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Latent moderated structural equation (LMS) analysis can produce biased results if predictor variables or disturbances are nonnormal. A new Hausman-type test offers a reliable way to check LMS distributional assumptions.

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Area of Science:

  • Psychometrics
  • Statistical modeling
  • Quantitative psychology

Background:

  • Latent moderated structural equation (LMS) is widely used for latent variable interactions.
  • LMS analysis assumes variable normality, but violations can bias parameter estimates.
  • Current methods for detecting misspecification are unreliable.

Purpose of the Study:

  • To investigate the robustness of LMS to nonnormality.
  • To evaluate statistical tests for detecting distributional misspecifications in LMS.
  • To introduce a novel specification test for LMS distributional assumptions.

Main Methods:

  • Four simulation studies were conducted.
  • Examined the impact of nonnormality from different sources on LMS.
  • Developed and tested a Hausman-type specification test.

Main Results:

  • LMS is biased when latent predictors or structural disturbances are nonnormal.
  • Nonnormality in measurement errors does not bias LMS results.
  • Existing normality tests can yield incorrect conclusions about LMS bias.

Conclusions:

  • LMS is sensitive to nonnormality in predictors and disturbances.
  • A novel Hausman-type test effectively assesses LMS distributional assumptions.
  • Researchers should use the new test to ensure LMS validity.