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

[Rahul Chakraborty]

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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