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> 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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