Using Phantom Variables in Structural Equation Modeling to Assess Model Sensitivity to External Misspecification

Jeffrey R. Harring, Daniel McNeish, Gregory R. Hancock

Research output: Contribution to journalArticle

6 Scopus citations


External misspecification, the omission of key variables from a structural model, can fundamentally alter the inferences one makes without such variables present. This article presents 2 strategies for dealing with omitted variables, the first a fixed parameter approach incorporating the omitted variable into the model as a phantom variable where all associated parameter values are fixed, and the other a random parameter approach specifying prior distributions for all of the phantom variable's associated parameter values under a Bayesian framework. The logic and implementation of these methods are discussed and demonstrated on an applied example from the educational psychology literature. The argument is made that such external misspecification sensitivity analyses should become a routine part of measured and latent variable modeling where the inclusion of all salient variables might be in question.

Original languageEnglish (US)
Pages (from-to)616-631
Number of pages16
JournalPsychological Methods
Issue number4
StatePublished - Dec 1 2017
Externally publishedYes



  • Bayesian analysis
  • external misspecification
  • phantom variables
  • structural equation modeling

ASJC Scopus subject areas

  • Psychology (miscellaneous)

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