This paper is concerned with the study of similarities and differences in factor structures between different groups. A common situation occurs when a battery of tests has been administered to samples of examinees from several populations.
A very general model is presented, in which any parameter in the factor analysis models (factor loadings, factor variances, factor covariances, and unique variances) for the different groups may be assigned an arbitrary value or constrained to be equal to some other parameter. Given such a specification, the model is estimated by the maximum likelihood method yielding a large samplex2 of goodness of fit. By computing several solutions under different specifications one can test various hypotheses.
The method is capable of dealing with any degree of invariance, from the one extreme, where nothing is invariant, to the other extreme, where everything is invariant. Neither the number of tests nor the number of common factors need to be the same for all groups, but to be at all interesting, it is assumed that there is a common core of tests in each battery that is the same or at least content-wise comparable.
KeywordsCovariance General Model Public Policy Factor Structure Factor Loading
Unable to display preview. Download preview PDF.
- Box, G. E. P. A general distribution theory for a class of likelihood criteria.Biometrika, 1949,36, 317–346.Google Scholar
- Fletcher, R. & Powell, M. J. D. A rapidly convergent descent method for minimization.The Computer Journal, 1963,6, 163–168.Google Scholar
- Gruvaeus, G. T. & Jöreskog, K. G. A computer program for minimizing a function of several variables. Research Bulletin 70-14. Princeton, N. J.: Educational Testing Service, 1970.Google Scholar
- Holzinger, K. J. & Swineford, F. A study in factor analysis: The stability of a bi-factor solution.Supplementary Educational Monograph No.48. Chicago: University of Chicago, 1939.Google Scholar
- Jöreskog, K. G. Some contributions to maximum likelihood factor analysis.Psychometrika, 1967,32, 443–482.Google Scholar
- Jöreskog, K. G. A general approach to confirmatory maximum likelihood factor analysis.Psychometrika, 1969,34, 183–220.Google Scholar
- Lawley, D. N. A note on Karl Pearson's selection formulae.Proceedings of the Royal Society of Edinburgh, Section A, 1943–44,62, 28–30.Google Scholar
- Lawley, D. N. & Maxwell, A. E.Factor analysis as a statistical method. London: Butterworths, 1963.Google Scholar
- McGaw, B. & Jöreskog, K. G. Factorial invariance of ability measures in groups differing in intelligence and socioeconomic status.British Journal of Mathematical and Statistical Psychology, 1971,24,in press.Google Scholar
- Meredith, W. Rotation to achieve factorial invariance.Psychometrika, 1964,19, 187–206. (a)Google Scholar
- Meredith, W. Notes on factorial invariance.Psychometrika, 1964,29, 177–185. (b)Google Scholar
- van Thillo, M. & Jöreskog, K. G. A general computer program for simultaneous factor analysis in several populations. Research Bulletin 70-62. Princeton, N. J.: Educational Testing Service, 1970.Google Scholar