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.

No abstract

We describe a general procedure by which any number of parameters of the factor analytic model can be held fixed at any values and the remaining free parameters estimated by the maximum likelihood method. The generality of the approach makes it possible to deal with all kinds of solutions: orthogonal, oblique and various mixtures of these. By choosing the fixed parameters appropriately, factors can be defined to have desired properties and make subsequent rotation unnecessary. The goodness of fit of the maximum likelihood solution under the hypothesis represented by the fixed parameters is tested by a large sample χ2 test based on the likelihood ratio technique. A by‐product of the procedure is an estimate of the variance‐covariance matrix of the estimated parameters. From this, approximate confidence intervals for the parameters can be obtained. Several examples illustrating the usefulness of the procedure are given.

Various models for sets of congeneric tests are considered, including models appropriate for the analysis of multitrait-multimethod data. All models are illustrated with real data. The special cases when two or more tests within a set are tau-equivalent or parallel are also considered. All data analyses are done vTithin the framework of a general model by J8reskog (1969b). statistical Analysis of Sets of Congeneric Tests* 1If the test scores x l,x2 " " ' X m are congeneric, then any pair of true scores t. and t. correlate unity and hence there exists a random variable 1 J T such that each t. is linearly related to T, i.e., 1 t. = IJ.. + 13. T 1 1 1

Intraclass correlation reliablity estimates are based on the assumption that the various measures are equivalent. Jöreskog's (1970) general model for the analysis of covariance structures can be used to test the validity of this assumption.