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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Unpublished and future papers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). -
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).