Of course, I representing Sawtooth Software am going to tell you that this is precisely what our design algorithms (for our CBC software) do... come up with unique versions for respondents and within each version there will be (in this case) typically perfect 1-way level balance and approximate 2-way level balance.  Across all respondents and all designs, it gives perfect 1-way and nearly perfect 2-way level balance in this case.  See the counts report below, for 1-way and 2-way level balance.

CBC Design Efficiency Test
Copyright Sawtooth Software
7/25/2011 8:41:14 AM

Task generation method is 'Complete Enumeration' using a seed of 2.
Based on 500 version(s).
Includes 1500 total choice tasks (3 per version).
Each choice task includes 4 concepts and 3 attributes.


A Priori Estimates of Standard Errors for Attribute Levels
-------------------------------------------------------------
Att/Lev   Freq. 
 1    1      3000 
 1    2      3000   

 2    1      2000 
 2    2      2000   
 2    3      2000   

 3    1      2000 
 3    2      2000  
 3    3      2000  


Two-Way Frequencies
-------------------------------------------------------------
Att/Lev         1/1       1/2       2/1       2/2       2/3       3/1       3/2       3/3
1/1            3000         0      1000      1000      1000      1000      1000      1000
1/2               0      3000      1000      1000      1000      1000      1000      1000
2/1            1000      1000      2000         0         0       667       666       667
2/2            1000      1000         0      2000         0       666       666       668
2/3            1000      1000         0         0      2000       667       668       665
3/1            1000      1000       667       666       667      2000         0         0
3/2            1000      1000       666       666       668         0      2000         0
3/3            1000      1000       667       668       665         0         0      2000

--Bryan Orme, Sawtooth Software


From: Aline Deschamps 
Sent: Monday, July 25, 2011 8:33 AM
To: Bryan Orme 
Cc: r-sig-dcm@r-project.org 
Subject: Re : [R-sig-DCM] Balanced design of experiments for CBC


Thank you for your answer.
I realise that my example was poorly chosen, what I'm looking for is a way to program a balanced design of experiments where each respondent sees approximately the same number of times each combination of levels of two variables. I don't know if I'm really clear, but someone showed me a software ("Design Expert") which seems to do it well, unfortunately I haven't any clue of how, except that it's based on the Fedorov algorithm apparently.

So, if anyone has a clue, I'm still looking for :)

Aline Deschamps
Nantes, France





--------------------------------------------------------------------------------
De : Bryan Orme <bryan@sawtoothsoftware.com>
À : Aline Deschamps <deschamps.aline@yahoo.fr>
Envoyé le : Lun 25 juillet 2011, 16h 27min 46s
Objet : Re: [R-sig-DCM] Balanced design of experiments for CBC

Mathematically not possible.  For each respondent, you have 3 tasks x 4 products = 12 products.  Then, your two 3-level factors crossed together make 9 possible combinations of those two factors.  So, it's impossible to evenly fill that 2-way counts matrix of 9 cells using 12 product concepts. So, perfect 2-way level balance within each respondent questionnaire is impossible.

--Bryan Orme, Sawtooth Software

--------------------------------------------------
From: "Aline Deschamps" <deschamps.aline@yahoo.fr>
Sent: Monday, July 25, 2011 3:12 AM
To: <r-sig-dcm@r-project.org>
Subject: [R-sig-DCM] Balanced design of experiments for CBC

> Hi all,
> 
> I'm working on CBC (Choice-Based Conjoint) studies and my problem today (in
> fact, it's a problem I have since so many days ;) is how to generate a balanced
> design of experiments for that kind of study.
> 
> Here is the background of my study (based on an example) :
> 
> I have 3 variables X, Y and Z. Each could take respectively 2, 3 and 3 levels. I
> have 500 respondents.
> All of them see 3 tasks of 4 products (I remind you that a product is a
> combination of levels of each variable).
> Then, I want to program the generation of the design of experiments for such a
> case.
> 
> 
> The design of experiments should verify two conditions :
> 
> 1/ Each task should not have two identical products, and each respondent should
> not see two identical tasks (and all respondents don't see the same tasks).
> 
> 2/ Each respondent should see the same number of times each possible combination
> of levels of two variables.
> 
> My major issue is how to have this second condition.
> 
> In fact, I've seen that the Fedorov algorithm is often used in order to generate
> design of experiments for CBC but with the "optFederov" function (of the
> "AlgDesign" package), I haven't be able to obtain such a balanced design of
> experiments...
> So, I thought to program it myself (in R or may be in an other language, I don't
> know yet) but I'm afraid it would be complicated and mostly not very effective
> to check all the possible combinations of levels of two variables.
> 
> 
> I hope my message is not too confused, and if you have any clue of how to
> program the generation of design of experiments in such a case, I would be very
> grateful.
> 
> Thanks :)
> 
> 
> Aline Deschamps
> Nantes, France
> 
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> 
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