# Choice of the tuning parameter (number of groups) related to predictor matrix for gPLS 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 gPLS model. ```r tuning.gPLS.X(X,Y,folds=10,validation=c("Mfold","loo"), ncomp,keepX=NULL,grid.X,setseed,progressBar=FALSE, ind.block.x=ind.block.x) ``` ## 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. - `grid.X`: Vector of integers defining the values of the tuning parameter (corresponding to the number of group 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. - `ind.block.x`: A vector of integers describing the grouping of the X variables. (see an example in details section) ## 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`. ## Returns The returned value is a list with components: - **MSEP**: Matrix containing the cross-validation score computed on the grid. - **keepX**: Value of the tuning parameter (lambda) on which the cross-validation method reached it minimum. ## Author(s) Benoit Liquet and Pierre Lafaye de Micheaux ## Examples ```r ## Not run: ## 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,0,1) gam2 <- rnorm(n,0,1) 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)$v) +rmvnorm(n,mean=rep(0,q),sigma=Sigmay,method="svd") ind.block.x <- seq(20,380,20) grid.X <- 1:16 ## Strategy with same value for both components tun.gPLS <- tuning.gPLS.X(X, Y, folds = 10, validation = c("Mfold", "loo"), ncomp=2,keepX = NULL, grid.X=grid.X, setseed=1, progressBar = FALSE, ind.block.x = ind.block.x) tun.gPLS$keepX # for each component ##For a sequential strategy tun.gPLS.1 <- tuning.gPLS.X(X, Y, folds = 10, validation = c("Mfold", "loo"), ncomp=1, keepX = NULL, grid.X=grid.X, setseed=1, ind.block.x = ind.block.x) tun.gPLS.1$keepX # for the first component tun.gPLS.2 <- tuning.gPLS.X(X, Y, folds = 10, validation = c("Mfold", "loo"), ncomp=2, keepX = tun.gPLS.1$keepX , grid.X=grid.X, setseed=1, ind.block.x = ind.block.x) tun.gPLS.2$keepX # for the second component ## End(Not run) ```

tuning.gPLS.X function