# ccd.pick: Find a good central-composite design In rvlenth/rsm: Response-Surface Analysis

## Description

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.

## Usage

 ```1 2 3``` ```ccd.pick(k, n.c = 2^k, n0.c = 1:10, blks.c = 1, n0.s = 1:10, bbr.c = 1, wbr.s = 1, bbr.s = 1, best = 10, sortby = c("agreement", "N"), restrict) ```

## Arguments

 `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 `best=NULL` to list them all `sortby` String(s) containing numeric expressions that are each evaluated and used as sorting key(s). Specify `sortby=NULL` if no sorting is desired. `restrict` Optional string(s) containing Boolean expressions that are each evaluated. Only combinations where all expressions are `TRUE` are retained.

## Details

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.

## Value

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

## References

Lenth RV (2009) “Response-Surface Methods in R, Using rsm”, Journal of Statistical Software, 32(7), 1–17. http://www.jstatsoft.org/v32/i07/.

Myers, RH, Montgomery, DC, and Anderson-Cook, CM (2009) Response Surface Methodology (3rd ed.), Wiley.

`ccd`

## Examples

 ``` 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") ```

rvlenth/rsm documentation built on Sept. 2, 2018, 10:06 a.m.