Function for augmenting an existing fractional factorial with a star portion in case of a late decision for a sequential procedure.
ccd.augment(cube, ncenter = 4, columns="all", block.name="Block.ccd", alpha = "orthogonal", randomize=TRUE, seed=NULL, ...)
design generated by function
integer number of center points,
or vector with two numbers, the first for the cube and the second for
the star portion of the design.
name of block factor that distinguishes (at least) between blocks; even for unblocked cubes, the ccd design has a cube and a star point block
“orthogonal”, “rotatable”, or a number that indicates the position of the star points; the number 1 would create a face-centered design.
logical that indicates whether or not randomization should occur
NULL or a vector of two integer seeds for random number generation in randomization
reserved for future usage
not yet implemented; it is intended to later allow to add star points for only some factors of a design (after eliminating the others as unimportant in a sequential process), and columns will be used to indicate those
The statistical background of central composite designs is briefly described
ccd.augment augments an existing 2-level fractional factorial
that should already have been run with center points and should have resolution V.
In exceptional situations, it may be useful to base a ccd on a resolution IV design
that allows estimation of all 2-factor interactions of interest. Thus, it can be
interesting to apply function
ccd.augment to a cube
based on the
estimable functionality of function
in cases where a resolution V cube is not feasible.
Of course, this does not allow to estimate the aliased 2-factor interactions
and therefore generates a warning.
The function returns a data frame of S3 class
with attributes attached. The data frame itself is in the original data scale.
The data frame
desnum attached as attribute
desnum is the original data frame
returned by package
rsm. The attribute
design.info is a list of various design properties.
type of that list is the character string
Besides the elements present in all class
there are the elements quantitative (vector with
nfactor TRUE entries),
codings element usable in the coding functions available in the rsm
Note that the row names and the standard order column in the
attribute of ccd designs based on
estimability requirements (cf. also the details section) are not in conventional order
and should not be used as the basis for any calculations. The same is true for
blocked designs, if the blocking routine
blockpick.big was used.
Since R version 3.6.0, the behavior of function
sample has changed
(correction of a biased previous behavior that should not be relevant for the randomization of designs).
For reproducing a randomized design that was produced with an earlier R version,
please follow the steps described with the argument
This package is still under (slow) development. Reports about bugs and inconveniences are welcome.
ccd.augment is based on version 1 of package rsm.
Box, G.E.P., Hunter, J.S. and Hunter, W.G. (2005, 2nd ed.). Statistics for Experimenters. Wiley, New York.
Box, G.E.P. and Wilson, K.B. (1951). On the Experimental Attainment of Optimum Conditions. J. Royal Statistical Society, B13, 1-45.
NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/pri/section3/pri3361.htm, accessed August 20th, 2009.
Myers, R.H., Montgomery, D.C. and Anderson-Cook, C.M. (2009). Response Surface Methodology. Process and Product Optimization Using Designed Experiments. Wiley, New York.
## purely technical examples for the sequential design creation process ## start with a fractional factorial with center points plan <- FrF2(16,5,default.levels=c(10,30),ncenter=6) ## collect data and add them to the design y <- rexp(22) plan <- add.response(plan,y) ## assuming that an analysis has created the suspicion that a second order ## model should be fitted (not to be expected for the above random numbers): plan.augmented <- ccd.augment(plan, ncenter=4) ## add new responses to the design y <- c(y, rexp(14)) ## append responses for the 14=5*2 + 4 star points r.plan.augmented <- add.response(plan.augmented, y, replace=TRUE) ## for info: how to analyse results from such a desgin lm.result <- lm(y~Block.ccd+(.-Block.ccd)^2+I(A^2)+I(B^2)+I(C^2)+I(D^2)+I(E^2), r.plan.augmented) summary(lm.result) ## analysis with function rsm rsm.result <- rsm(y~Block.ccd+SO(A,B,C,D,E), r.plan.augmented) summary(rsm.result) ## provides more information than lm.result loftest(rsm.result) ## separate lack of fit test ## graphical analysis ## (NOTE: purely for demo purposes, the model is meaningless here) ## individual contour plot contour(rsm.result,B~A) ## several contour plots par(mfrow=c(1,2)) contour(rsm.result,list(B~A, C~E)) ## many contourplots, all pairs of some factors par(mfrow=c(2,3)) contour(rsm.result,~A+B+C+D)
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