# Choice of the tuning parameters (number of groups and mixing parameter) related to predictor matrix for sgPLS model (regression mode) 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. ```r 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) ``` ## 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. ## 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`. ## Returns 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. ## 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) 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 ## End(Not run) ```

tuning.sgPLS.X function