od_DEL {OptimalDesign}

Removal of redundant design points

Description

Removes the design points (or, equivalently, candidate regressors) that cannot support an optimal approximate design.

Usage

od_DEL(Fx, w, crit = "D", h=NULL, echo = TRUE)

Arguments

Fx

the n times m (where m>=2, m<=n) matrix containing all candidate regressors (as rows), i.e., n is the number of candidate design points, and m is the number of parameters

w

a non-negative vector of length n representing the design

crit

the optimality criterion. Possible values are "D", "A", "I", "C".

h

a non-zero vector of length m corresponding to the coefficients of the linear parameter combination of interest. If crit is not "C" nor "c" then h is ignored. If crit is "C" or "c" and h=NULL then h is assumed to be c(0,...,0,1).

echo

Print the call of the function?

Value

Output is the list with components:

call

the call of the function

keep

the indices of w that have not been removed

w.keep

the approximate design on the reduced space

Fx.keep

the model matrix of the regressors on the reduced space

Note

The design vector w should have a non-singular information matrix. The procedure is valid only for the standard (size) constraint.

Author(s)

Radoslav Harman, Lenka Filova

References

Harman R, Pronzato L (2007): Improvements on removing non-optimal support points in D-optimum design algorithms, Statistics & Probability Letters 77, 90-94

Pronzato L (2013): A delimitation of the support of optimal designs for Kiefers Phi_p-class of criteria. Statistics & Probability Letters 83, 2721-2728

Examples

## Not run: 
# Generate a model matrix for the quadratic model
# on a semi-circle with a huge number of design points
form.q <- ~x1 + x2 + I(x1^2) + I(x2^2) + I(x1*x2)
Fx <- Fx_cube(form.q, lower = c(-1, 0), n.levels = c(1001, 501))
remove <- (1:nrow(Fx))[Fx[ ,2]^2 + Fx[ ,3]^2 > 1]
Fx <- Fx[-remove, ]

# Compute an approximate design w with an efficiency of cca 0.999
w <- od_REX(Fx, eff = 0.999)$w.best

# Remove the redundant design points based on w
Fx <- od_DEL(Fx, w)$Fx.keep

# Now an almost perfect design can be computed very rapidly:
w <- od_REX(Fx, eff = 0.9999999999)$w.best

# Plotting of the relevant directional derivative is also faster:
od_plot(Fx, w, Fx[ , 2:3], dd.size = 0.1)

## End(Not run)