sliceMat: Slicing matrix computation

In edrGraphicalTools: Provides Tools for Dimension Reduction Methods

Description

Returns the slicing matrix required for the "SIR-I" method.

Usage

sliceMat(Y, X, H, details=FALSE, rdSup=FALSE)

Arguments

Y	A numeric vector representing the dependent variable (a response vector).
X	A matrix representing the quantitative explanatory variables (bind by column).
H	The chosen number of slices.
details	A boolean that determines whether or not some matrices used to construct the slicing matrix should be sent back. See also 'Value'.
rdSup	When the number of slices is not a divisor of the sample size, this boolean determines whether or not the slices which contain an extra point are randomly chosen.

Details

This function divides the range of Y in H distinct intervals, or slices. It then puts every row of X into a slice with respect to the corresponding element of Y. It finally computes a matrix M = X_h' P_h X_h where each row of X_h is the mean vector over the vectors of X that belong to a given slice. The matrix P_h is diagonal and contains the number of rows of X placed in each sliced. The matrix M is required when trying to perform a sliced inverse regression.

Value

If details=FALSE, the p x p slicing matrix M, where p is the number of columns of X.

If details=TRUE, a list made of M, X_h and P_h.

Author(s)

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

See Also

edr, edrUnderdet

Examples

 

#The "SIR-I" method whithout using 'edr'
n <- 500
p <- 5
H <- 10
beta <- c(1, 1, 1, 0, 0)
X <- rmvnorm(n,rep(0,p),diag(p))
eps <- rnorm(n, 0, 10)
Y <- (X %*% beta)^3 + eps
M <- sliceMat(Y,X,H)
hatBeta <- eigen(solve(var(X)) %*% M)$vectors[,1]
cor(hatBeta,beta)^2
 

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