View source: R/GDS_givencols.R
GDS_givencols | R Documentation |
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.
GDS_givencols(delta.n = 10, design, Y, which.cols = c("main2fi"))
delta.n |
a positive integer suggesting the number of delta values
to be tried. |
design |
a n x m matrix of |
Y |
a vector of |
which.cols |
a string with either |
A list returning the selected effects as well as the corresponding important factors.
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
GDSARM
, dantzig.delta
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")
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