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Article

Bivariate Distributions Underlying Responses to Ordinal Variables

Faculty of Social and Behavioural Sciences, University of Amsterdam, 1012 WX Amsterdam, The Netherlands
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Academic Editor: Alexander Robitzsch
Psych 2021, 3(4), 562-578; https://doi.org/10.3390/psych3040037
Received: 6 August 2021 / Revised: 17 September 2021 / Accepted: 18 September 2021 / Published: 1 October 2021
The association between two ordinal variables can be expressed with a polychoric correlation coefficient. This coefficient is conventionally based on the assumption that responses to ordinal variables are generated by two underlying continuous latent variables with a bivariate normal distribution. When the underlying bivariate normality assumption is violated, the estimated polychoric correlation coefficient may be biased. In such a case, we may consider other distributions. In this paper, we aimed to provide an illustration of fitting various bivariate distributions to empirical ordinal data and examining how estimates of the polychoric correlation may vary under different distributional assumptions. Results suggested that the bivariate normal and skew-normal distributions rarely hold in the empirical datasets. In contrast, mixtures of bivariate normal distributions were often not rejected. View Full-Text
Keywords: polychoric correlation; ordinal data; underlying bivariate normality; mixture of bivariate normal distributions polychoric correlation; ordinal data; underlying bivariate normality; mixture of bivariate normal distributions
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MDPI and ACS Style

Kolbe, L.; Oort, F.; Jak, S. Bivariate Distributions Underlying Responses to Ordinal Variables. Psych 2021, 3, 562-578. https://doi.org/10.3390/psych3040037

AMA Style

Kolbe L, Oort F, Jak S. Bivariate Distributions Underlying Responses to Ordinal Variables. Psych. 2021; 3(4):562-578. https://doi.org/10.3390/psych3040037

Chicago/Turabian Style

Kolbe, Laura, Frans Oort, and Suzanne Jak. 2021. "Bivariate Distributions Underlying Responses to Ordinal Variables" Psych 3, no. 4: 562-578. https://doi.org/10.3390/psych3040037

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