This article is a comment on the paper by Spirtes, Scheines, and Glymour. The problem of equivalent models is discussed. The conclusion of the authors that the automatic model modification procedure in LISREL performs poorly may be due to the fact that all equivalent models are not counted as correct models. Our own experiment based on their model 8 demonstrates that the automatic model modification procedure in LISREL indeed performs very well when all equivalent models are counted as correct. Contrary to what the authors claim, the modification index in LISREL can be used to detect equivalent models and give useful insight into the problem of model modification.

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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.

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The authors describe new developments in structural equation modeling as incorporated in LISREL V. The procedures are illustrated on data from three previous studies.