multistageoptimum.grid: Function for optimizing multi-stage selection with grid algorithm for a given correlation matrix

Description

This function is used to calculate the maximum of $\Delta G$ for a given correlation matrix by grid search algorithm.

Usage

multistageoptimum.grid(corr, Vg,
num.grid, width, Budget, CostProd,
CostTest,Nf,alg,detail,fig,N.upper, N.lower)

Arguments

is genotypic variance $\delta_y^2$. The default value is 1.

corr

is the correlation matrix of y and X, which is introduced in the function multistagecorr. The correlation matrix must be symmetric and positive-definite. If the estimated correlation matrix is negative-definite, it must be adjusted before using this funct

num.grid

is the number of equally distanced points that divided the axis of $x_1$ into $num.grid_i-1$ intervals and there are $\prod_i(num.grid_i)$ grids in a n dimensional hyper cube. If $num.grid > N_i$, then the number of grid points for the i-th axis is $N_i

width

is the width between the equally distanced points. The default value is NA.

Budget

contains the value of total budget.

CostProd

contains the initial costs of producing or providing a candidate in each stage

CostTest

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.

is the number of finally selected candidates.

detail

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

alg

is used to switch between two algorithms. If alg = GenzBretz(), which is by default, the quasi-Monte Carlo algorithm from Genz et al. (2009, 2013), will be used. If alg = Miwa(), the program will use the Miwa algorithm (Mi et al.

fig

is the control parameter to decide if a figure of contour plot will be saved in the default folder of R. The default value is FALSE, which means no figure will be saved.

N.upper

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

N.lower

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

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 $\Delta G$. Otherwise, the result for all the grid points, which have been calculated, will be exported as a table.

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 0.9-9995, 2013. G.M. Tallis. Moment generating function of truncated multi-normal distribution. J. Royal Stat. Soc., Ser. B, 23(1):223-229, 1961. W.G. Cochran. Improvement by means of selection. In J. Neyman (ed.) Proc. 2nd Berkeley Symp. on Mathematical Statistics and Probability. University of California Press, Berkeley, 1951. X. Mi, T. Miwa and T. Hothorn. Implement of Miwa's analytical algorithm of multi-normal distribution. R Journal, 1:37-39, 2009.

Examples

Run this code

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  
)

Budget=200

multistageoptimum.grid( Vg=1, num.grid=11, corr=corr, Budget=Budget,
 CostProd=c(0.5,0,0), CostTest=c(0.5,1,1), Nf=5, 
N.upper=rep(Budget,3), N.lower=rep(1,3))

multistageoptimum.grid( Vg=1, num.grid=11, corr=corr, Budget=Budget,
 CostProd=c(0.5,0,0), CostTest=c(0.5,1,1), Nf=5, 
N.upper=rep(Budget,3), N.lower=rep(1,3),detail=TRUE,fig=TRUE)