Comparison of factorial structures

Factorial structures can be compared on basis of the criterion rotation originally proposed by Cliff (1966). The congruence coefficient by Tucker (1951) describes the similarity of two factors, while the coefficent FC by Gebhardt (1967) compares factor structures as a whole. However, these coefficients are only of descriptive nature as their distributions are unknown. Skakun, Maguire and Hakistan (1976, 1977) additionally provide significance tests for the dissimilarity of factorial structures. The exact procedures are detailed in Bortz (1999, pp. 538).

Literature

• Bortz, J. (1999). Statistik für Sozialwissenschafter. Berlin: Springer. ISBN: 3540650881.
• Gebhardt, F. (1967). Über die Ähnlichkeit von Faktorenmatrizen. Psychologische Beiträge, 10, 591-599.
• Skakun, E. N., Maguire, T. O. & Hakistan, A. R. (1976). An application of inferential statistics to the factorial invariance problem. Multivariate behavioural research, 11, 325-328. doi: 10.1207/s15327906mbr1103_4.
• Skakun, E. N., Maguire, T. O. & Hakistan, A. R. (1977). Erratum. Multivariate behavioural research, 12, 68.
• Tucker, L. R. (1951). A method for synthesis of factor analytic studies. Personnel research section report no. 984. Washington: Departement of the Army.

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