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Asymptotic Robustness Study of the Polychoric Correlation Estimation.

Shaobo Jin1, Fan Yang-Wallentin2

  • 1Department of Statistics, Uppsala University, 751 20 , Uppsala, Sweden. shaobo.jin@statistik.uu.se.

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|September 24, 2016
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Robustness in polychoric correlation estimation is crucial. Using non-normal assumptions like skew-normal distributions can reduce bias when the underlying data distribution is uncertain, improving accuracy.

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asymptotic covariance matrixnon-normalitypseudo-maximum likelihoodunderlying distribution

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Area of Science:

  • Statistics
  • Econometrics
  • Psychometrics

Background:

  • Polychoric correlation is widely used for ordinal variables.
  • Standard estimation methods often assume underlying normality.
  • Distributional misspecification can lead to biased correlation estimates.

Purpose of the Study:

  • To investigate the asymptotic robustness of polychoric correlation estimation.
  • To evaluate the impact of non-normal distributional assumptions on estimation bias.
  • To compare bias under normal, t-distribution, and skew-normal assumptions.

Main Methods:

  • Derivation of asymptotic normality for the pseudo-maximum likelihood estimator.
  • Implementation of a two-step estimation procedure.
  • Numerical simulations using t-distribution and skew-normal distributions as alternatives to normality.

Main Results:

  • The normal distribution assumption can introduce substantial bias, even with minor deviations in skewness and kurtosis.
  • The skew-normal distribution assumption generally yields lower bias compared to the normal distribution assumption.
  • The t-distribution assumption also shows potential for bias reduction over the normal assumption.

Conclusions:

  • Asymptotic robustness of polychoric correlation estimation is demonstrated.
  • Employing non-normal distributional assumptions is recommended when normality is questionable.
  • The skew-normal assumption offers a promising alternative for more accurate polychoric correlation estimation in practice.