On the distribution of the correlation coefficient when sampling from a mixture of two bivariate normal densities: Robustness and the effect of outliers

1984 ◽  
Vol 12 (2) ◽  
pp. 119-133 ◽  
Author(s):  
M. S. Srivastava ◽  
G. C. Lee
Keyword(s):  
Correlation Coefficient ◽  
Bivariate Normal

Effects of Scaling on the Correlation Coefficient: Additional Considerations

1978 ◽  
Vol 15 (2) ◽  
pp. 304-308 ◽  
Author(s):  
Warren S. Martin
Keyword(s):  
Normal Distribution ◽  
Correlation Coefficient ◽  
Correlation Coefficients ◽  
Bivariate Normal Distribution ◽  
Information Loss ◽  
Simulation Data ◽  
Pearson Product Moment Correlation ◽  
Bivariate Normal ◽  
Amount Of Information ◽  
Restricted Number

Distortion in the Pearson product moment correlation due to a restricted number of scale points is evaluated in two ways. First, a simulation of the bivariate normal distribution is used to estimate the effects of varying the number of scale points on the product moment correlation. This procedure demonstrates a substantial amount of information loss. Second, other correlation coefficients and some methods to correct for this loss are discussed and related to the simulation data.

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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