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(since 2/6/2000).
Unpublished and future papers
- Meyer, K. (2003).
"Random regression models for analyses of longitudinal data in animal
breeding."
Manuscript
(pdf file, 245 KB,
377 downloads).
-
Mixed model analyses via restricted maximum likelihood, fitting the
so-called animal model, have become standard methodology for the
estimation of genetic variances. Models involving multiple genetic
variance components, due to different modes of gene action, are
readily fitted. It is shown that likelihood based calculations may
provide insight into the quality of the resulting parameter estimates,
and are readily applicable to the validation of experimental designs.
This is illustrated for the example of a design suggested recently to
estimate X-linked genetic variances. In particular, large sample
variances and sampling correlations are demonstrated to provide an
indication of 'problem' scenarios. Using simulation, it is shown that
the profile likelihood function provides more appropriate estimates of
confidence intervals than large sample variances. Examination of the
likelihood function and its derivatives are recommended as part of the
design stage of quantitative genetic experiments.
Meyer, K. (2008). "Likelihood calculations to evaluate experimental
designs to estimate genetic variances."
Heredity (in
press).
doi:10.1038/hdy.2008.46
· Manuscript
(pdf file, 614 KB,
198 downloads).
-
Properties of reduced rank estimates of genetic covariance matrices
from restricted maximum likelihood analyses are examined for the
example of a balanced, paternal half-sib design. Estimation is
equivalent to considering the leading genetic principal components
only. It is shown that estimates can be biased over and above the
bias due to ignoring the least important principal components. This
`extra' bias is attributed to picking up a wrong subset of
components. The theoretical bias is inverse proportional to the
degree of genetic relationship among family members but independent
of sample size. A simulation study demonstrates close agreement
between predicted and observed bias for large samples, while
agreement for small samples is less good, due to effects of sampling
variation on the spread of estimated eigenvalues and constraints
imposed on the parameter space. It is emphasized that the rank of
the genetic covariance matrix should be chosen sufficiently large to
accommodate all important genetic principal components, even though,
paradoxically, this may require including number of components with
negligible eigenvalues. A strategy for rank selection in practical
analyses is outlined.
Meyer, K. and Kirkpatrick, M. (2008).
"Perils of parsimony: Properties of reduced rank estimates of genetic covariance matrices"
Manuscript
(pdf file, 593 KB,
233 downloads).
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A review of the literature is presented, showing that the mixed
model analogues of models employed in the analysis of
multi-environment trials in plant breeding are directly applicable
to genotype X environment and related problems in animal breeding.
In particular, the so-called 'additive main effect, multiplicative
interaction' models accommodate heterogeneity of variance, and are
characterised by a factor-analytic covariance structure. While this
can be implemented by imposing such structure on the genetic
covariance matrix in a multi-trait model, an equivalent model is to
fit the genetic common factors and specific effects separately.
This increases the total number of equations in the model. However,
as both common factors and specific effects for an individual are
uncorrelated, the coefficient matrix in the pertaining mixed model
equations is sparse, with dramatically reduced non-zero off-diagonal
elements. Using international genetic evaluation as an example, it
is shown that such `extended' factor analytic model can
substantially reduce computational requirements of genetic
evaluation schemes, in addition to providing a parameterisation
which is of interest in its own right. Cases investigated include
simulated data for a trait recorded in 8, 12 or 16 countries, and
data on weaning weight in beef cattle, including those from a
current feasibility study for a world-wide genetic evaluation in
Hereford. Results suggest that with judicious implementation,
reductions in computing time of 50\% or more are feasible.
Meyer, K. (2008).
"Sweet FA: Scope for a
factor-analytic model for genotype x environment problems such as
international genetic evaluation"
Manuscript
(pdf file, 281 KB,
21 downloads).