Estimation for a Common Correlation Coefficient in Bivariate Normal Distributions with Missing Observations

Biometrics ◽  
1998 ◽  
Vol 54 (3) ◽  
pp. 1136 ◽  
Author(s):  
Mihoko Minami ◽  
Kunio Shimizu
Keyword(s):  
Correlation Coefficient ◽  
Missing Observations ◽  
Normal Distributions ◽  
Bivariate Normal

scholarly journals Bivariate Distributions Underlying Responses to Ordinal Variables

Psych ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 562-578
Author(s):  
Laura Kolbe ◽  
Frans Oort ◽  
Suzanne Jak
Keyword(s):  
Correlation Coefficient ◽  
Latent Variables ◽  
Ordinal Data ◽  
Bivariate Normal Distribution ◽  
Polychoric Correlation ◽  
Bivariate Distributions ◽  
Normal Distributions ◽  
Ordinal Variables ◽  
Bivariate Normal ◽  
Bivariate Normality

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.

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