Selectiongain: an R package for optimizing multi-stage selection. (English) Zbl 1342.65050

Mi, Xuefei; Utz, H. Friedrich; Melchinger, Albrecht E.

Comput. Stat. 31, No. 2, 533-543 (2016).

Summary: Multi-stage selection is practised in numerous fields of the life sciences and particularly in breeding. A special characteristic of multi-stage selection is that candidates are evaluated in successive stages with increasing intensity and efforts, and only a fraction of the superior candidates is selected and promoted to the next stage. For the optimum design of such selection programs, the selection gain \(\varDelta G(y)\) plays a central role. It can be calculated by integration of a truncated multivariate normal distribution. While mathematical formulas for calculating \(\varDelta G(y)\) and \(\psi (y)\), the variance among the selected candidates, were developed a long time ago, solutions and software for numerical calculations were not available. We developed the R package selectiongain for efficient and precise calculation of \(\varDelta G(y)\) and \(\psi (y)\) for (i) a given matrix \(\boldsymbol{\Sigma}^*\) of correlations among the unobservable target character and the selection criteria and (ii) given coordinates \(\mathbf Q\) of the truncation point or the selected fractions \(\boldsymbol{\alpha}\) in each stage. In addition, our software can be used for optimizing multi-stage selection programs under a given total budget and different costs of evaluating the candidates in each stage. Besides a detailed description of the functions of the software, the package is illustrated with two examples.

MSC:

62-08	Computational methods for problems pertaining to statistics
62-04	Software, source code, etc. for problems pertaining to statistics
62L10	Sequential statistical analysis
62F07	Statistical ranking and selection procedures

Keywords:

selection gain; multivariate normal integral; optimal allocations

Software:

mvtnorm; R; Selectiongain; BRENT

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