[R] R: fractional factorial design in R

Bob Wheeler rwheeler at echip.com
Tue Jan 24 04:55:16 CET 2006

If an orthogonal main effect plan exists for the number of trials you 
specify, optFederov() in AlgDesign will more than likely find it for 
you, since such a design should be an optimal design.

Ulrike Grömping wrote:
> I think that there is an understandable wish to have the simple orthogonal 
> plans (and be it only for non-experts to be able to analyse the results 
> themselves). For mixed levels, there is e.g. the L36 that should be able to 
> accomodate plans like 2x2x2x3x3x3. Unfortunately, R is not very strong in 
> this arena.
> If I had more time, I would think about writing a package on comfortably 
> designing experiments supported e.g. by the catalogues of  Chen, J., Sun, 
> D.X., and Wu, C.F.J. (1993). (A catalogue of two-level and three-level 
> fractional factorial designs with small runs. International Statistical 
> Review 61, 131-145.) Such a package should also provide the analysis
> facilities for any design generated with it, once it has been enriched with 
> observed data. (This is a bit different from the typical R spirit, where 
> users are often required to be experts themselves.) If anyone is planning a 
> project like this or wants to make a diploma student work on it I would be 
> interested in contributing. 
> For the moment, if you want to implement main effects plans of the orthogonal 
> sort (e.g. a Taguchi-plan like the L36) you have to use books or tables 
> published on the internet, if you don't want to use expensive software like 
> SPSS - not very comfortable, but possible. For example, you can find the L36 -
>  which would be able to accomodate your 2x2x2x3x3x3 - in 
> http://www.itl.nist.gov/div898/handbook/pri/section3/pri33a.htm.
> With kind regards,
> Ulrike
>>In general, a "main effects design" need not be orthogonal -- the main
>>effects merely need to be estimable. The trick is to estimate them with good
>>efficiency, etc. I think you need to consult a local statistician for help
>>to understand what these statistical concepts mean.
>>In your example you could cross the 2^(3-1) with the 3^(3-1) to produce an
>>orthogonal design to estimate main effects. But of course that's 72 runs,
>>which I don't think you would consider "small." As a previous poster
>>commented, there are orthogonal mixed level arrays ("Addleman", "Kempthorne"
>>"Youden" -designs are a couple of phrases to try googling on) which stem
>>from the 1960's. I doubt that, in general, they would satisfy your needs.
>>I have not used the AlgDesign package myself. I suggest you direct questions
>>about it to the author/maintainer, Bob Wheeler.
>>-- Bert Gunter
>>Genentech Non-Clinical Statistics
>>South San Francisco, CA
>>"The business of the statistician is to catalyze the scientific learning
>>process." - George E. P. Box
>>-----Original Message-----
>>From: r-help-bounces at stat.math.ethz.ch 
>>[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of 
>>statistical.model at googlemail.com
>>Sent: Monday, January 23, 2006 12:20 PM
>>To: Berton Gunter; statistical.model at googlemail.com; 
>>r-help at stat.math.ethz.ch
>>Subject: [R] R: fractional factorial design in R
>>>Yes, you're right. For, say, a 3 x 5 design, one can do 
>>this in as few as
>>runs -- but only in general by some version of 
>>one-factor-at-a-time (OFAT)
>>designs, which are inefficient. It is easy, via, say 
>>model.matrix() to
>>write a general function to produce these. But I think it's a 
>>bad idea; more
>>efiicient algorithmic designs are better, IMO, which is why I 
>>AlgDesign. You and others are free to disagree, of course.
>>Hi Bert,
>>thanks for your suggestion.
>>However, let us say that i need a 2x2x2x3x3x3 design, which 
>>should not be
>>too hard.
>>I've loaded AlgDesign, and i am aware now that gen.factorial 
>>allows me to
>>create a full desing. But how to create a main-effects-only 
>>factorial design
>>I am still not able to produce what i need. The function
>>model.matrix.formula is not very clear... :(
>>Could you please indicate which syntax should i use? I'd 
>>really appreciate
>>your help.
>>Thanks in advance,
>>Roberto Furlan
>>University of Turin, Italy
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Bob Wheeler --- http://www.bobwheeler.com/
    ECHIP, Inc. --- Randomness comes in bunches.

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