On measures of association among genetic variables.
Bottom Line: These are more general than correlations, which are pairwise measures, and lack a clear interpretation beyond the bivariate normal distribution.Our measures are based on logarithmic (Kullback-Leibler) and on relative 'distances' between distributions.Two multivariate beta and multivariate beta-binomial processes are examined, and new distributions are introduced: the GMS-Sarmanov multivariate beta and its beta-binomial counterpart.
Affiliation: Department of Animal Sciences, University of Wisconsin-Madison, Madison, WI, 53706, USA. email@example.comShow MeSH
Related in: MedlinePlus
Mentions: Where 0 < X < 1 and 0 < Y < 1. Moments E(XkYl) cannot be written in closed form but can be approximated numerically or using sampling methods. Large c and small a, b produce correlations close to 0, whereas large a, b or small c produce correlations close to 1 (Olkin & Liu 2003). For example, a correlation equal to 0.002 is obtained for a = b = 0.01 and c = 5, whereas the correlation is 0.91 for a = 2.5, b = 4 and c = 0.1. Figure 4 displays scatter plots of 5000 samples obtained from each of four bivariate beta distributions. Plot 1 represents a distribution in which the correlation is very low, and yet, there is considerable association between pairs of values near 0, illustrating inadequacy of correlation to reveal association. In plot 2 (resembling a ‘meteorite’) clustering takes place primarily at large values of X and Y. The two bottom plots depict bivariate beta distributions with similar correlations but with a completely different pattern of association. Clearly, correlation often fails as measure of statistical association.
Affiliation: Department of Animal Sciences, University of Wisconsin-Madison, Madison, WI, 53706, USA. firstname.lastname@example.org