Derivative free methods in covariance components estimation
Kovac, Milena
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https://hdl.handle.net/2142/19767
Description
Title
Derivative free methods in covariance components estimation
Author(s)
Kovac, Milena
Issue Date
1992
Department of Study
Animal Sciences
Discipline
Animal Sciences
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Agriculture, Animal Culture and Nutrition
Engineering, Agricultural
Language
eng
Abstract
The downhill simplex (DS), Powell's (PO), and Rosenbrock's (RO) algorithm were optimized and applied to estimation of dispersion parameters. The optimization is independent of the log-likelihood function and thus, from the model. The model can accommodate two additive genetic effects and genetic groups for unknown ancestors.
Memory requirements and CPU time are determined by the size of equation system. While memory requirements of optimization algorithms are negligible, the CPU time depends on the number of evaluations. Convergence rate is linear for the three algorithms. Numerical stability was increased by scaling and by elimination of dependent equations. Robustness was increased by scaling and by minimum optimization steps. Frequent restarts improved robustness in DS. PO and RO are sensitive to linearly dependent directions. In addition, they fail more often with severe restrictions within linear search.
DS performed more efficiently with frequent restarts which were triggered by an allowance step and a lower decreasing rate. Contrary, the other two algorithms were less affected by the allowance step. PO and RO were efficient if started in the middle of parameter space, i.e. correlations close to zero and equal ratios for variances. The efficiency of the two algorithms was also affected by restrictions on the number of evaluations per linear search, the order of optimization and scaling.
In addition, covariances were estimated for daily gain on three growing intervals of boars and the post-birth daily gain and backfat of gilts. Records on boars contained missing values due to multiple stage selection. Heritability estimates were.17,.16,.20,.24, and.23 for daily gain in boars from birth to 30, 30 to 60, and 60 to 100 kg and for post-birth daily gain and backfat in gilts, respectively. The corresponding proportions for common litter effects were.26,.18,.11,.12, and.04. Correlations between adjacent intervals for daily gain were higher than estimates between nonadjacent intervals for both random effects. In gilts, the correlations were.11 and $-$.14 for genetic and litter effect. Correlations between daily gain in boars and post-birth daily gain in gilts were high for genetic and moderate for litter effects.
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