# Percentage of variance of the $Y$ matrix explained by the score-vectors obtained by PLS approaches The `per.variance` function computes the percentage of variance of the $Y$ matrix explained by the score-vectors obtained by PLS approaches (sPLS, gPLS or sgPLS) in a regression mode. ```r per.variance(object) ``` ## Arguments - `object`: object of class inheriting from `"sPLS"`, `"gPLS"`, or `"sgPLS"`. The function will retrieve some key parameters stored in that object. ## Returns `per.variance` produces a list with the following components: - **perX**: Percentage of variance of the $Y$ matrix explained by each score-vectors. - **cum.perX**: The cumulative of the percentage of variance of the $Y$ matrix explained by the score-vectors. ## Author(s) Benoit Liquet, b.liquet@uq.edu.au , Pierre Lafaye de Micheaux lafaye@dms.umontreal.ca ## Examples ```r ## Not run: ## Simulation of datasets X and Y with group variables n <- 100 sigma.gamma <- 1 sigma.e <- 1.5 p <- 400 q <- 500 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)) theta.y1 <- 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, 425)) theta.y2 <- c(rep(0, 420), 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)) Sigmax <- matrix(0, nrow = p, ncol = p) diag(Sigmax) <- sigma.e ^ 2 Sigmay <- matrix(0, nrow = q, ncol = q) diag(Sigmay) <- sigma.e ^ 2 set.seed(125) 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) %*% matrix(c(theta.y1, theta.y2), nrow = 2, byrow = TRUE) + rmvnorm(n, mean = rep(0, q), sigma = Sigmay, method = "svd") ind.block.x <- seq(20, 380, 20) ind.block.y <- seq(20, 480, 20) #### gPLS model model.sgPLS <- sgPLS(X, Y, ncomp = 2, mode = "regression", keepX = c(4, 4), keepY = c(4, 4), ind.block.x = ind.block.x, ind.block.y = ind.block.y, alpha.x = c(0.5, 0.5), alpha.y = c(0.5, 0.5)) result.sgPLS <- select.sgpls(model.sgPLS) result.sgPLS$group.size.X result.sgPLS$group.size.Y #### gPLS model model.gPLS <- gPLS(X, Y, ncomp = 2, mode = "regression", keepX = c(4, 4), keepY = c(4, 4), ind.block.x = ind.block.x ,ind.block.y = ind.block.y) result.gPLS <- select.sgpls(model.gPLS) result.gPLS$group.size.X result.gPLS$group.size.Y per.variance(model.gPLS) per.variance(model.sgPLS) ## End(Not run) ```

per.variance function