edrUnderdet: EDR space estimation for underdetermined cases.

In edrGraphicalTools: Provides Tools for Dimension Reduction Methods

Description

Gathers several procedures to estimate the effective dimension regression (EDR) space when the number of explanatory variables is greater than the sample size. Creates an object of class edr.

Usage

edrUnderdet(Y, X, H, K, method, initEDR=NULL, maxIter=NULL, 
regulParam=NULL, sMin=1e-16, sChg=10, btspSamp=NULL)

Arguments

Y	A numeric vector representing the dependent variable (a response vector).
X	A matrix representing the quantitative explanatory variables (bind by column).
H	When method="SR-SIR" or method="RSIR", the chosen number of slices. When method="SIR-QZ", a vector with various numbers of slices.
K	The chosen dimension K.
method	This character string specifies the method of fitting. It should be either "SIR-QZ", "RSIR" or "SR-SIR".
initEDR	When method="SR-SIR", a p x K matrix which contains initial values for the iterative algorithm that estimates EDR directions.
maxIter	When method="SR-SIR", a maximum number of iterations after which the algorithm stops.
regulParam	When method="SR-SIR" or method="RSIR", a vector containing possible values of the regularization parameter, from which the optimal one will be chosen.
sMin	When method="SIR-QZ", the smallest regularization parameter to test.
sChg	When method="SIR-QZ", a positive real by which a regularization parameter is multiplied to produce the next one to consider.
btspSamp	When method="RSIR", the bootstrap sample size for estimating the mean squared error.

Details

The "SIR-QZ" method estimates the indices rather than the EDR directions. It makes use of several estimations from several numbers of slices. It tries to find a minimal regularization of the covariance matrix of X. The "RSIR" procedure uses a bootstrap estimator of the mean squared error of regularized estimates of the EDR directions. It was translated from a Matlab code made by Peng Zeng. The "SR-SIR" procedure relies on a generalized cross-validation criterion and on an alternating least squares algorithm to find an optimal regularization parameter. It was written using a R code made by Lexin Li.

Value

edrUnderdet returns an object of class edr, with some of the following attributes, depending on the value of method:

matEDR	A matrix spanning the estimated EDR space.
indices	The estimated indices from the "SIR-QZ" method.
eigvalEDR	The eigenvalues of a matrix of interest.
K	The chosen dimension.
H	The chosen number(s) of slices.
n	The sample size.
method	The dimension reduction method used.
X	The matrix of the quantitative explanatory variables (bind by column).
Y	The numeric vector of the dependent variable (a response vector).
s	The optimal regularization parameter(s) found by the chosen method.
estMSE	For each tested regularization parameter, the estimated mean squared error from the "RSIR" method.
testedEDR	For each tested regularization parameter, a matrix spanning the estimated EDR space from the "SR-SIR" method.
iter	For each tested regularization parameter, the number of iterations needed for the alternating least squares algorithm from the "SR-SIR" method to converge.
gcv	For each tested regularization parameter, the corresponding generalized cross-validation criterion from the "SR-SIR" method.

Author(s)

Raphaël Coudret <[e-mail]>, Benoît Liquet <[e-mail]> and Jérôme Saracco <[e-mail]>

References

Coudret, R., Liquet, B. and Saracco, J. Comparison of sliced inverse regression approaches for underdetermined cases. Journal de la Société Française de Statistique, in press.

Li, L. and Yin, X. (2008). Sliced inverse regression with regularizations. Biometrics, 64(1):124-131.

Zhong, W., Zeng, P., Ma, P., Liu, J. S., and Zhu, Y. (2005). RSIR: regularized sliced inverse regression for motif discovery. Bioinformatics, 21(22):4169-4175.

See Also

edr, sliceMat

Examples

## Not run: 
n <- 100
p <- 200
K <- 2
H <- 3:8
beta1 <- c(1,1,1,1,rep(0,p-4))
beta2 <- c(rep(0,p-4), 1,1,1,1)
X <- rmvnorm(n,sigma=diag(p))
eps <- rnorm(n,sd=10)
Y <- (X%*%beta1)^3 + (X%*%beta2)^3+eps
result <- edrUnderdet(Y,X,H,K,"SIR-QZ")
summary(result)
plot(result)

## End(Not run)

edrGraphicalTools documentation built on May 2, 2019, 3:44 a.m.