multistagevariance {selectiongain} | R Documentation |
Expected variance after selection after k stages selection
Description
This function uses the algorithm described by Tallis (1961) to calculate the variance after multi-stage selection.
The variance among candidates of y in the selected area \textbf{S}_{Q}
is defined as the second central moment, \psi_n(y)=E(Y^2|\textbf{S}_{Q}) - \left[E(Y|\textbf{S}_{Q})\right]^2
,
where
E(Y^2|\textbf{S}_{Q}) = \alpha^{-1} \int_{-\infty} ^\infty \int_{q_{1}}^\infty...\int_{q_{n}}^\infty y^2\, \phi_{n+1}(\textbf{x}^{*}; \bm{\Sigma}^{*}) \, d \textbf{x}^*
Usage
multistagevariance(Q, corr, alg, Vg)
Arguments
Q |
are the coordinates of the truncation points, which are the output of the function multistagetp that we are going to introduce. |
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 |
Vg |
correspond to the genetic variance or variance of the GCA effects. The default value is 1 |
Value
The output is the value of \psi_n(y|\textbf{S}_{Q})
.
Note
No further notes
Author(s)
Xuefei Mi
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.
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
No link
Examples
# first example
Q =c(0.4308,0.9804,1.8603)
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
)
multistagevariance(Q=Q,corr=corr,alg=Miwa)
# time comparsion
var.time.miwa=system.time (var.miwa<-multistagevariance(Q=Q,corr=corr,alg=Miwa))
var.time.bretz=system.time (var.bretz<-multistagevariance(Q=Q,corr=corr))
# second examples
Q= c(0.9674216, 1.6185430)
corr=matrix( c(1, 0.7071068, 0.9354143,
0.7071068, 1, 0.7559289,
0.9354143, 0.7559289, 1),
nrow=3
)
multistagevariance(Q=Q,corr=corr,alg=Miwa)
var.time.miwa=system.time (var.miwa<-multistagevariance(Q=Q, corr=corr, alg=Miwa))
var.time.bretz=system.time (var.bretz<-multistagevariance(Q=Q, corr=corr))
# third examples
alpha1<- 1/(24)^0.5
alpha2<- 1/(24)^0.5
Q=multistagetp(alpha=c(alpha1,alpha2),corr=corr)
corr=matrix( c(1, 0.7071068,0.9354143,
0.7071068, 1, 0.7559289,
0.9354143, 0.7559289,1),
nrow=3
)
multistagevariance(Q=Q, corr=corr, alg=Miwa)