1994 Volume 21 Issue 1 Pages 79-96
This paper concerns with the generation of equivalent path models in the linear structural equation models. Equivalent path models are defined as the set of different path models which give the same value of global fit indices to a data matrix. Therefore, by definition, the data matrix at hand cannot distinguish those models. After deriving some algebraic results, a graphical method to generate a set of equivalent models of a given path matrix is presented. As the result, it is demonstrated that, for most of the four-variable cases, there exists a set of equivalent path models. This implies that the cause-effect terminology used in the interpretation of the result of the data analysis using the linear structural equation models is questionable in most of the cases, unless the causal order is determined prior to the analysis on some theoretic basis.
