per.variance function

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.

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

## 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)