Partial Identification of Latent Correlations with Ordinal Data.

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.