OMD: Objective Model Discrimination (OMD) in Follow-Up Experiments
In OBsMD: Objective Bayesian Model Discrimination in Follow-Up Designs
OMD R Documentation
Objective Model Discrimination (OMD) in Follow-Up Experiments
Description
Optimal follow-up experiments to discriminate between competing models. The extra-runs are
derived from the maximization of the objective model discrimination criterion represented by a weighted average
of Kullback-Leibler divergences between all possible pairs of rival models
Usage
OMD(OBsProb, nFac, nBlk = 0, nMod, nFoll, Xcand, mIter, nStart, startDes, top = 20)
Arguments
OBsProb
list. OBsProb class list. Output list of OBsProb function.
nFac
integer. Number of factors in the initial experiment.
nBlk
integer >=0. Number of blocking factors in the initial experiment.
They are accommodated in the first columns of matrix X.
nMod
integer. Number of competing models considered to compute OMD.
nFoll
integer. Number of additional runs in the follow-up experiment.
Xcand
matrix. Matrix [2^nFac x (nBlk + nFac)] of candidate runs for the follow-up design.
It generally rapresents the full 2^nFac design.
mIter
integer >=0. Maximum number of iterations in the exchange algorithm.
If mIter = 0 exachange algorithm doesn't work.
nStart
integer. Number of different designs of dimension nFoll
to be evaluated by OMD criterion.
When exchange algorithm is used nStart represents the number of random starts
to initialize the algorithm; otherwise nStart = nrow(startDes).
startDes
matrix. Input matrix [nStart x nFoll] containing different
nStart designs to be evaluated by OMD criterion.
If the exchange algorithm is used startDes = NULL.
top
integer. Number of highest OMD follow-up designs recorded.
Details
The OMD criterion, proposed by Consonni and Deldossi, is used to discriminate
among competing models. Random starting runs chosen from Xcand are used
for the Wynn search of best OMD 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 residual
variances of the competing models are obtained from OBsProb.
The function calls the FORTRAN subroutine ‘omd’ and captures
summary results. The complete output of the FORTRAN code is save in
the ‘MDPrint.out’ file in the working directory.
Value
Below a list with all input and output parameters of the FORTRAN
subroutine OMD. Most of the variable names kept to match FORTRAN code.
NSTART
integer. Number of different designs of dimension nFoll
to be evaluated by OMD criterion.
When exchange algorithm is used nStart represents the number of random starts
to initialize the algorithm; otherwise nStart = nrow(startDes).
NRUNS
integer. Number nFoll of runs used in follow-up designs.
ITMAX
integer. Maximum number mIter of iterations in the exchange algorithm.
INITDES
integer. Indicator variable. If INITDES = 1 exachange
alghoritm is used, otherwise INITDES = 0 exachange alghoritm doesn't work.
N0
integer. Numbers of runs nrow(X) of the initial experiment before follow-up.
X
matrix. Matrix from initial experiment (nrow(X); ncol(X)=nBlk+nFac).
Y
double. Response values from initial experiment (length(Y)=nrow(X)).
BL
integer >=0. The number of blocking factors in the initial experiment.
They are accommodated in the first columns of matrix X and Xcand.
COLS
integer. Number of factors nFac.
N
integer. Number of candidate runs nrow(Xcand).
Xcand
matrix. Matrix [2^nFac x (nBlk + nFac)] candidate runs for the follow-up design.
It generally represents the full 2^nFac design [nrow(Xcand)=N, ncol(Xcand)=ncol(X)].
NM
integer. Number of competing models nMod considered to compute OMD .
P
double. Models posterior probability optop. It derives from the OBsProb output.
SIGMA2
double. Competing models residual variances osigtop. It derives from the OBsProb output.
NF
integer. Number of main factors in each competing models onftop. It derives from the OBsProb output.
MNF
integer. Maximum number of factor in models (MNF=max(onftop)).
JFAC
matrix. Matrix ojtop of dimension [nMod x max(onftop)] of the labels of the main factors present in
each competing models. It derives from the OBsProb output.
CUT
integer. Maximum order of the interaction among factors in the models mInt.
MBEST
matrix. 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.
NTOP
integer. Number of the top best OMD designs top.
TOPD
double. The OMD value for the best top NTOP designs.
TOPDES
matrix. Top NTOP optimal OMD follow-up designs.
flag
integer. Indicator = 1, if the ‘md’ subroutine finished properly,
-1 otherwise.
Note
The function is a wrapper to call the modified FORTAN subroutine ‘omd’,
‘OMD.f’, part of the
mdopt bundle for Bayesian model discrimination of multifactor
experiments.
Author(s)
Laura Deldossi. Adapted for R by Marta Nai Ruscone.
References
Box, G. E. P. and Meyer, R. D. (1993)
Finding the Active Factors in Fractionated Screening Experiments.,
Journal of Quality Technology 25(2), 94–105.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00224065.1993.11979432")}.
Consonni, G. and Deldossi, L. (2016)
Objective Bayesian Model Discrimination in Follow-up design.,
Test 25(3), 397–412.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11749-015-0461-3")}.
Meyer, R. D., Steinberg, D. M. and Box, G. E. P. (1996)
Follow-Up Designs to Resolve Confounding in Multifactor Experiments (with discussion).,
Technometrics 38(4), 303–332.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/1271297")}.
See Also
print.OMD, OBsProb
Examples
library(OBsMD)
data(OBsMD.es5, package="OBsMD")
X <- as.matrix(OBsMD.es5[,1:5])
y <- OBsMD.es5[,6]
es5.OBsProb <- OBsProb(X=X,y=y,blk=0,mFac=5,mInt=2,nTop=32)
nMod <- 26
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,
-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=32,ncol=5,dimnames=list(1:32,c("A","B","C","D","E")),byrow=TRUE)
p_omd <- OMD(OBsProb=es5.OBsProb,nFac=5,nBlk=0,nMod=26,nFoll=4,Xcand=Xcand,
mIter=20,nStart=25,startDes=NULL,top=30)
print(p_omd)
OBsMD documentation built on Nov. 14, 2023, 5:10 p.m.
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| OMD | R Documentation |
Objective Model Discrimination (OMD) in Follow-Up Experiments
Description
Optimal follow-up experiments to discriminate between competing models. The extra-runs are derived from the maximization of the objective model discrimination criterion represented by a weighted average of Kullback-Leibler divergences between all possible pairs of rival models
Usage
OMD(OBsProb, nFac, nBlk = 0, nMod, nFoll, Xcand, mIter, nStart, startDes, top = 20)
Arguments
OBsProb |
list. |
nFac |
integer. Number of factors in the initial experiment. |
nBlk |
integer >=0. Number of blocking factors in the initial experiment.
They are accommodated in the first columns of matrix |
nMod |
integer. Number of competing models considered to compute |
nFoll |
integer. Number of additional runs in the follow-up experiment. |
Xcand |
matrix. Matrix [ |
mIter |
integer >=0. Maximum number of iterations in the exchange algorithm.
If |
nStart |
integer. Number of different designs of dimension |
startDes |
matrix. Input matrix [ |
top |
integer. Number of highest OMD follow-up designs recorded. |
Details
The OMD criterion, proposed by Consonni and Deldossi, is used to discriminate
among competing models. Random starting runs chosen from Xcand are used
for the Wynn search of best OMD 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 residual
variances of the competing models are obtained from OBsProb.
The function calls the FORTRAN subroutine ‘omd’ and captures
summary results. The complete output of the FORTRAN code is save in
the ‘MDPrint.out’ file in the working directory.
Value
Below a list with all input and output parameters of the FORTRAN
subroutine OMD. Most of the variable names kept to match FORTRAN code.
NSTART |
integer. Number of different designs of dimension |
NRUNS |
integer. Number |
ITMAX |
integer. Maximum number |
INITDES |
integer. Indicator variable. If |
N0 |
integer. Numbers of runs |
X |
matrix. Matrix from initial experiment ( |
Y |
double. Response values from initial experiment ( |
BL |
integer >=0. The number of blocking factors in the initial experiment.
They are accommodated in the first columns of matrix |
COLS |
integer. Number of factors |
N |
integer. Number of candidate runs |
Xcand |
matrix. Matrix [ |
NM |
integer. Number of competing models |
P |
double. Models posterior probability |
SIGMA2 |
double. Competing models residual variances |
NF |
integer. Number of main factors in each competing models |
MNF |
integer. Maximum number of factor in models ( |
JFAC |
matrix. Matrix |
CUT |
integer. Maximum order of the interaction among factors in the models |
MBEST |
matrix. If |
NTOP |
integer. Number of the top best OMD designs |
TOPD |
double. The OMD value for the best top |
TOPDES |
matrix. Top |
flag |
integer. Indicator = 1, if the ‘md’ subroutine finished properly, -1 otherwise. |
Note
The function is a wrapper to call the modified FORTAN subroutine ‘omd’, ‘OMD.f’, part of the mdopt bundle for Bayesian model discrimination of multifactor experiments.
Author(s)
Laura Deldossi. Adapted for R by Marta Nai Ruscone.
References
Box, G. E. P. and Meyer, R. D. (1993) Finding the Active Factors in Fractionated Screening Experiments., Journal of Quality Technology 25(2), 94–105. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00224065.1993.11979432")}.
Consonni, G. and Deldossi, L. (2016) Objective Bayesian Model Discrimination in Follow-up design., Test 25(3), 397–412. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11749-015-0461-3")}.
Meyer, R. D., Steinberg, D. M. and Box, G. E. P. (1996) Follow-Up Designs to Resolve Confounding in Multifactor Experiments (with discussion)., Technometrics 38(4), 303–332. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/1271297")}.
See Also
print.OMD, OBsProb
Examples
library(OBsMD)
data(OBsMD.es5, package="OBsMD")
X <- as.matrix(OBsMD.es5[,1:5])
y <- OBsMD.es5[,6]
es5.OBsProb <- OBsProb(X=X,y=y,blk=0,mFac=5,mInt=2,nTop=32)
nMod <- 26
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,
-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=32,ncol=5,dimnames=list(1:32,c("A","B","C","D","E")),byrow=TRUE)
p_omd <- OMD(OBsProb=es5.OBsProb,nFac=5,nBlk=0,nMod=26,nFoll=4,Xcand=Xcand,
mIter=20,nStart=25,startDes=NULL,top=30)
print(p_omd)
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