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Polychoric correlation estimates latent correlations for ordinal data but assumes bivariate normality. This study calculates possible latent correlation values without this assumption, showing they converge with more categories.

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Area of Science:

  • Statistics
  • Psychometrics
  • Data Analysis

Background:

  • Polychoric correlation is widely used for ordinal data association.
  • It estimates latent correlations assuming bivariate normality.
  • This normality assumption is often not met in practice.

Purpose of the Study:

  • To determine the range of possible latent correlations when bivariate normality is not assumed.
  • To investigate how this range changes with the number of ordinal categories.
  • To explore partial identification under latent symmetry and mixed-variable scenarios.

Main Methods:

  • Calculating partial identification sets for latent correlations.
  • Analyzing the convergence of these sets with increasing categories.
  • Investigating partial identification with symmetric latent copulas and mixed continuous-ordinal data.

Main Results:

  • Partial identification sets provide a range of possible latent correlations when normality is violated.
  • These sets shrink towards the true latent correlation as the number of categories increases.
  • Limited information about latent correlations is available without many categories or distributional knowledge.

Conclusions:

  • The polychoric correlation's validity is questionable without justified bivariate normality.
  • Partial identification offers a more robust approach to estimating latent correlations.
  • Practical application requires careful consideration of category numbers and distributional assumptions, with an R package available.