Equivalent Structural Equation Models: A Challenge and Responsibility

Relevant aspects of the example provided by Raykov and Marcoulides (2001) Raykov, T. and Marcoulides, G. A. 2001. Can there be infinitely many models equivalent to a given covariance structure model?. Structural Equation Modeling, 8: 142–149. Taylor & Francis Online], Web of Science ®] , Google Scholar] are emphasized, specifically the distinctiveness of infinitely many members of its sequence of equivalent structural equation models. This emphasis appears to be needed in light of recent statements by Markus (2002) Markus, K. A. 2002. Statistical equivalence, semantic equivalence, eliminative induction and the Raykov–Marcoulides proof of infinite equivalence. Structural Equation Modeling, 9: 503–522. Taylor & Francis Online], Web of Science ®] , Google Scholar], whose intended counterexamples do not present a disconfirmation of any of the developments of Raykov and Marcoulides (2001) Raykov, T. and Marcoulides, G. A. 2001. Can there be infinitely many models equivalent to a given covariance structure model?. Structural Equation Modeling, 8: 142–149. Taylor & Francis Online], Web of Science ®] , Google Scholar]. Issues pertaining to differentiation between equivalent models are also discussed.