blockpick | R Documentation |
Functions to investigate potential assignments of blocks and show alias information of resulting designs, meant for expert users
blockpick(k, gen, k.block, design = NULL, show = 10,
alias.block.2fis = FALSE, select.catlg = catlg)
blockpick.big(k, gen, k.block, design = NULL, show = 10,
alias.block.2fis = FALSE, select.catlg = catlg)
k |
the number of base factors (designs have |
gen |
vector of generating columns from Yates matrix;
for a full factorial, choose |
k.block |
number of base factors needed for constructing blocks;
there will be |
design |
design name (character string) of a specific design from the catalogue given in select.catlg |
show |
numeric integer indicating how many results are to be shown;
the search for possible allocations stops, once |
alias.block.2fis |
logical, indicates whether 2fis may be aliased with blocks |
select.catlg |
design catalogue of class |
Function blockpick
is used per default by function FrF2
for problems with choose(nruns-1-nfactors,k.block) < 100000
and without
estimability requirements. blockpick
will find a design, if it exists.
However, it may take a long time and/or much storage space in problems with
large numbers of runs and blocks.
In FrF2 versions before 2.0, function blockpick.big
was used for
large use cases; this can still be requested using argument block.old=TRUE
.
Since FrF2 version 2, the Godolphin (2021) based approach
is used instead, both for
large cases and for cases where blocking is combined with estimability requirements
(clear=TRUE
only); the big advantage is the ability of combining blocking with
estimability requirements, and a substantial speed gain if small blocks are needed.
All approaches investigate the potential assignment of blocks such that
main effects of treatment factors are not aliased with block main effects.
It is left to the user whether or not 2fis amoong treatment effects may be
aliased with block main effects (option alias.block.2fis
). (For the Godolphin
approach to work, one will usually need to set alias.block.2fis
to TRUE.)
Following Sun, Wu and Chen (1997), there is no single best block assignment.
blockpick
uses their catalogue for full factorials (implemented up to 256 runs).
For fractional factorials, it develops designs according to a
principle similar to that underlying the Sun Wu Chen catalogue that works also in
uncatalogued situations.
Function blockpick.big
uses a strategy similar to splitpick
and leftadjust
and often finds a solution quickly where blockpick
does not work with the
given ressources. However, it is not guaranteed to find existing solutions
or a best solution.
The function blockpick
outputs a list of entries with information on at most show
suitable
assignments. It ends with an error, if no suitable solution can be found.
gen |
generator column numbers of the base design (w.r.t. the Yates matrix) |
basics |
named vector with number of runs ( |
blockcols |
matrix with at most show rows; each row contains the |
alias.2fis.block |
list of character vectors, which contain the 2fis
aliased with block main effects for the respective rows of |
nblock.2fis |
vector with number of 2fis aliased with block main effects
for the respective rows of |
nclear.2fis |
vector with number of 2fis clear (of aliasing with block main effects
and treatment main effects or 2fis)
for the respective rows of |
clear.2fis |
list of character vectors, which contain the 2fis that are
counted in |
Ulrike Groemping
Chen, J., Sun, D.X. and Wu, C.F.J. (1993) A catalogue of 2-level and 3-level orthogonal arrays. International Statistical Review 61, 131-145.
Sun, D.X., Wu, C.F.J. and Chen, Y.Y. (1997).
Optimal blocking schemes for 2^n
and 2^{n-p}
designs. Technometrics 39,
298-307.
See Also FrF2
## look at possibilities for running a 32 run design with 6 factors in 8 blocks
## running this without alias.block.2fis=TRUE throws an error: not possible
## Not run: blockpick(k=5,design="6-1.1",k.block=3)
## the 8th to 10th design have more clear 2fis than the earlier ones
blockpick(k=5,design="6-1.1",k.block=3,alias.block.2fis=TRUE)
## function FrF2 can be used to manually accomodate this
des32.6fac.8blocks.MaxC2 <- FrF2(32,6,blocks=c(3,12,21),alias.block.2fis=TRUE)
summary(des32.6fac.8blocks.MaxC2)
## automatic block generation leads to more aliased 2fis
summary(FrF2(32,6,blocks=8,alias.block.2fis=TRUE))
## look at possibilities for blocking design 7-3.1 from Chen, Sun, Wu catalogue
blockpick(4,design="7-3.1",k.block=2,alias.block.2fis=TRUE)
## big design
## running this throws an error on many machines because of too little memory
## Not run: blockpick(6,design="7-1.2",k.block=5,alias.block.2fis=TRUE)
## for obtaining a design for this scenario with blockpick.big,
## the number of factors must be increased to 7+k.block=12
## designs 12-6.1 and 12-6.2 dont do it, 12-6.3 does
bpb <- blockpick.big(6,design="12-6.3",k.block=5,alias.block.2fis=TRUE)
bpb
## based on the result of blockpick.big, a blocked design can be obtained as follows:
## (not run for saving check time on CRAN)
## Not run:
des64.7fac.32blocks <- FrF2(64,gen=bpb$gen[1,], blocks = as.list(1:5),
alias.block.2fis=TRUE)
str(des64.7fac.32blocks)
## if the seven factors are to be named A,...,G:
des64.7fac.32blocks <- FrF2(64,gen=bpb$gen[1,], blocks = as.list(1:5),
alias.block.2fis=TRUE, factor.names=c(paste("b",1:5,sep=""),Letters[1:7]))
str(des64.7fac.32blocks)
## End(Not run)
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