[R] R: fractional factorial design in R

Ulrike Grömping groemping at tfh-berlin.de
Mon Jan 23 22:22:42 CET 2006

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 

With kind regards,

>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
> 7
> 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 
> suggested
> 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
> (orthogonal)?
> 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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