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Robust Estimation of Polychoric Correlation.

Max Welz1,2, Patrick Mair3, Andreas Alfons2

  • 1Department of Psychology, https://ror.org/02crff812University of Zurich, Switzerland.

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|November 30, 2025
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Summary
This summary is machine-generated.

A new robust estimator for polychoric correlation is introduced, offering improved accuracy for rating data analysis, especially with structural equation models, by handling partially misspecified models effectively.

Keywords:
careless respondingmodel misspecificationpolychoric correlationrobust estimation

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Area of Science:

  • Statistics
  • Psychometrics

Background:

  • Polychoric correlation is crucial for analyzing rating data and structural equation models.
  • Maximum likelihood (ML) estimation is sensitive to model misspecification, such as non-latent normality.

Purpose of the Study:

  • To develop a novel estimator for polychoric correlation robust to partial model misspecification.
  • To address issues caused by unknown fractions of misspecified observations, like careless respondents.

Main Methods:

  • A robust loss function minimizing divergence between observed and theoretical frequencies.
  • The estimator generalizes ML, is consistent, asymptotically normal, and computationally efficient.

Main Results:

  • The proposed estimator demonstrates robustness against partial misspecification in simulations.
  • Empirical application on Big Five data revealed substantial differences from ML estimates, likely due to careless respondents.

Conclusions:

  • The novel estimator offers a robust alternative to ML for polychoric correlations, particularly when dealing with potential data anomalies.
  • This method enhances the reliability of structural equation modeling with rating scale data and aids in identifying problematic responses.