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Asymptotic Robustness Study of the Polychoric Correlation Estimation

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  • Shaobo Jin

    (Uppsala University)

  • Fan Yang-Wallentin

    (Uppsala University)

Abstract

Asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied. The asymptotic normality of the pseudo-maximum likelihood estimator is derived using the two-step estimation procedure. The t distribution assumption and the skew-normal distribution assumption are used as alternatives to the normal distribution assumption in a numerical study. The numerical results show that the underlying normal distribution can be substantially biased, even though skewness and kurtosis are not large. The skew-normal assumption generally produces a lower bias than the normal assumption. Thus, it is worth using a non-normal distributional assumption if the normal assumption is dubious.

Suggested Citation

  • Shaobo Jin & Fan Yang-Wallentin, 2017. "Asymptotic Robustness Study of the Polychoric Correlation Estimation," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 67-85, March.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:1:d:10.1007_s11336-016-9512-2
    DOI: 10.1007/s11336-016-9512-2
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    1. Alessandro Barbiero & Asmerilda Hitaj, 2020. "Goodman and Kruskal’s Gamma Coefficient for Ordinalized Bivariate Normal Distributions," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 905-925, December.
    2. Shaobo Jin, 2022. "Frequentist Model Averaging in Structure Equation Model With Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 1130-1145, September.

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