2
$\begingroup$

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.

$\endgroup$
2
  • 1
    $\begingroup$ If a variable is numerical, then a model which is linear in that variable will only need the extreme levels for an optimal design. The reason to include, say, a midpoint, is that you suspect )or want to check for) some curvature, but then you need to include in model say the square of that variable. Try that with ` optFederov ` and see what happens! $\endgroup$ Nov 19, 2022 at 20:36
  • $\begingroup$ See my answer at stats.stackexchange.com/questions/596056/… $\endgroup$ Nov 24, 2022 at 23:37

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