Assessing Model Similarity in Structural Equation Modeling

Abstract

Two models can be nonequivalent, but fit very similarly across a wide range of data sets. These near-equivalent models, like equivalent models, should be considered rival explanations for results of a study if they represent plausible explanations for the phenomenon of interest. Prior to conducting a study, researchers should evaluate plausible models that are alternatives to those hypothesized to evaluate whether they are near-equivalent or equivalent and, in so doing, address the adequacy of the study’s methodology. To assess the extent to which alternative models for a study are empirically distinguishable, we propose 5 indexes that quantify the degree of similarity in fit between 2 models across a specified universe of data sets. These indexes compare either the maximum likelihood fit function values or the residual covariance matrices of models. Illustrations are provided to support interpretations of these similarity indexes.

Keywords:

• equivalent models
• model comparison
• model similarity
• near-equivalent models
• structural equation modeling

Notes

¹ The conclusion is the same for other choices for the correlation coefficient (except for 0).

² The values for δ₁₂ and and those for π₁₂ and were essentially identical to each other across all conditions. These results were expected in that and are equivalent to δ₁₂ and π₁₂, respectively, except and are transformed so they are in a correlational metric. For our examples, the universes consist of correlation matrices, and thus the transformation is unnecessary.