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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

Measures of association of two bivariate Gaussian variables as a function of their correlation (ρ). The straight lines give the strength of the association as measured by the absolute value of ρ. The dotted (‘holds water’: θ) and dashed (‘spills water’: 1 − θ) lines depict the relative contributions to the Kullback-Leibler distance due to discrepancies under independence and dependence models, respectively. Values of the association measure γ=2θ − 1 are represented by the dark solid line.
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fig01: Measures of association of two bivariate Gaussian variables as a function of their correlation (ρ). The straight lines give the strength of the association as measured by the absolute value of ρ. The dotted (‘holds water’: θ) and dashed (‘spills water’: 1 − θ) lines depict the relative contributions to the Kullback-Leibler distance due to discrepancies under independence and dependence models, respectively. Values of the association measure γ=2θ − 1 are represented by the dark solid line.

Mentions: The values of θ and of 1 − θ are plotted against ρ in Fig. 1. The dotted line (‘holds water’) gives the relative discrepancy (θ) away from the independence models when this is true, and the dashed line (‘spills water’) depicts the trajectory of 1 − θ, i.e. the relative discrepancy under association; note that a given curve is a mirror image of the other. As the absolute value of the correlation increases θ → 1, as one would expect. Since an association index with values ranging between 0 and 1 may be easier to interpret, an alternative measure could be


On measures of association among genetic variables.

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

Measures of association of two bivariate Gaussian variables as a function of their correlation (ρ). The straight lines give the strength of the association as measured by the absolute value of ρ. The dotted (‘holds water’: θ) and dashed (‘spills water’: 1 − θ) lines depict the relative contributions to the Kullback-Leibler distance due to discrepancies under independence and dependence models, respectively. Values of the association measure γ=2θ − 1 are represented by the dark solid line.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig01: Measures of association of two bivariate Gaussian variables as a function of their correlation (ρ). The straight lines give the strength of the association as measured by the absolute value of ρ. The dotted (‘holds water’: θ) and dashed (‘spills water’: 1 − θ) lines depict the relative contributions to the Kullback-Leibler distance due to discrepancies under independence and dependence models, respectively. Values of the association measure γ=2θ − 1 are represented by the dark solid line.
Mentions: The values of θ and of 1 − θ are plotted against ρ in Fig. 1. The dotted line (‘holds water’) gives the relative discrepancy (θ) away from the independence models when this is true, and the dashed line (‘spills water’) depicts the trajectory of 1 − θ, i.e. the relative discrepancy under association; note that a given curve is a mirror image of the other. As the absolute value of the correlation increases θ → 1, as one would expect. Since an association index with values ranging between 0 and 1 may be easier to interpret, an alternative measure could be

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