selectiongain (version 2.0.1)

multistageoptimal.grid: Function for optimizing multi-stage selection with grid algorithm for fixed correlation matrix

Description

This function is used to calculate the maximum of $\Delta G(y)$ with fixed correlation matrix.

Usage

multistageoptimal.grid(N.upper, N.lower=rep(1,length(N.upper)), corr, 
num.grid=11, Budget, CostC=1, CostTv=rep(1,length(N.upper)),N.fs, 
detail=FALSE,alg)

Arguments

N.upper

is the vector of up limits of number of candidates X.

N.lower

is the vector of low limits of number of candidates X.

corr

Correlation matrix of X.

num.grid

is the number of equally distanced points which divided the axis of $x_1$ into $num.grid-1$ intervals and there are $(num.grid-1)^n$ grids in a n dimensional hyper cube. The default value of num.grid is 11, so the hyper cube is divided into $10^n$ parts b

Budget

contains the value of total budget.

CostC

contains the costs of producing or identifying a candidate.

CostTv

contains a vector with length n reflecting the cost of evaluating a candidate in the tests performed at stage i, i=1,...,n. The cost might vary in different stages.

N.fs

is the number of final selected candidates.

detail

is the control parameter to decide if the result of all the grids will be given or only the maximum.

alg

is used to switch between two algorithms. If alg = GenzBretz(), which is by default, the quasi-Monte Carlo algorithm from Genz(1999) will be used. If alg = Miwa(), the program will use the Miwa algorithm (Mi2009), which an analytical solution of the MVN i

Value

• If $\texttt{detail}$ = FALSE, the output of this functions is a vector with the optimal number of candidates in each stage ($\textbf{N}$) and the maximum $\Delta G(y)$. Otherwise, the result for all the grid points, which have been calculated, will be exported as a table.

Details

More details are in the JSS paper section 3.5.

References

A. Genz and F. Bretz. Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics, Vol. 195, Springer-Verlag, Heidelberg, 2009. A. Genz, F. Bretz, T. Miwa, X. Mi, F. Leisch, F. Scheipl and T. Hothorn. mvtnorm: Multivariate normal and t distributions. R package version 0.9-9, 2010. G.M. Tallis. Moment generating function of truncated multi-normal distribution. Journal of the Royal Statistical Society, Series B, 23(1):223-229, 1961. H.F. Utz. Mehrstufenselecktion in der Pflanzenzuechtung. Doctor thesis, University Hohenheim, 1969. W.G. Cochran. Improvent by means of selection. In: Proceedings Second Berkeley Symposium on Math Stat Prof, pp449-470, 1951. X. Mi, T. Miwa and T. Hothorn. Implement of Miwa's analytical algorithm of multi-normal distribution, R Journal, 1:37-39, 2009. X. Mi, H.F. Utz. and A.E. Melchinger. R package selectiongain: A tool for efficient calculation and optimization of the expected gain from multi-stage selection. J Stat Softw. (submitted)

See Also

selectiongain()

Examples

corr=matrix( c(1,       0.3508,0.3508,0.4979,
               0.3508  ,1,     0.3016,0.5630,
               0.3508,  0.3016,1     ,0.5630,
               0.4979,  0.5630,0.5630,1), 
              nrow=4  
)

multistageoptimal.grid(N.upper=rep(100,3), corr=corr, Budget=200, CostC=0.5, N.fs=5)