GDS_givencols {GDSARM}

Gauss-Dantzig Selector

Description

This function runs the Gauss-Dantzig selector on the given columns. We have two options: either (a) GDS(m) on the m main effects, and (b) GDS(m+2fi) on the m main effects and the corresponding two-factor interactions. For a given delta, DS minimizes the L_1-norm (sum of absolute values) of beta subject to the constraint that max(|t(X)(y-X * beta)|) <= delta. The GDS is run for multiple values of delta. We use kmeans and BIC to select a best model.

Usage

GDS_givencols(delta.n = 10, design, Y, which.cols = c("main2fi"))

Arguments

delta.n

a positive integer suggesting the number of delta values to be tried. delta.n equally spaced values of delta will be used strictly between 0 and max(|t(X)y|). The default value is set to 10.

design

a n \times m matrix of m two-level factors. The levels should be coded as +1 and -1.

Y

a vector of n responses.

which.cols

a string with either main or main2fi. Denotes whether the Gauss-Dantzig Selector should be run on the main effect columns (main), or on all main effects plus all 2 factor interaction columns (main2fi). The default value is main2fi.

Value

A list returning the selected effects as well as the corresponding important factors.

Source

Cand\'es, E. and Tao, T. (2007). The Dantzig selector: Statistical estimation when p is much larger than n. Annals of Statistics 35 (6), 2313–2351.

Dopico-Garc\' ia, M.S., Valentao, P., Guerra, L., Andrade, P. B., and Seabra, R. M. (2007). Experimental design for extraction and quantification of phenolic compounds and organic acids in white "Vinho Verde" grapes Analytica Chimica Acta, 583(1): 15–22.

Hamada, M. and Wu, C. F. J. (1992). Analysis of designed experiments with complex aliasing. Journal of Quality Technology 24 (3), 130–137.

Hunter, G. B., Hodi, F. S. and Eagar, T. W. (1982). High cycle fatigue of weld repaired cast Ti-6AI-4V. Metallurgical Transactions A 13 (9), 1589–1594.

Phoa, F. K., Pan, Y. H. and Xu, H. (2009). Analysis of supersaturated designs via the Dantzig selector. Journal of Statistical Planning and Inference 139 (7), 2362–2372.

Singh, R. and Stufken, J. (2022). Factor selection in screening experiments by aggregation over random models, 1–31. doi: 10.48550/arXiv.2205.13497

See Also

GDSARM, dantzig.delta

Examples

data(dataHamadaWu)
X = dataHamadaWu[,-8]
Y = dataHamadaWu[,8]
delta.n = 10
# GDS on main effects 
GDS_givencols(delta.n, design = X, Y=Y, which.cols = "main")

# GDS on main effects and two-factor interactions
GDS_givencols(delta.n, design = X, Y=Y)

data(dataCompoundExt)
X = dataCompoundExt[,-9]
Y = dataCompoundExt[,9]
delta.n = 10
# GDS on main effects
GDS_givencols(delta.n, design = X, Y=Y, which.cols = "main")
# GDS on main effects and two-factor interactions
GDS_givencols(delta.n, design = X, Y=Y, which.cols = "main2fi")