R/morris_oat.R

In sensitivity: Sensitivity Analysis

# Morris's OAT method sub-routines. (See main file morris.R)

random.oat <- function(p, nl, design.step) {
  # orientation matrix B
  B <- matrix(-1, nrow = p + 1, ncol = p)                 
  B[lower.tri(B)] <- 1
  # directions matrix D
  D <- diag(sample(c(-1, 1), size = p, replace = TRUE)) 
  # permutation matrix P
  perm <- sample(p)
  P <- matrix(0, nrow = p, ncol = p)
  for (i in 1 : p) {
    P[i, perm[i]] <- 1
  }
  # starting point
  x.base <- matrix(nrow = p + 1, ncol = p)               
  for (i in 1 : p) {                                    
    x.base[,i] <- ((sample(nl[i] - design.step[i], size = 1) - 1) / (nl[i] - 1))
  }
  # grid step
  delta <- design.step / (nl - 1)
  return(0.5 * (B %*% P %*% D + 1) %*% diag(delta) + x.base)
}


ee.oat <- function(X, y) {
# compute the elementary effects for a OAT design
  p <- ncol(X)
  r <- nrow(X) / (p + 1)
  ee <- matrix(nr = r, nc = p)
  colnames(ee) <- colnames(X)
  for (i in 1 : r) {
    j <- ind.rep(i, p)
    j1 <- j[1 : p]
    j2 <- j[2 : (p + 1)]
	A <- X[j2,] - X[j1,]
	b <- y[j2] - y[j1]
	ee[i,] <- solve(A, b)
  }
  return(ee)
}