can refer to

Sample Size Requirements for Discrete-Choice Experiments in Healthcare: a Practical Guide.

Design considerations of a choice experiment to estimate likely participation by north Australian pastoralists in contractual biodiversity conservation.

I think one of the best explanations of how to design an orthogonal fractional design fro a Choice Experiment could be found in: Bateman, I. et al (2002) Economic Valuation with Stated preference Techniques.Edward Elgar Publishing.  It is an old text book. but is very didactic and easy to understand.

Using (L-1)*M*A+1, where L, M and A are numbers of levels, alternatives and attributes respectively.

This gives 31, which will be made 36 in order to have each level being shown equal number of times.

This further can be made into three blocks by adding a blocking variable.

Therefore, 12 choice sets can be shown to each respondent.

Please correct me if I have done it incorrectly. I am also learning, and welcome your feedback.

Cheers

The minimum number of profiles that must be evaluated by each respondent is:

Minimum number of profiles = Total number of levels across all factors - Number of factors + 1

Multivariate Data Analysis,Joseph F. Hair Jr. William C. Black

Barry J. Babin Rolph E. Anderson, Seventh Edition, Pg 361

Hi Bosco Lliso

Did you find the answer to your question? I have the same question as well so any advice from you will be super helpful. Thanks!

It depends on whether you require generic estimates or alternative specific estimates. If generic you'll require (L-1) degrees of freedom for each attribute where L is number of levels. So for a 2 level attribute that's 1df and 3 level attribute is 2df for each main effect

.Now given you want 5 attributes that's 5 X df or (L-1)*A. So if with 5 two-level attributes that is 5df. Some add one for the intercept for the two options vs none and 1df for the error. That means conservatively you need an experiment with at least 7df... Given your working in power of 2, that'd be 8 sets. If your working with a mixture of 2 and 3 level attributes it starts getting messier as finding a fractional design to suit both 2s and 3s is not always as efficient when you have lots of attributes relative to keeping them all 2s or all 3s.

Now if you want alternative specific estimates, then multiply the number of effects by M, ie (L-1)*M*A