Limits...
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

Show MeSH

Related in: MedlinePlus

Indexes of association as a function of the coefficient of correlation in an equi-correlated trivariate normal distribution. The thick solid line gives the relative Kullback-Leibler discrepancy between distributions when independence holds (θ), and the dashed line gives the relative discrepancy when association is true (1 − θ). The thin line gives the trajectory of γ=2θ − 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3569618&req=5

fig02: Indexes of association as a function of the coefficient of correlation in an equi-correlated trivariate normal distribution. The thick solid line gives the relative Kullback-Leibler discrepancy between distributions when independence holds (θ), and the dashed line gives the relative discrepancy when association is true (1 − θ). The thin line gives the trajectory of γ=2θ − 1.

Mentions: With 0 < θ < 1. For example, for ρ = 0.25, 0.50 and 0.75, the index of association θ takes values 0.49, 0.54 and 0.66 respectively. Figure 2 depicts θ, 1 − θ and θ as a function of the coefficient of correlation. At ρ = 0, θ = 0.5, but then it decreases slightly as the correlation increases such that γ does not attain a positive value until γ reaches a value of about 0.3. Note that θ is not symmetric with respect to ρ (the same is true of /R/); for instance, when θ = 0.59 so that association would be viewed as stronger than when since θ = 0.49 then. This is a consequence of the values that the discrepancies DIA and DAI take at varying values of ρ.


On measures of association among genetic variables.

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

Indexes of association as a function of the coefficient of correlation in an equi-correlated trivariate normal distribution. The thick solid line gives the relative Kullback-Leibler discrepancy between distributions when independence holds (θ), and the dashed line gives the relative discrepancy when association is true (1 − θ). The thin line gives the trajectory of γ=2θ − 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig02: Indexes of association as a function of the coefficient of correlation in an equi-correlated trivariate normal distribution. The thick solid line gives the relative Kullback-Leibler discrepancy between distributions when independence holds (θ), and the dashed line gives the relative discrepancy when association is true (1 − θ). The thin line gives the trajectory of γ=2θ − 1.
Mentions: With 0 < θ < 1. For example, for ρ = 0.25, 0.50 and 0.75, the index of association θ takes values 0.49, 0.54 and 0.66 respectively. Figure 2 depicts θ, 1 − θ and θ as a function of the coefficient of correlation. At ρ = 0, θ = 0.5, but then it decreases slightly as the correlation increases such that γ does not attain a positive value until γ reaches a value of about 0.3. Note that θ is not symmetric with respect to ρ (the same is true of /R/); for instance, when θ = 0.59 so that association would be viewed as stronger than when since θ = 0.49 then. This is a consequence of the values that the discrepancies DIA and DAI take at varying values of ρ.

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