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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))

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.