor Analysis: An Introduction and Manual for the Psychologist and Social Scientist , 1953 .

[10]  B. Fruchter,et al.  Introduction to Factor Analysis , 1955 .

[11]  E. Heermann.  The geometry of factorial indeterminancy , 1964 .

[12]  Louis Guttman,et al.  “Best possible” systematic estimates of communalities , 1956 .

[13]  E. J. Burr,et al.  A comparison of four methods of constructing factor scores , 1967 .

[14]  Louis Guttman,et al.  THE DETERMINACY OF FACTOR SCORE MATRICES WITH IMPLICATIONS FOR FIVE OTHER BASIC PROBLEMS OF COMMON‐FACTOR THEORY1 , 1955 .

[15]  G. Thomson.  Some points of mathematical technique in the factorial analysis of ability. , 1936 .

[16]  G. H. Thomson.  The definition and measurement of "g" (general intelligence). , 1935 .

[17]  H. Kestelman,et al.  THE FUNDAMENTAL EQUATION OF FACTOR ANALYSIS , 1952 .

[18]  E. B. Andersen,et al.  Modern factor analysis , 1961 .

[19]  D. R. Saunders.  Book Reviews : Fruchter, Benjamin. Introduction to Factor Analysis. New York: Van Nostrand, I954. xii + 280 pp. ($5.00 , 1955 .

[20]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

[21]  Faktorenanalyse.@@@Dimensionen des Verhaltens. , 1969 .

[22]  Walter Lederman,et al.  The orthogonal transformations of a factorial matrix into itself , 1938 .

[23]  E B Wilson,et al.  On Hierarchical Correlation Systems. , 1928, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Chester W. Harris,et al.  On factors and factor scores , 1967 .

[25]  J. Tukey,et al.  Multiple-Factor Analysis , 1947 .