SLSEdesign

Optimal Design under Second-order Least Squares Estimator

Chi-Kuang Yeh and Julie Zhou
University of Waterloo and University of Victoria

2024-05-29

Installation

# required dependencies
require(SLSEdesign)
#> Loading required package: SLSEdesign
require(CVXR)
#> Loading required package: CVXR
#> 
#> Attaching package: 'CVXR'
#> The following object is masked from 'package:stats':
#> 
#>     power

Specify the input for the program

  1. N: Number of design points

  2. S: The design space

  3. tt: The level of skewness

  4. \(\theta\): The parameter vector

  5. 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

res$design
#>    location weight
#> 1      -1.0  0.182
#> 8      -0.3  0.313
#> 14      0.3  0.313
#> 21      1.0  0.182

Or we can plot them

plot_weight(res$design)

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_direction_Dopt(u, design, tt=0, FUN = poly3,
  theta = rep(0, 4))

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_direction_Aopt(u, design, tt=0, FUN = poly3, theta = rep(0,4))

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