FACTREL program information and links
Important note: The
utility of this procedure has been called into
question by Jos M. F. ten Berg (1996), and rightly so. Harman (1976)
distinguished between factor matching (rotation to achieve similarity)
and factor congruence (measures of the degree of congruence between two
sets of factor loadings). Whereas Kaiser, Hunka, and Bianchini
(1971) presented their method, and specifically the cosines between
rotated factors, as measures of congruence, they really represent
"...the degree to which factors cannot be improved by rotation"
(ten Berg, p. 5). Thus the KHB procedure can be used for factor
matching, but is not really acceptable for assessing factor
Even so, the KHB method is not (in my
opinion) the best program for matching factors in exploratory factor
analysis. For that task see Cliff (1966) for orthogonal rotation to
congruence and Korth and Tucker (1976) for the oblique case. Tucker's
(1951) coefficient of congruence is (again in my opinon) the best
measure of congruence between factors from two studies in exploratory
factor analysis. (My COMPARE program perfoms both the Korth-Tucker
proctustean rotation for factor matching and computes the congruence
coefficients as well as other measures of factor similarity.)
then, is the use of this procedure? It is the only one I know of for
matching factors in exploratory factor analysis when there is less than
complelte overlap in the variables from two studies being compared. In
other words, only some variables are common to both studies.
Cliff, N. (1966). Orthogonal rotation to congruence. Psychometrika, 31, 33-42.
Fleming, J. S. (1991). COMPARE: An interactive program for computing
measures of factor loadings, with procrustes rotation options [computer software].
Prescott, AZ: Author.
Fleming, J. S. (1992). FACTREL: A general program for relating factors between studies using the Kaiser-Hunka-Bianchini method. Educational and Psychological Measurement, 52, 113-115.
Kaiser, H. F., Hunka, S., & Bianchini, J. (1971). Relating factor
studies based upon different individuals. Multivariate Behavioral Research, 6, 409-422.
Korth, B., & Tucker, L. R (1976). Procrustes matching by congruence coefficients. Psychometrika, 41, 531-535.
Harman, H. H. (1976). Modern factor analysis (2nd Ed.). Chicago: University of Chicago Press.
ten Berg, J. M. F. (1996). The Kaiser, Hunka and Bianchini factor
similarity coefficients: A cautionary note. Multivariate Behavioral Research, 31, 1-6.
Tucker, L. R (1951). A method of synthesis for factor analysis studies.
Personnel Research Section Report No. 984. Wachington, D.C.: Department
of the Army.
Use of the program is documented on the first page of the source code in the download zip file.
Download FACTREL.zip using ftp. It contains two
zipped files: FACTREL.f (a Fortran source program) and FACTREL.exe (the executable module).