Assessing Model Similarity in Structural Equation Modeling

Keke Lai, Samuel B. Green, Roy Levy, Ray E. Reichenberg, Yuning Xu, Marilyn Thompson, Nedim Yel, Natalie D. Eggum-Wilkens, Katie L. Kunze, Masumi Iida

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)491-506
Number of pages16
JournalStructural Equation Modeling
Issue number4
StatePublished - Jul 3 2016


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

ASJC Scopus subject areas

  • Decision Sciences(all)
  • Modeling and Simulation
  • Sociology and Political Science
  • Economics, Econometrics and Finance(all)


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