plot_dispersion: Verify the optimality condition for an optimal design (A-, c-...

In SLSEdesign: Optimal Regression Design under the Second-Order Least Squares Estimator

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))
)

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

Value

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

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")

SLSEdesign documentation built on June 8, 2025, 1:47 p.m.