multistagetp | R Documentation |
This function calculates the coordinates of the truncation points Q for given selected fractions \vec{α}=\{ α_{1},α_{2},...,α_{n} \} and correlation matrix of X. The R function uniroot in core package stats is called internally to solve the truncation point equations.
multistagetp(alpha, corr, alg)
alpha |
is probability vector \vec{α} for random variable X. In plant breeding, it is also called the selected fraction. |
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 function. Before starting the calculations, it is recommended to check the correlation matrix. |
alg |
is used to switch between two algorithms. If |
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{α}. 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 \vec{α}. The function multistagetp is used by function mulistagegain to calculate the expected gain.
The output is a vector of the coordinates.
When a \vec{α} is given, the quantiles are calculated consecutively to satisfy the given \vec{α}. The calculation from other direction to -∞ of the integral is also possible for qmvnorm().
Xuefei Mi
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.
selectiongain(), qnorm()
# 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)
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