A general method for studying differences in factor means and factor structure between groups

TLDR: In this article, a statistical model is developed for the study of similarities and differences in factor structure between several groups, assuming that the observed variables satisfy a factor analysis model in each group, i.e. factor means, factor loadings, factor variances and covariances and unique variances.

Abstract: A statistical model is developed for the study of similarities and differences in factor structure between several groups. The model assumes that the observed variables satisfy a factor analysis model in each group. A method of data analysis is presented which, in contrast to earlier work, makes use of information in the observed means as well as the observed variances and covariances to estimate the parameters in each group, i.e. factor means, factor loadings, factor variances and covariances and unique variances. Usually the units of measurement in the observed variables have no intrinsic meaning and therefore it is only meaningful to compare the relative magnitudes of the parameters for the different groups. The method estimates the parameters for all groups simultaneously and can take into account a priori information about factorial invariance of various degrees.