Specify the input for the program
N: Number of design points
S: The design space
tt: The level of skewness
\(\theta\): The parameter vector
FUN: The function for calculating the derivatives of the given model
N <- 21
S <- c(-1, 1)
tt <- 0
theta <- rep(1, 4)
poly3 <- function(xi,theta){
matrix(c(1, xi, xi^2, xi^3), ncol = 1)
}
u <- seq(from = S[1], to = S[2], length.out = N)
res <- Aopt(N = N, u = u, tt = tt, FUN = poly3,
theta = theta)Manage the outputs
Showing the optimal design and the support points
Or we can plot them
Plot the directional derivative to use the equivalence theorem for 3rd order polynomial models
D-optimal design
poly3 <- function(xi,theta){
matrix(c(1, xi, xi^2, xi^3), ncol = 1)
}
design <- data.frame(location = c(-1, -0.447, 0.447, 1),
weight = rep(0.25, 4))
u = seq(-1, 1, length.out = 201)
plot_dispersion(u, design, tt = 0, FUN = poly3,
theta = rep(0, 4), criterion = "D")
A-optimal design
poly3 <- function(xi, theta){
matrix(c(1, xi, xi^2, xi^3), ncol = 1)
}
design <- data.frame(location = c(-1, -0.464, 0.464, 1),
weight = c(0.151, 0.349, 0.349, 0.151))
u = seq(-1, 1, length.out = 201)
plot_dispersion(u, design, tt = 0, FUN = poly3, theta = rep(0,4), criterion = "A")