A major component of contemporary applied multivariate methodology appears to be the use of latent variable concepts and the models involving latent variables. Advances in covariance structure modeling as a tool for testing structural relations among variables has been complemented by a greater attention given to different data analytic problems, and the issue of equivalent models, in particular. Two or more models are defined as equivalent if they reproduce the same set of covariance matrices, with an equal set of fit indices as a necessary consequence of the equivalence. Since the substantive interpretations implied by these models may be very different, equivalent models pose a considerable limitation on the use of structural equation modeling in theory development and construct validation within psychology and other behavioral sciences. Specific rules for generation of equivalent models developed by Stelzl (1986), and Lee and Hershberger (1990), as well as necessary and sufficient condition for equivalence of structural equation models proposed by Raykov and Penev (1999), will be demonstrated and compared using several empirical examples. The issues on how to handle the problem of equivalence and the advantages of identifying equivalent models will further be discussed. |