OptimaRegion (version 1.2)

GloptiPolyRegion: Confidence region for optima of higher order polynomial models in multiple factors

Description

Computes and displays an approximated (1 - alpha)*100% confidence region (CR) for the bound-constrained optimum of a fitted polynomial regression model of up to cubic order with up to 5 controllable factors DelCastilloCROptimaRegion.

Usage

GloptiPolyRegion(
  X,
  y,
  degree,
  lb,
  ub,
  B = 200,
  alpha = 0.05,
  maximization = TRUE,
  axes_labels = NULL,
  outputPDFFile = "CRplot.pdf",
  verbose = TRUE,
  local_plot = FALSE
)

Value

Upon completion, a pdf file with the plot displaying the confidence region of the global optimum projected onto each pairwise-variable planes. If local_plot = TRUE, the plot will also be created on the screen. The function also returns a list consisting of 2 components:

boot_optima

numeric matrix of dimension ((1 - alpha)*B, k); it contains the (1 - alpha)*B bootstrap optima

bagged_optimum

numeric vector of dimension (1, k) containing the bagged optimum, computed by taking the column average of boot_optima

Arguments

X

an N*k numeric matrix where N is the number of experiments and k is the number of variables/factors (an integer in [2,5]). X specifies the design matrix

y

N*1 numeric vector that specifies the responses

degree

integer scalar; degree specifies the order of the polynomial model, which can be 2 or 3

lb

numeric vector of dimension (1, k); lb specifies the lower bounds for the k variables

ub

1*k numeric vector that specifies the upper bounds for the k variables

B

integer scalar; B specifies the number of bootstrap operations

alpha

numeric scalar between 0 and 1; alpha specifies the nominal confidence level, (1 - alpha)*100%, of the confidence region

maximization

boolean scalar; specifies whether the algorithm computes the confidence region for a maximum or a minimun

axes_labels

vector of strings; specifies the name of each variable or experimental factor to be displayed on the CR plot; the default value is NULL, which sets labels as "x1", "x2", etc.

outputPDFFile

name of the PDF file where the CR plot is saved (default: "CR_plot.pdf")

verbose

boolean scalar; specifies whether or not to display status of the bootstrapping/optimization iterations

local_plot

boolean scalar; specifies whether or to display the confidence region on the screen

Author(s)

Enrique del Castillo , Peng Chen , Adam Meyers , John Hunt and James Rapkin .

References

Examples

if (FALSE) {
# Example 1: run GloptiPolyRegion on a quadratic, 3 vars example
out <- GloptiPolyRegion(
  X = quad_3D[, 1:3], y = quad_3D[, 4], degree = 2,
  lb = c(-2, -2, -2), ub = c(2, 2, 2), B = 500, alpha = 0.1,
  maximization = TRUE,
  outputPDFFile = "CR_quad_3D.pdf", verbose = TRUE
)
# check result
str(out)

# Example 2: run GloptiPolyRegion on a cubic, 5 vars example
out <- GloptiPolyRegion(
  X = cubic_5D$design_matrix, y = cubic_5D$response,
  degree = 3, lb = rep(0, 5), ub = rep(5, 5), B = 200,
  alpha = 0.05, maximization = TRUE,
  outputPDFFile = "CR_cubic_5D.pdf", verbose = TRUE
)
# check result
str(out)
}