Re: [R] R: fractional factorial design in R

From: Berton Gunter <>
Date: Tue 24 Jan 2006 - 07:48:58 EST

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.

"The business of the statistician is to catalyze the scientific learning process." - George E. P. Box    

> -----Original Message-----
> From:
> [] On Behalf Of
> Sent: Monday, January 23, 2006 12:20 PM
> To: Berton Gunter;;
> 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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