A Simple Rule for Generating Equivalent Models in Covariance Structure Modeling

The replacing rule is introduced as a simplification of Stelzl's (1986) four rules for the generation of recursive equivalent models, and generates equivalent models through the replacement of direct paths with residual correlations, through the Replacement of residual correlations with direct paths, or through the inversion of path directions.

Abstract

This study introduces the replacing rule as a simplification of Stelzl's (1986) four rules for the generation of recursive equivalent models. The replacing rule is applicable to nonrecursive as well as recursive models, and generates equivalent models through the replacement of direct paths with residual correlations, through the replacement of residual correlations with direct paths, or through the inversion of path directions. Examples of the use of the replacing rule are provided, and its advantages over Stelzl's four rules are discussed.