Invariant Standardized Estimated Parameter Change for Model Modification in Covariance Structure Analysis

An estimated parameter change (EPC) has recently been introduced as another criterion to be considered in the process of model modification in covariance structure analysis. Kaplan (1989) provided a standardized version of this statistic (SEPC-K). It has been found that SEPC-K is only partially standardized; specifically, it is not invariant under different scalings of latent and measured variables. In this article, a new SEPC that is invariant to the original metrics of the measured and latent variables is suggested for use in model modification. A multivariate estimated parameter change (MEPC) which estimates changes for a set of fixed parameters to be freed simultaneously is also introduced. A standardized MEPC (SMEPC) is, furthermore, provided. Because there are now three different types of standardized solutions in structural modeling programs, general discussion of standardized solution in covariance structure analysis is provided. The inappropriate use of standardization for scale-specific models is noted.