Description Usage Arguments Details Value Author(s) References See Also Examples
This function looks at all combinations of specified design parameters
for central-composite designs, calculates other quantities such as
the alpha
values for rotatability and orthogonal blocking, imposes
specified restrictions, and outputs the best combinations in a specified order.
This serves as an aid in identifying good designs. The design itself can
then be generated using ccd
, or in pieces using cube
, star
, etc.
1 2 3 |
k |
Number of factors in the design |
n.c |
Number(s) of factorial points in each cube block |
n0.c |
Numbers(s) of center points in each cube block |
blks.c |
Number(s) of cube blocks that together comprise one rep of the cube portion |
n0.s |
Numbers(s) of center points in each star (axis-point) block |
bbr.c |
Number(s) of copies of each cube block |
wbr.s |
Number(s) of replications of each star poit within a block |
bbr.s |
Number(s) of copies of each star block |
best |
How many designs to list. Use |
sortby |
String(s) containing numeric expressions that are each evaluated and used as sorting key(s).
Specify |
restrict |
Optional string(s) containing Boolean expressions that are each evaluated. Only combinations where all
expressions are |
A grid is created with all combinations of n.c
, n0.c
, ..., bbr.s
.
Then for each row of the grid, several additional variables
are computed:
n.s
The total number of axis points in each star block
N
The total number of observations in the design
alpha.rot
The position of axis points that make the design rotatable. Rotatability is achieved when design moment [iiii] = 3[iijj] for i and j unequal.
alpha.orth
The position of axis points that make the blocks mutually orthogonal. This is achieved when design moments [ii] within each block are proprtional to the number of observations within the block.
agreement
The absolute value of the log of the ratio of
alpha.rot
and alpha.orth
. This measures agreement between
the two alpha
s.
If restrict
is provided, only the cases where the expressions are all TRUE
are kept.
(Regardless of restrict
, rows are eliminated where there are
insufficient degrees of freedom to estimate all needed effects for a
second-order model.)
The rows are
sorted according to the expressions in sortby
; the default is to sort
by agreement
and N
, which is suitable for finding designs
that are both rotatable and orthogonally blocked.
A data.frame
containing best
or fewer rows, and variables
n.c
, n0.c
, blks.c
, n.s
, n0.s
, bbr.c
,
wbr.s
, bbr.s
, N
, alpha.rot
, and alpha.orth
,
as described above.
Russell V. Lenth
Lenth RV (2009) “Response-Surface Methods in R, Using rsm”, Journal of Statistical Software, 32(7), 1–17. doi: 10.18637/jss.v032.i07
Myers, RH, Montgomery, DC, and Anderson-Cook, CM (2009) Response Surface Methodology (3rd ed.), Wiley.
1 2 3 4 5 6 7 8 9 10 11 | library(rsm)
### List CCDs in 3 factors with between 10 and 14 runs per block
ccd.pick(3, n0.c=2:6, n0.s=2:8)
# (Generate the design that is listed first:)
# ccd(3, n0=c(6,4))
### Find designs in 5 factors containing 1, 2, or 4 cube blocks
### of 8 or 16 runs, 1 or 2 reps of each axis point,
### and no more than 70 runs altogether
ccd.pick(5, n.c=c(8,16), blks.c=c(1,2,4), wbr.s=1:2, restrict="N<=70")
|
n.c n0.c blks.c n.s n0.s bbr.c wbr.s bbr.s N alpha.rot alpha.orth
1 8 6 1 6 4 1 1 1 24 1.681793 1.690309
2 8 5 1 6 3 1 1 1 22 1.681793 1.664101
3 8 3 1 6 2 1 1 1 19 1.681793 1.705606
4 8 4 1 6 2 1 1 1 20 1.681793 1.632993
5 8 4 1 6 3 1 1 1 21 1.681793 1.732051
6 8 5 1 6 4 1 1 1 23 1.681793 1.754116
7 8 6 1 6 3 1 1 1 23 1.681793 1.603567
8 8 6 1 6 5 1 1 1 25 1.681793 1.772811
9 8 2 1 6 2 1 1 1 18 1.681793 1.788854
10 8 5 1 6 2 1 1 1 21 1.681793 1.568929
n.c n0.c blks.c n.s n0.s bbr.c wbr.s bbr.s N alpha.rot alpha.orth
1 16 6 1 10 1 1 1 1 33 2.000000 2.000000
2 16 8 1 10 2 1 1 1 36 2.000000 2.000000
3 16 10 1 10 3 1 1 1 39 2.000000 2.000000
4 16 5 2 20 1 1 2 1 63 2.000000 2.000000
5 16 6 2 20 2 1 2 1 66 2.000000 2.000000
6 8 3 4 20 2 1 2 1 66 2.000000 2.000000
7 16 7 2 20 3 1 2 1 69 2.000000 2.000000
8 16 8 2 10 7 1 1 1 65 2.378414 2.380476
9 8 4 4 10 7 1 1 1 65 2.378414 2.380476
10 16 1 2 10 2 1 1 1 46 2.378414 2.376354
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