Fx_cube: Matrix of candidate regressors for a model on a cuboid grid

Description

Creates the matrix of all candidate regressors for a factor regression model on a cuboid grid (up to 9 factors).

Usage

Fx_cube(formula, lower=NULL, upper=NULL, n.levels=NULL, echo=TRUE)

Value

The n times m matrix of all candidate regressors for a factor regression model on a cuboid grid. The rows of Fx are the regressors f(x) for all candidate design points x.

Arguments

formula: the formula of the model. The rules for creating the formula are standard for R but: 1) the formula must not contain the dependent variable (it is one-sided); 2) the d factors (variables) must be labeled x1,x2,x3,...
lower: the d-dimensional vector of the smallest values of factors. If lower=NULL, the program sets lower <- rep(-1, d).
upper: the d-dimensional vector of the largest values of factors. If upper=NULL, the program sets upper <- rep(1, d).
n.levels: the d-dimensional vector of the numbers of levels of each factor. If n.levels=NULL, the program sets n.levels <- rep(2, d).
echo: Print the call of the function?

Author

Radoslav Harman, Lenka Filova

Examples

Run this code

if (FALSE) {
# The Fx for the cubic model on a discretized interval
Fx <- Fx_cube(~x1 + I(x1^2) + I(x1^3), lower=0, upper=2, n.levels=101)

# The D-optimal design of size 20
w <- od_KL(Fx, 20, t.max=5)$w.best
od_plot(Fx, w, Fx[, 2])


# The Fx for the full quadratic response surface model on a non-convex region
Fx <- Fx_cube(~x1 + x2 + I(x1^2) + I(x2^2) + I(x1*x2), n.levels=c(51, 51))
keep <- rep(TRUE, nrow(Fx))
for(i in 1:nrow(Fx)) if(prod(abs(Fx[i, 2:3])) > 0.2) keep[i] <- FALSE
Fx <- Fx[keep, ]

# The D-optimal design of size 29 without replications
w <- od_KL(Fx, 29, bin=TRUE, t.max=5)$w.best
od_plot(Fx, w, Fx[, 2:3])


# The Fx for the chemical weighing with 3 items and a bias term
Fx <- Fx_cube(~x1 + x2 + x3, n.levels=c(3, 3, 3))

# The D-optimal design of size 12
w <- od_KL(Fx, 12, t.max=2)$w.best
od_plot(Fx, w, Fx[, 2:4])
}