如何在 R 中创建部分因子设计？

Question

I'm struggling to create a rather elaborate fractional factorial design using R.

(see http://en.wikipedia.org/wiki/Fractional_factorial_design )

I've searched the Google and the R-lists and have checked out several promising packages (AlgDesign, DoE.base, acepack)

But I have not found anything thing that can handle a fractional design (only interested in main effects) with 8 factors that have either 3, 4, 6, or 11 levels each!

Can anyone point me in the right direction?

Thanks!

Answer 1

I have used the package AlgDesign to generate fractional factorial designs:

1. Generate the full factorial design using the function gen.factorial() .
2. Pass the results to optFederov() - this will try to find an optimum fractional design, using the Federov algorithm.

The following code takes about 3 minutes to run on my Windows laptop. The example finds an approximate optimum fractional factorial design with 8 factors with 3, 4, 6 or 11 levels each, as you specified.

Note that I use optFederov(..., approximate=TRUE) - this finds an approximate solution. On my machine, when I set approximate=FALSE the code takes too long to run and Windows throws a strop. You may wish to experiment with different settings.

library(AlgDesign)

levels.design = c(3,4,6,11,3,4,6,11)
f.design <- gen.factorial(levels.design)

fract.design <- optFederov(
        data=f.design,
        nTrials=sum(levels.design),
        approximate=TRUE)

And the output:

head(f.design)

  X1 X2 X3 X4 X5 X6 X7 X8
1 -1 -3 -5 -5 -1 -3 -5 -5
2  0 -3 -5 -5 -1 -3 -5 -5
3  1 -3 -5 -5 -1 -3 -5 -5
4 -1 -1 -5 -5 -1 -3 -5 -5
5  0 -1 -5 -5 -1 -3 -5 -5
6  1 -1 -5 -5 -1 -3 -5 -5


fract.design
$D
[1] 6.813321

$A
[1] 0.375804

$Ge
[1] 0.998

$Dea
[1] 0.998

$design
       Rep.. X1 X2 X3 X4 X5 X6 X7 X8
1          1 -1 -3 -5 -5 -1 -3 -5 -5
10         1 -1  3 -5 -5 -1 -3 -5 -5
...
626475     1  1 -3 -5 -5  1  3  5  5
627253     1 -1 -3  5  5  1  3  5  5

$rows
 [1]      1     10     61    723    790   1596   2307   2314   2365   2374
[11]   2376   7129   7140   7198   7849   7911   7918   7920   8713   8724
[21]   9433   9504  48252  48301  48303  49105  49107  49114  49174  54660
[31]  54711  56233  56304 570241 570963 571834 571836 572556 578151 579015
[41] 617821 617823 619414 620127 620134 625618 626475 627253

Answer 2

Just to add to Andrie's answer. This is how we interpret strength of optimual design.

Design efficiency is judged by Ge. It should be 1 or close to 1. Below links have some explanation and i referred the book "Design and Analysis of Experiments with R". Thought this might be useful for those who are looking for answer. Below are the source from which i got this information.

https://stat.ethz.ch/pipermail/r-help/2007-October/143217.html

Error in Hierarchical Bayesn in R : Bayesn Package

Answer 3

The D, A, I, G-optimal designs are all bounded designs(the designs are on the bounds of design space), I don't think the optimal design results are good at fitting response surface or surrogate model. Meanwhile, the optimal design is usually not orthogonal.