SLSEdesign (version 0.0.5)

plot_dispersion: Verify the optimality condition for an optimal design (A-, c- or D-optimality)

Description

Verify the optimality condition for an optimal design (A-, c- or D-optimality)

Usage

plot_dispersion(
  u,
  design,
  tt,
  FUN,
  theta,
  criterion = "D",
  cVec = rep(0, length(theta))
)

Value

A plot verifying the general equivalence condition for the specified optimal design

Arguments

u

The discretized design points

design

The optimal design containing the design points and the associated weights

tt

The level of skewness

FUN

The function to calculate the derivative of the given model

theta

The parameter value of the model

criterion

The optimality criterion: one of "A", "c", or "D"

cVec

c vector used to determine the combination of the parameters. This is only used in c-optimality

Details

This function visualizes the directional derivative under A-, c-, or D-optimality using the general equivalence theorem. For an optimal design, the directional derivative should not exceed the reference threshold

Examples

poly3 <- function(xi, theta){
  matrix(c(1, xi, xi^2, xi^3), ncol = 1)
}
design_A <- data.frame(location = c(-1, -0.464, 0.464, 1),
                       weight = c(0.151, 0.349, 0.349, 0.151))
design_D = data.frame(location = c(-1, -0.447, 0.447, 1),
                      weight = rep(0.25, 4))
u <- seq(-1, 1, length.out = 201)
par(mfrow = c(2,2))
plot_dispersion(u, design_A, tt = 0, FUN = poly3, theta = rep(0, 4), criterion = "A")
plot_dispersion(u, design_A, tt = 0, FUN = poly3, theta = rep(0, 4), criterion = "D")

plot_dispersion(u, design_D, tt = 0, FUN = poly3, theta = rep(0, 4), criterion = "A")
plot_dispersion(u, design_D, tt = 0, FUN = poly3, theta = rep(0, 4), criterion = "D")