Analytical methods of factoring score profiles are impractical to apply to large cross-products matrices of profile similarities. Basic matrix relationships are presented and illustrated which permit computation of loadings of people on factors from the factor analysis of the usually smaller variable by variable cross-products matrix. Some important additional issues are discussed and mathematical relationships are stated, particularly those concerning the rotation of factor axes.
Get full access to this article
View all access options for this article.
References
1.
Broverman, D. M.Effects of score transformations in Q and R factor analysis techniques . Psychological Review, 1961, 68, 68-80.
2.
Broverman, D. M.Comments on the note by MacAndrew and Forgy . Psychological Review, 1963, 70, 119-120.
3.
Burt, C.Correlations between persons . British Journal of Psychology, 1937, 28, 167-185.
4.
Cronbach, L. J. and Gleser, G. C.Assessing similarity between profiles. Psychological Bulletin, 1953, 50, 456-473.
5.
Eckart, C. and Young, G.The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1, 211-218.
6.
Gollob, H. F.A statistical model which combines features of factor analytic and analysis of variance techniques . Psychometrika, 1968, 33, 73-115. (a)
7.
Gollob, H. F.Confounding of sources of variation in factor-analytic techniques . Psychological Bulletin, 1968, 70, 330-344. (b)
8.
Gollob, H. F.Rejoinder to Tucker's "Comments on confounding of sources of variation in factor-analytic techniques."Psychological Bulletin, 1968, 70, 355-360. (c)
9.
Jones, J. J.Relation of R-analysis factor scores and Q-analysis factor loadings . Psychological Reports, 1967, 20, 247-249.
10.
MacAndrew, C. and Forgy, E.A note on the effect of score transformations in Q and R factor analysis techniques. Psychological Review, 1963, 70, 116-118.
11.
Nunnally, J. C.Psychometric theory, 2nd edition. New York: McGraw-Hill, 1978.
12.
Nunnally, J. C.The analysis of profile data . Psychological Bulletin, 1962, 59, 311-319.
13.
Osgood, C. E. and Suci, G. J.A measure of relation determined by both mean differences and profile information. Psychological Bulletin, 1952, 49, 251-262.
14.
Overall, J. E. and Klett, C. J.Applied multivariate analysis. New York: McGraw-Hill, 1972.
15.
Ross, J.The relation between test and person factors . Psychological Review, 1963, 70, 432-445.
16.
Ryder, R. G.Profile factor analysis and variable factor analysis . Psychological Reports, 1964, 15, 119-127.
17.
Sander, J.The reciprocity principle as an aid to factor analysis . British Journal of Psychology (Statistics Section), 1949, 2, 180.
18.
Skinner, H. A.Differentiating the contribution of elevation, scatter and shape in profile similarity . EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, 1978, 38, 297-308.
19.
Stephenson, W.Introduction to inverted factor analysis with some applications to studies in orexis . Journal of Educational Psychology, 1936, 27, 353-367.
20.
Tucker, L. R.Comments on "Confounding of sources of variation in factor-analytic techniques."Psychological Bulletin, 1968, 70, 345-354.
