GDSARM | R Documentation |
The GDS-ARM procedure consists of three steps. First, it runs
the Gauss Dantzig Selector (GDS) nrep
times, each time
with a different set of nint
randomly selected two-factor interactions.
All m
main effects are included in each GDS run. Second, the best
ntop
models are identified with the smallest BIC. Effects that
appear in at least pkeep x ntop
of the ntop
models are then passed on to the third stage. In the third stage, stepwise
regression is used. With
n
being the number of runs, the stepwise regression starts
with at most n-3
selected effects from the previous step. The
remaining effects from the previous step as well as all main effects are
given a chance to enter into the model using the forward-backward stepwise
regression. The function also has the option of using the modified GDS-ARM.
The modified version incorporates effect heredity in two steps, first, for
each model found by GDS, we ignore active interactions when at least one of
the main effects is not active (for weak heredity) or when both main effects are not
active (for strong heredity); and second, we do the same for the model found
after the stepwise stage of GDS-ARM.
GDSARM( delta.n = 10, nint, nrep, ntop, pkeep, design, Y, cri.penter = 0.01, cri.premove = 0.05, opt.heredity = c("none"), seedvalue = 1234 )
delta.n |
a positive integer suggesting the number of delta values
to be tried. |
nint |
a positive integer representing the number of randomly
chosen interactions. The suggested value to use is the ceiling of 20%
of the total number of interactions, that is, for |
nrep |
a positive integer representing the number of times GDS should
be run. The suggested value is |
ntop |
a positive integer representing the number of top models
to be selected among the |
pkeep |
a number between 0 and 1 representing the proportion of |
design |
a n x m matrix of |
Y |
a vector of |
cri.penter |
the p-value cutoff for the most significant effect to enter into the stepwise regression model. The suggested value is 0.01. |
cri.premove |
the p-value cutoff for the least significant effect to exit from the stepwise regression model. The suggested value is 0.05. |
opt.heredity |
a string with either |
seedvalue |
a seed value that will fix the set of interactions being selected. The default value is seed to 1234. |
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.
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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
GDS_givencols
, dantzig.delta
data(dataHamadaWu) X = dataHamadaWu[,-8] Y = dataHamadaWu[,8] delta.n = 10 n = dim(X)[1] m = dim(X)[2] nint = ceiling(0.2*choose(m,2)) nrep = choose(m,2) ntop = max(20, nint*nrep/(2*choose(m,2))) pkeep = 0.25 cri.penter = 0.01 cri.premove = 0.05 design = X # GDS-ARM with default values GDSARM(delta.n, nint, nrep, ntop, pkeep, X, Y, cri.penter, cri.premove) # GDS-ARM with default values but with weak heredity opt.heredity="weak" GDSARM(delta.n, nint, nrep, ntop, pkeep, X, Y, cri.penter, cri.premove, opt.heredity) data(dataCompoundExt) X = dataCompoundExt[,-9] Y = dataCompoundExt[,9] delta.n = 10 n = dim(X)[1] m = dim(X)[2] nint = ceiling(0.2*choose(m,2)) nrep = choose(m,2) ntop = max(20, nint*nrep/(2*choose(m,2))) pkeep = 0.25 cri.penter = 0.01 cri.premove = 0.05 design = X # GDS-ARM on compound extraction GDSARM(delta.n, nint, nrep, ntop, pkeep, X, Y, cri.penter, cri.premove) # GDS-ARM on compound extraction with strong heredity opt.heredity = "strong" GDSARM(delta.n, nint, nrep, ntop, pkeep, X, Y, cri.penter, cri.premove, opt.heredity)
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