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Using phantom variables in structural equation modeling to assess model sensitivity to external misspecification.

Jeffrey R Harring1, Daniel M McNeish2, Gregory R Hancock1

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This study introduces two methods to address omitted variables in structural models: a fixed parameter approach and a Bayesian random parameter approach. These techniques improve model accuracy when key variables are missing.

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Area of Science:

  • Statistics
  • Psychometrics
  • Educational Psychology

Background:

  • Structural models are susceptible to external misspecification due to omitted variables.
  • Omitted variables can significantly distort model inferences and conclusions.

Purpose of the Study:

  • To present and evaluate two novel strategies for handling omitted variables in structural modeling.
  • To enhance the robustness of statistical inferences in the presence of potential model misspecification.

Main Methods:

  • A fixed parameter approach using a 'phantom variable' with pre-set parameter values.
  • A Bayesian random parameter approach, defining prior distributions for the phantom variable's parameters.

Main Results:

  • Both methods provide viable strategies for sensitivity analysis regarding omitted variables.
  • Demonstrated effectiveness on an applied example from educational psychology.

Conclusions:

  • External misspecification sensitivity analyses should be standard practice in measured and latent variable modeling.
  • These methods aid researchers in assessing the impact of potentially unobserved salient variables.