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

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

### Software:

mvtnorm; R; Selectiongain; BRENT
Full Text:

### References:

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