[gov3009-l] Sorensen on "Modelling components of variation"

Matt Blackwell mblackwell at iq.harvard.edu
Tue Apr 27 08:23:37 EDT 2010

Hi there,

We hope you will join us this Wednesday, April 28th at the Applied
Statistics workshop when we will be happy to have Daniel Sorensen from
University of Aarhus. Details and an abstract are below. A light lunch
will be served. Thanks!

"Modelling components of variation: is environmental variance of
quantitative traits genetically controlled?"
Daniel Sorensen
University of Aarhus
April 28th, 2010, 12 noon
K354 CGIS Knafel (1737 Cambridge St)

    The classical model of quantitative genetics assumes that
genotypes affect phenotypic values and means but that the variance of
phenotype, given genotype (environmental variance) is the same for all
genotypes. An extension (HET) postulates that both mean and
variability differ between genotypes. Over recent years, statistical
support for a genetic component at the level of the environmental
variance has come from fitting the HET model to field or experimental
data in various species. Since the skewness of the marginal
distribution of the data under the HET model is directly proportional
to the coefficient of correlation between genes affecting mean and
variance, there is the concern that statistical support for the HET
model may be an artifact of the scale of measurement. One may pose the
question: Is there still support for the HET model when the data are
analyzed in the “correct”scale? Here this was investigated by
extending the HET model to accommodate the family of Box-Cox
transformations. Litter size data in rabbits and pigs that had
previously been analyzed in the untransformed scale were reanalyzed in
a scale equal to the mode of the marginal posterior distribution of
the Box-Cox parameter. In the rabbit data, the statistical evidence
for a genetic component at the level of the environmental variance is
considerably weaker than that resulting from an analysis in the
original metric. In the pig data, the statistical evidence is
stronger, but the coefficient of correlation between additive genetic
effects affecting mean and variance changes sign, compared to the
results in the untransformed scale. The study confirms that inferences
on variances can be strongly affected by the presence of asymmetry in
the distribution of the data. We recommend that to avoid one important
source of spurious inferences, future work seeking support for a
genetic component acting on environmental variation using a parametric
approach based on normality assumptions, confirms that these are met.


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