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Best follow-up experiments based on the MD criterion are suggested to discriminate between competing models.
MD(X, y, nFac, nBlk = 0, mInt = 3, g = 2, nMod, p, s2, nf, facs, nFDes = 4,
Xcand, mIter = 20, nStart = 5, startDes = NULL, top = 20, eps = 1e-05)matrix. Design matrix of the initial experiment.
vector. Response vector of the initial experiment.
integer. Number of factors in the initial experiment.
integer >=1. The number of blocking factors in the initial experiment.
They are accommodated in the first columns of matrix X.
integer. Maximum order of the interactions in the models.
vector. Variance inflation factor for main effects (g[1])
and interactions effects (g[2]). If vector length
is 1 the same inflation factor is used for main and
interactions effects.
integer. Number of competing models.
vector. Posterior probabilities of the competing models.
vector. Competing model variances.
vector. Factors considered in each of the models.
matrix. Matrix [nMod x max(nf)] of factor numbers in the design matrix.
integer. Number of runs to consider in the follow-up experiment.
matrix. Candidate runs to be chosen for the follow-up design.
integer. If 0, then user-entered designs startDes are
evaluated, otherwise the maximum number of iterations for each Wynn search.
integer. Number of starting designs.
matrix. Matrix [nStart x nFDes]. Each row has the row numbers
of the user-supplied starting design.
integer. Highest MD follow-up designs recorded.
numeric. A small number (1e-5 by default) used for computations.
A list with all input and output parameters of the FORTRAN
subroutine MD. Most of the variable names kept to match FORTRAN code.
Number of starting designs.
Number of runs used in follow-up designs.
Maximum number of iterations for each Wynn search.
Number of starting points.
Numbers of runs already completed before follow-up.
Indicator; 0 indicates the user supplied starting designs.
Matrix for initial data (nrow(X)=N0; ncol(X)=COLS+BL).
Response values from initial experiment (length(Y)=N0).
Variance inflation factor.
If IND=1, GAM2 was used for interaction factors.
Number of blocks (>=1) accommodated in first columns of X and Xcand
Number of factors.
Number of candidate runs.
Matrix of candidate runs. (nrow(Xcand)=N, ncol(Xcand)=ncol(X)).
Number of models considered.
Models posterior probability.
Models variances.
Number of factors per model.
Maximum number of factor in models. (MNF=max(NF)).
Matrix with the factor numbers for each of the models.
Maximum interaction order considered.
If INITDES=0, the first row of the MBEST[1,] matrix
has the first user-supplied starting design. The last row the
NSTART-th user-supplied starting design.
Number of the top best designs.
The D value for the best NTOP designs.
Top NTOP design factors.
"Small number" provided to the md FORTRAN
subroutine. 1e-5 by default.
Indicator = 1, if the md subroutine finished properly,
-1 otherwise.
The MD criterion, proposed by Meyer, Steinberg and Box is used to discriminate
among competing models. Random starting runs chosen from Xcand are used
for the Wynn search of best MD follow-up designs. nStart starting points are
tried in the search limited to mIter iterations. If mIter=0 then
startDes user-provided designs are used. Posterior probabilities and
variances of the competing models are obtained from BsProb.
The function calls the FORTRAN subroutine md and captures
summary results.
Meyer, R. D., Steinberg, D. M. and Box, G. E. P. (1996). "Follow-Up Designs to Resolve Confounding in Multifactor Experiments (with discussion)". Technometrics, Vol. 38, No. 4, pp. 303--332.
Box, G. E. P and R. D. Meyer (1993). "Finding the Active Factors in Fractionated Screening Experiments". Journal of Quality Technology. Vol. 25. No. 2. pp. 94--105.
# NOT RUN {
### Injection Molding Experiment. Meyer et al. 1996, example 2.
library(BsMD)
data(BM93.e3.data,package="BsMD")
X <- as.matrix(BM93.e3.data[1:16,c(1,2,4,6,9)])
y <- BM93.e3.data[1:16,10]
p <- c(0.2356,0.2356,0.2356,0.2356,0.0566)
s2 <- c(0.5815,0.5815,0.5815,0.5815,0.4412)
nf <- c(3,3,3,3,4)
facs <- matrix(c(2,1,1,1,1,3,3,2,2,2,4,4,3,4,3,0,0,0,0,4),nrow=5,
dimnames=list(1:5,c("f1","f2","f3","f4")))
nFDes <- 4
Xcand <- matrix(c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,
-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,
-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,
-1,1,1,-1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1),
nrow=16,dimnames=list(1:16,c("blk","f1","f2","f3","f4"))
)
injectionMolding.MD <- MD(X = X, y = y, nFac = 4, nBlk = 1, mInt = 3,
g = 2, nMod = 5, p = p, s2 = s2, nf = nf, facs = facs,
nFDes = 4, Xcand = Xcand, mIter = 20, nStart = 25, top = 10)
summary(injectionMolding.MD)
### Reactor Experiment. Meyer et al. 1996, example 3.
par(mfrow=c(1,2),pty="s")
data(Reactor.data,package="BsMD")
# Posterior probabilities based on first 8 runs
X <- as.matrix(cbind(blk = rep(-1,8), Reactor.data[c(25,2,19,12,13,22,7,32), 1:5]))
y <- Reactor.data[c(25,2,19,12,13,22,7,32), 6]
reactor8.BsProb <- BsProb(X = X, y = y, blk = 1, mFac = 5, mInt = 3,
p =0.25, g =0.40, ng = 1, nMod = 32)
plot(reactor8.BsProb,prt=TRUE,,main="(8 runs)")
# MD optimal 4-run design
p <- reactor8.BsProb$ptop
s2 <- reactor8.BsProb$sigtop
nf <- reactor8.BsProb$nftop
facs <- reactor8.BsProb$jtop
nFDes <- 4
Xcand <- as.matrix(cbind(blk = rep(+1,32), Reactor.data[,1:5]))
reactor.MD <- MD(X = X, y = y, nFac = 5, nBlk = 1, mInt = 3, g =0.40, nMod = 32,
p = p,s2 = s2, nf = nf, facs = facs, nFDes = 4, Xcand = Xcand,
mIter = 20, nStart = 25, top = 5)
summary(reactor.MD)
# Posterior probabilities based on all 12 runs
X <- rbind(X, Xcand[c(4,10,11,26), ])
y <- c(y, Reactor.data[c(4,10,11,26),6])
reactor12.BsProb <- BsProb(X = X, y = y, blk = 1, mFac = 5, mInt = 3,
p = 0.25, g =1.20,ng = 1, nMod = 5)
plot(reactor12.BsProb,prt=TRUE,main="(12 runs)")
# }
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