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

Area of Science:

• Structural Equation Modeling
• Covariance Structure Analysis
• Multivariate Statistics

Background:

• The Estimated Parameter Change (EPC) is a criterion for model modification in covariance structure analysis.
• Kaplan's standardized version (SEPC-K) has limitations, as it is not fully standardized and lacks invariance to variable scaling.

Purpose of the Study:

• To introduce a new, fully standardized SEPC that is invariant to the original metrics of measured and latent variables.
• To present a Multivariate Estimated Parameter Change (MEPC) and its standardized version (SMEPC) for simultaneous parameter freeing.
• To discuss the appropriate use of standardized solutions in covariance structure analysis.

Main Methods:

• Development of a novel SEPC metric ensuring scale invariance.
• Introduction of MEPC for assessing simultaneous parameter changes.
• Derivation of SMEPC for standardized assessment of multiple parameter changes.

Main Results:

• The proposed SEPC is invariant to variable scaling, offering a more reliable measure for model modification.
• MEPC and SMEPC provide tools for evaluating simultaneous changes in multiple parameters.
• The study highlights the inappropriate application of standardization in scale-specific models.

Conclusions:

• The new invariant SEPC offers a superior approach to model modification in covariance structure analysis.
• MEPC and SMEPC extend the utility of parameter change estimation to multivariate contexts.
• Careful consideration of standardization is crucial for accurate interpretation in structural modeling.