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 congruence. 

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.)

What, 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 information

    Download FACTREL.zip  using ftp. It contains two zipped files: FACTREL.f (a Fortran source program) and FACTREL.exe (the executable module).