Including categorical factors in a design

[rvlenth]

A user noted that design-generation functions only accommodate quantitative predictors. It'd be nice to have some provision for a response-surface design that can be used with additional categorical factors, e.g., suppliers.

I suggested as a short-term remedy to create a design for the categorical factor(s) and cross it with an RS design. I provided a quick-and-dirty function for this purpose:

# Cross a response-surface design `design` with another design `extras`
# `extras` may be a data frame or a list. If a list, it is converted to a data frame 
# via expand.grid() (thus creating all combinations of the provided factor levels)
# This function does NOT randomize the design!
cross.with = function(design, extras) {
    if (missing(extras))
        return(design)
    if (!is.list(extras))
        stop("'extras' must be a list or data.frame")
    if(!inherits(extras, "data.frame"))
        extras = do.call(expand.grid, extras)
    pieces = lapply(seq_len(nrow(extras)), function(i) {
        des = design
        for (nm in names(extras))
            des[[nm]] = extras[[nm]][i]
        des
    })
    do.call(rbind, pieces)
}

Illustration of use:

> des = rsm::ccd(2, random = FALSE)
> cross.with(des, list(trt = c("A", "B")))
   run.order std.order  x1.as.is  x2.as.is Block trt
1          1         1 -1.000000 -1.000000     1   A
2          2         2  1.000000 -1.000000     1   A
3          3         3 -1.000000  1.000000     1   A
4          4         4  1.000000  1.000000     1   A
5          5         5  0.000000  0.000000     1   A
6          6         6  0.000000  0.000000     1   A
7          7         7  0.000000  0.000000     1   A
8          8         8  0.000000  0.000000     1   A
9          1         1 -1.414214  0.000000     2   A
10         2         2  1.414214  0.000000     2   A
11         3         3  0.000000 -1.414214     2   A
12         4         4  0.000000  1.414214     2   A
13         5         5  0.000000  0.000000     2   A
14         6         6  0.000000  0.000000     2   A
15         7         7  0.000000  0.000000     2   A
16         8         8  0.000000  0.000000     2   A
17         1         1 -1.000000 -1.000000     1   B
18         2         2  1.000000 -1.000000     1   B
19         3         3 -1.000000  1.000000     1   B
20         4         4  1.000000  1.000000     1   B
21         5         5  0.000000  0.000000     1   B
22         6         6  0.000000  0.000000     1   B
23         7         7  0.000000  0.000000     1   B
24         8         8  0.000000  0.000000     1   B
25         1         1 -1.414214  0.000000     2   B
26         2         2  1.414214  0.000000     2   B
27         3         3  0.000000 -1.414214     2   B
28         4         4  0.000000  1.414214     2   B
29         5         5  0.000000  0.000000     2   B
30         6         6  0.000000  0.000000     2   B
31         7         7  0.000000  0.000000     2   B
32         8         8  0.000000  0.000000     2   B

Data are stored in coded form using these coding formulas ...
x1 ~ x1.as.is
x2 ~ x2.as.is