[R] Problem in generating an "Orthogonal fractional design"

[Bert Gunter]

Sorry, Off topic. This list deals with R programming questions, not
statistical questions. Try stats.stackexchange.com for those.

Bert Gunter

"The trouble with having an open mind is that people keep coming along and
sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Wed, May 27, 2020 at 1:25 AM Rahul Chakraborty <chakrarahul using gmail.com>
wrote:

> Dear all,
>
> Presently I am working on designing a questionnaire for my discrete choice
> experiment. I want to generate an orthogonal fractional factorial design
> for the following problem-
>
> The respondent has to choose one out of 4 objects (*X1, X2, X3, X4*). Each
> of the 4 objects are classified by 10 different attributes. However, the
> levels are not the same under each of the objects. The table below displays
> the situation.
>
> Attributes No. of Levels  Choices and values
> X1 X2 X3 X4
> A 5 1 1,2,3 3,4,5 3,4,5
> B 4 1 1 1,2 3,4
> C 4 1 1 2,4 3,4
> D 5 1 1,2,3 1,2,3 1,4,5
> E  5 1,2 2,3 3,4 5
> F 2 1 1 1,2 1,2
> G 2 1 1 1,2 2
> H 2 1 1 1,2 1,2
> I 4 1 2,3,4 2,3,4 2,3,4
> J 3 1 2,3 2,3 2,3
> *X* 4 1 2 3 4
>
> The last row denotes the 4 objects.
>
> Now I want to generate the choice sets for my questionnaire. I would like
> to use *orthogonal fractional factorial design*. I kept the row with *X* in
> order to sort out the redundant combinations from the choice sets.
>
> I have the following questions-
> 1. *How to decide on the number of runs that one has to chose for
> fractional factorial design?*  I used *AlgDesign* to generate the full
> factorial which consists of 0.768 million combinations. So, I need a modest
> number of runs, but how much should I target? I do not see any document
> where one explains how to choose the number of trials/experimental runs.
> The papers I am following only tell that they have used N number of runs
> instead of the full factorial.
>
> 2. Out of 0.768 million combinations in the full factorial, there will be
> many which are redundant. For example- I don't want those rows where (X=X1)
> and A=(2 or 3 or 4 or 5). There are many other such cases which I don't
> want in my design. I have coded all levels for each attribute and that's
> why they are in the full factorial. *How do I generate an orthogonal
> fractional factorial so that it does not contain such redundant
> combinations?* I included the X attribute with the purpose of dropping
> those combinations conditioned upon specific values of X and other factors.
> Should I execute that and then generate the fractional factorial using
> *optFederov* from the remaining data in the dataframe?
>
> I would be highly obliged if you can kindly help me in this regard. I am a
> student of Economics, so I do not have very deep understanding of the
> statistical procedure of such algorithms. So, my question might sound
> extremely naive for which I am sorry.
>
>
> -- Regards,
> Rahul Chakraborty
> Research Fellow
> National Institute of Public Finance and Policy
> New Delhi- 110067
>
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>
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