I'm aware of e.g. FrF2 which allows to create 2-level experiment designs. I'm also aware of e.g. gen_design or optFederov which seem to consider multiple levels but when using these I always receive only experiment designs where the lowest and highest levels are considered:
candidateset <- expand.grid(T = c(5, 10, 15, 20, 25, 30, 35, 40),
rH = c(10, 40, 70))
design <- gen_design(candidateset = candidateset
+ , model = ~ T^2 + rH + T:rH
+ , trials = dim(candidateset)[1]
+ , add_blocking_columns = TRUE
+ , randomized = TRUE
+ )
design
T rH
1 5 70
2 5 70
3 40 70
4 40 10
5 5 10
6 40 70
7 5 70
8 40 70
9 5 70
10 5 10
11 40 10
12 40 10
13 40 70
14 5 70
15 5 10
16 40 70
17 40 10
18 5 10
19 40 10
20 40 70
21 5 70
22 5 10
23 40 10
24 5 10
As you can see, only two levels are used for each factor and the next experiment design looks like a full factorial design I could come up with on my own (wonder about the meaning).
cand.list = expand.grid(T = c("5", "10", "15", "20", "25", "30",
"35", "40"),
rH = c("10", "40", "70"))
set.seed(70)
optFederov( ~ .
+ , data = cand.list
+ , nTrials = dim(cand.list)[1]
+ , criterion = "D"
+ )
$D
[1] 0.1362673
$A
[1] 13.4
$Ge
[1] 1
$Dea
[1] 1
$design
T rH
1 5 10
2 10 10
3 15 10
4 20 10
5 25 10
6 30 10
7 35 10
8 40 10
9 5 40
10 10 40
11 15 40
12 20 40
13 25 40
14 30 40
15 35 40
16 40 40
17 5 70
18 10 70
19 15 70
20 20 70
21 25 70
22 30 70
23 35 70
24 40 70
When I reduce the nTrials = 15
it'll be:
optFederov( ~ .
+ , data = cand.list
+ , nTrials = 15
+ , criterion = "D"
+ )
$D
[1] 0.1244044
$A
[1] 15
$Ge
[1] 0.41
$Dea
[1] 0.238
$design
T rH
1 5 10
2 10 10
4 20 10
6 30 10
8 40 10
9 5 40
10 10 40
11 15 40
13 25 40
15 35 40
16 40 40
19 15 70
20 20 70
21 25 70
22 30 70
so there isn't much difference. Are there packages with which I can create experiment designs with multiple factors and multiple levels? Preferably also with randomization.