ccd.design | R Documentation |
Function for accessing central composite designs from package rsm, with automatic creation of an appropriate cube portion
ccd.design(nfactors=NULL, factor.names=NULL, default.levels=c(-1,1), ncube=NULL,
resolution=if (identical(blocks,1) & is.null(ncube)) 5 else NULL,
generators=NULL, ncenter = 4, alpha = "orthogonal",
replications=1,
block.name="Block.ccd", blocks=1,
randomize=TRUE, seed=NULL, ...)
nfactors |
number of factors |
factor.names |
list of cube corner values for each factor;
names are used as variable names;
the names must not be x1, x2, ..., as these are used for the variables
in coded units; |
default.levels |
default levels (vector of length 2) for all factors for which no specific levels are given |
ncube |
integer number of cube points (without center points for the cube) |
resolution |
arabic numeral for the requested resolution of the cube portion
of the design; cubes for ccd designs should usually be at least of resolution V.
the default value for resolution is therefore 5, unless |
generators |
generators in the form allowed in function |
ncenter |
integer number of center points for each cube or star point block, or vector with two numbers, the first for the cube and the second for the star portion of the design |
alpha |
“orthogonal”, “rotatable”, or a number that indicates the position of the star points; the number 1 would create a face-centered design. |
replications |
the number of replications of the design; currently, only proper replications can be generated; these are randomized in blocks within the center point and star blocks. The same number of replications is used for both the cube and the star blocks. |
block.name |
name of block factor that distinguishes between blocks; even for unblocked cubes, the ccd design has at least one cube and one star point block |
blocks |
the same as in function
If If the experiment is randomized, randomization happens within blocks. For the statistical and algorithmic background of blocked designs, see |
randomize |
logical that indicates whether or not randomization should occur |
seed |
NULL or a vector of two integer seeds for random number generation in randomization |
... |
reserved for future usage |
The statistical background of central composite designs is briefly described
under CentralCompositeDesigns
.
Function ccd.design
creates a central composite design from scratch.
It proceeds by generating a cube design with function FrF2
and then
augmenting this cube design using functions add.center
from package
FrF2 for adding center points to the cube and subsequently function
ccd
from package rsm for generating the star portion of
the design.
There are two main purposes for this function: one is to provide
central composite designs within the same syntax philosophy
used in packages DoE.base-package
and FrF2
.
The other is to automatically identify good (=resolution V) cube portions,
which can be achieved by using the resolution parameter.
In comparison to direct usage of package ccd, the functions make the syntax closer to that of the other packages in the DoE.wrapper suite and allow automatic selection of fractional factorials as cubes.
Function ccd.design
does not allow direct use of the estimable
functionality
that is available in function FrF2
. Nevertheless, ccd designs with a cube
based on the estimable
functionality can be generated
by first using function FrF2
and subsequently applying
function ccd.augment
. It may for example be interesting to use designs based on
estimability requirements for 2-factor interactions in cases where a resolution V cube
for the ccd is not feasible - of course, this does not allow to estimate the full second order model
and therefore generates a warning.
The function returns a data frame of S3 class design
with attributes attached. The data frame itself is in the original data scale.
The data frame desnum
attached as attribute desnum
is the coded design.
The attribute design.info
is a list of various design properties.
The element type
of that list is the character string ccd
.
Besides the elements present in all class design
objects,
there are the elements quantitative (vector with nfactor
TRUE entries),
and a codings
element usable in the coding functions available in the rsm
package, e.g. coded.data
.
Note that the row names and the standard order column in the
run.order
attribute of ccd designs
are not in conventional order,
if the blocking routine blockpick.big
was used.
In such situations, these should not be used as the basis for any calculations.
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 seed
.
This package is still under (slow) development. Reports about bugs and inconveniences are welcome. ccd.design
is based on version 1 of package rsm.
Ulrike Groemping
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.
See also ccd.augment
, add.center
,
FrF2
, lhs-package
, rsm
ccd.design(5) ## per default uses the resolution V design in 16 runs for the cube
ccd.design(5, ncube=32) ## uses the full factorial for the cube
ccd.design(5, ncenter=6, default.levels=c(-10,10))
## blocked design (requires ncube to be specified)
ccd.design(5, ncube=32, blocks=4)
## there is only one star point block
## for usage of other options, look at the FrF2 documentation
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