Choice of the tuning parameter (number of variables) related to predictor matrix for sPLS model (regression mode)

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

Usage

tuning.sPLS.X(X, Y, folds = 10, validation = c("Mfold", "loo"), ncomp,
    keepX = NULL, grid.X, setseed, progressBar = FALSE)

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 variables to keep in each component. See Details for more information.
grid.X: Vector of integers defining the values of the tuning parameter (corresponding to the number of variables to select) 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.

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.

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.

Author

Benoit Liquet and Pierre Lafaye de Micheaux

Examples

if (FALSE) { # \dontrun{  
## 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")


grid.X <- c(20, 30, 40, 50, 60, 70, 80, 90, 100, 120, 150, 200, 250, 300)

## Strategy with same value for both components
tun.sPLS <- tuning.sPLS.X(X, Y, folds = 10, validation = c("Mfold", "loo"), 
    ncomp = 2, keepX = NULL, grid.X = grid.X, setseed = 1)
tun.sPLS$keepX # for each component

##For a sequential strategy
tun.sPLS.1 <- tuning.sPLS.X(X, Y, folds = 10, validation = c("Mfold", "loo"), 
    ncomp = 1, keepX = NULL, grid.X = grid.X, setseed = 1)

tun.sPLS.1$keepX # for the first component

tun.sPLS.2 <- tuning.sPLS.X(X, Y, folds = 10, validation = c("Mfold", "loo"),
     ncomp = 2, keepX = tun.sPLS.1$keepX , grid.X = grid.X, setseed = 1)
tun.sPLS.2$keepX # for the second component

} # }