selectiongain (version 2.0.23)

multistagetp: Function for calculating the truncation points

Description

This function calculates the coordinates of the truncation points Q for given selected fractions $\vec{\alpha}={ \alpha_{1},\alpha_{2},...,\alpha_{n} }$ and correlation matrix of X. The R function uniroot in core package stats is called internally to solve the truncation point equations. It is needed for multistagegain function to calculated the expected selection gain.

Usage

multistagetp(alpha,  corr,  alg)

Arguments

alpha

(n-dimensional vector) is probability vector $\vec{\alpha}$ for random variable X. In plant breeding, it is also called the selected fraction.

corr

(n+1-dimensional matrix) is the correlation matrix of y and X, which is introduced in function multistagecorr. The correlation matrix must be symmetric and positive-definite. The correlation matrix estimated from practices sometimes can be negative-defini

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.

Value

• The output is a vector of the coordinates.

Details

This function calculates the non-equi coordinate quantile vector $Q={q_{1},q_{2},...,q_{n}}$ for a multivariate normal distribution from a given $\vec{\alpha}$. It can be compared with the function qmvnorm() in R-package mvtnorm, which calculates only the equi coordinate quantile $q$ for multi-variate normal distribution from a given alpha scalar.

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. X. Mi, T. Miwa and T. Hothorn. Implement of Miwa's analytical algorithm of multi-normal distribution, R Journal, 1:37-39, 2009.

See Also

selectiongain(), qnorm()

Examples

# first example

VCGCAandError=c(0.40,0.20,0.20,0.40,2.00)
VCSCA=c(0.20,0.10,0.10,0.20)

corr.matrix = multistagecor(maseff=0.40, VGCAandE=VCGCAandError,
VSCA=VCSCA, T=c(1,1,5), L=c(1,3,8), Rep=c(1,1,1))

N1=4500;N2=919;N3=45;Nf=10

Q=multistagetp(c(N2/N1,N3/N2,Nf/N3),  corr=corr.matrix)