Assessing Model Similarity in Structural Equation Modeling

• In Event: Measurement and Modeling Issues in Structural Equation Modeling

Abstract

Two models can be non-equivalent, but produce very similar results across all possible datasets. We argue that if models are found that evidence very similar fit across all possible datasets relative to the hypothesized model, these models, like equivalent models, should be considered rival explanations to the hypothesized model. We propose two types of indices that assess the degree to which two models yield similar fit for a particular dataset as well as for all possible datasets: omega compares the maximum likelihood fit function for two models, and pi evaluates differences between the residual covariance matrices for two models. A conceptual case for the importance of assessing similarity is made and is illustrated with an example using omega and pi.

Authors

• Samuel B. Green, Arizona State University

• Keke Lai, Arizona State University - Tempe

• Roy Levy, Arizona State University

• Yuning Xu, Arizona State University

• Nedim Yel, Arizona State University

• Marilyn S. Thompson

• Natalie Eggum, Arizona State University

• Katie L. Kunze, Arizona State University

• Masumi Iida, Arizona State University

• Raymond Reichenberg, Arizona State University

• Linlin Zhang, Arizona State University