od_PIN {OptimalDesign}

Efficient saturated exact design

Description

Use a fast greedy method to compute an efficient saturated subset (saturated exact design).

Usage

od_PIN(Fx, alg.PIN="KYM", 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.

alg.PIN

the method used (either "KYM" or "GKM"). KYM is randomized, faster but provides somewhat less efficient subsets/designs. GKM is deterministic, slower, but tends to give more efficient subsets/designs.

echo

Print the call of the function?

Details

The function is developed with the criterion of D-optimality in mind, but it also gives reasonably efficient subset/designs with respect to other criteria. The main purpose of od_PIN is to initialize algorithms for computing optimal approximate and exact designs. It can also be used to verify whether a model, represented by a matrix Fx of candidate regressors, permits a non-singular design.

Value

Output is the list with components:

call

the call of the function

w.pin

the resulting exact design

supp

the indices of the support of w.pin

M.pin

the information matrix of w.pin

Phi.D

the D-criterion value of w.pin

t.act

the actual time of the computation

Author(s)

Radoslav Harman, Samuel Rosa, Lenka Filova

References

Harman R, Rosa S (2019): On greedy heuristics for computing D-efficient saturated subsets, (submitted to Operations Research Letters), https://arxiv.org/abs/1905.07647

Examples

# Compute a saturated subset of a random Fx
Fx <- matrix(rnorm(10000), ncol = 5)
w.KYM <- od_PIN(Fx)$w.pin
w.GKM <- od_PIN(Fx, alg.PIN = "GKM")$w.pin
w.REX <- 5*od_REX(Fx)$w.best
optcrit(Fx, w.KYM)
optcrit(Fx, w.GKM)
optcrit(Fx, w.REX)