OBsMD (version 12.0)

OMD: 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)

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.

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.

Author

Laura Deldossi. Adapted for R by Marta Nai Ruscone.

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.

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. 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. 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. 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)