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On measures of association among genetic variables.

Gianola D, Manfredi E, Simianer H - Anim. Genet. (2012)

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.

View Article: PubMed Central - PubMed

Affiliation: Department of Animal Sciences, University of Wisconsin-Madison, Madison, WI, 53706, USA. gianola@ansci.wisc.edu

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Related in: MedlinePlus

Discrepancies from independence to association (θ, solid line), and from association to independence (1 − θ, dashed line) as a fraction of the Kullback-Leibler distance between two tetravariate normal distributions. The straight lines give the absolute values of the correlation ρ.
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fig03: Discrepancies from independence to association (θ, solid line), and from association to independence (1 − θ, dashed line) as a fraction of the Kullback-Leibler distance between two tetravariate normal distributions. The straight lines give the absolute values of the correlation ρ.

Mentions: Figure 3 displays how θ and 1 − θ vary against ρ. At θ = 0 one has θ decreases somewhat subsequently and then increases, attaining 0.5 again at about ρ = 0.45. The values of the index of association suggest that the independence and association models are not ‘too distant’ unless the correlation is below −0.10, if negative, or above ρ = 0.50, if positive.


On measures of association among genetic variables.

Gianola D, Manfredi E, Simianer H - Anim. Genet. (2012)

Discrepancies from independence to association (θ, solid line), and from association to independence (1 − θ, dashed line) as a fraction of the Kullback-Leibler distance between two tetravariate normal distributions. The straight lines give the absolute values of the correlation ρ.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3569618&req=5

fig03: Discrepancies from independence to association (θ, solid line), and from association to independence (1 − θ, dashed line) as a fraction of the Kullback-Leibler distance between two tetravariate normal distributions. The straight lines give the absolute values of the correlation ρ.
Mentions: Figure 3 displays how θ and 1 − θ vary against ρ. At θ = 0 one has θ decreases somewhat subsequently and then increases, attaining 0.5 again at about ρ = 0.45. The values of the index of association suggest that the independence and association models are not ‘too distant’ unless the correlation is below −0.10, if negative, or above ρ = 0.50, if positive.

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.

View Article: PubMed Central - PubMed

Affiliation: Department of Animal Sciences, University of Wisconsin-Madison, Madison, WI, 53706, USA. gianola@ansci.wisc.edu

Show MeSH
Related in: MedlinePlus