sgPLS (version 1.8)

tuning.sgPLS.X: Choice of the tuning parameters (number of groups and mixing parameter) related to predictor matrix for sgPLS model (regression mode)

Description

For a grid in two dimension of tuning parameters, this function computes by leave-one-out or M-fold cross-validation the MSEP (Mean Square Error of Prediction) of a sgPLS model.

Usage

tuning.sgPLS.X(X, Y, folds = 10, validation = c("Mfold", "loo"), ncomp,
				keepX = NULL, alpha.x = NULL, grid.gX, grid.alpha.X,
				setseed, progressBar = FALSE, ind.block.x = ind.block.x,
				upper.lambda = 10 ^ 9)

Value

The returned value is a list with components:

MSEP

vector containing the cross-validation score computed on the grid

keepX

value of the tuning parameter on which the cross-validation method reached it minimum.

alphaX

value of the tuning parameter (alpha) on which the cross-validation method reached it minimum.

Arguments

X

Numeric matrix or data frame \((n \times p)\), the observations on the \(X\) variables.

Y

Numeric matrix or data frame \((n \times q)\), the observations on the \(Y\) variables.

folds

Positive integer. Number of folds to use if validation="Mfold". Defaults to folds=10.

validation

Character string. What kind of (internal) cross-validation method to use, (partially) matching one of "Mfolds" (M-folds) or "loo" (leave-one-out).

ncomp

Number of component for investigating the choice of the tuning parameter.

keepX

Vector of integer indicating the number of group of variables to keep in each component. See Details for more information.

alpha.x

Numeric vector indicating the number of group of variables to keep in each component. See Details for more information.

grid.gX,grid.alpha.X

Vector numeric defining the values of tuning parameter lambda (number of groups to select) and tuning parameter alpha (mixing paramter values between 0 and 1) at which cross-validation score should be computed

setseed

Integer indicating the random number generation state.

progressBar

By default set to FALSE to output the progress bar of the computation.

ind.block.x

A vector of integers describing the grouping of the X variables. (see an example in Details section).

upper.lambda

By default upper.lambda=10 ^ 9. A large value specifying the upper bound of the intervall of lambda values for searching the value of the tuning parameter (lambda) corresponding to a non-zero group of variables.

Author

Benoit Liquet and Pierre Lafaye de Micheaux

Details

If validation = "Mfolds", M-fold cross-validation is performed by calling Mfold. The folds are generated. The number of cross-validation folds is specified with the argument folds.

If validation = "loo", leave-one-out cross-validation is performed by calling the loo function. In this case the arguments folds are ignored.

if keepX is specified (by default is NULL), each element of keepX indicates the value of the tuning parameter for the corresponding component. Only the choice of the tuning parameters corresponding to the remaining components are investigating by evaluating the cross-validation score at different values defining by grid.X.

if alpha.x is specified (by default is NULL), each element of alpha.x indicates the value of the tuning parameter (alpha) for the corresponding component. Only the choice of the tuning parameters corresponding to the remaining components are investigating by evaluating the cross-vlidation score at different values defining by grid.alpha.X.

Examples

if (FALSE) {	
## Simulation of datasets X (with group variables) and Y a multivariate response variable 
n <- 200
sigma.e <- 0.5
p <- 400
q <- 10
theta.x1 <- c(rep(1, 15), rep(0, 5), rep(-1, 15), rep(0, 5), rep(1.5, 15),
			rep(0, 5), rep(-1.5, 15), rep(0, 325))
theta.x2 <- c(rep(0, 320), rep(1, 15), rep(0, 5), rep(-1, 15), rep(0, 5),
			rep(1.5, 15), rep(0, 5), rep(-1.5, 15), rep(0, 5))

set.seed(125)
theta.y1 <- runif(10, 0.5, 2)
theta.y2 <- runif(10, 0.5, 2)
  
temp <-  matrix(c(theta.y1, theta.y2), nrow = 2, byrow = TRUE)

Sigmax <- matrix(0, nrow = p, ncol = p)
diag(Sigmax) <- sigma.e ^ 2
Sigmay <- matrix(0, nrow = q, ncol = q)
diag(Sigmay) <- sigma.e ^ 2

gam1 <- rnorm(n)
gam2 <- rnorm(n)

X <- matrix(c(gam1, gam2), ncol = 2, byrow = FALSE) %*% matrix(c(theta.x1, theta.x2),
     nrow = 2, byrow = TRUE) + rmvnorm(n, mean = rep(0, p), sigma =
     Sigmax, method = "svd")
Y <- matrix(c(gam1, gam2), ncol = 2, byrow = FALSE) %*% t(svd(temp)$v) 
     + rmvnorm(n, mean = rep(0, q), sigma = Sigmay, method = "svd")

ind.block.x <- seq(20, 380, 20)

grid.X <- 2:16
grid.alpha.X <- c(0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 0.95)
## Strategy with same value of each tuning parameter for both components
tun.sgPLS <- tuning.sgPLS.X(X, Y, folds = 10, validation = c("Mfold", "loo"), 
				ncomp = 2,keepX = NULL, alpha.x = NULL,grid.gX = grid.X, 
				grid.alpha.X = grid.alpha.X, setseed = 1, progressBar = FALSE, 
				ind.block.x = ind.block.x) 

tun.sgPLS$keepX # for each component
tun.sgPLS$alphaX # for each component
##For a sequential strategy
tun.sgPLS.1 <- tuning.sgPLS.X(X, Y, folds = 10, validation = c("Mfold", "loo"),
			         ncomp = 1, keepX = NULL,  alpha.x = NULL, grid.gX = grid.X,
				 grid.alpha.X = grid.alpha.X, setseed = 1, 
				 ind.block.x = ind.block.x) 
					 
tun.sgPLS.1$keepX # for the first component
tun.sgPLS.1$alphaX # for the first component

tun.sgPLS.2 <- tuning.sgPLS.X(X, Y, folds = 10, validation = c("Mfold", "loo"), 
					ncomp = 2, keepX = tun.sgPLS.1$keepX,
					alpha.x = tun.sgPLS.1$alphaX,
					grid.gX = grid.X,
					grid.alpha.X = grid.alpha.X,
					setseed = 1,
					ind.block.x = ind.block.x) 

tun.sgPLS.2$keepX # for the second component
tun.sgPLS.2$alphaX # for the second component
}