, Volume 36, Issue 4, pp 409–426

Simultaneous factor analysis in several populations

  • K. G. Jöreskog

DOI: 10.1007/BF02291366

Cite this article as:
Jöreskog, K.G. Psychometrika (1971) 36: 409. doi:10.1007/BF02291366


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.


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Copyright information

© Psychometric Society 1971

Authors and Affiliations

  • K. G. Jöreskog
    • 1
  1. 1.Educational Testing ServiceUSA

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