I have been asked to program a partial conjoint exercise with 14 attributes in total (ranging from 2 to 5 levels), and I have been given "complete" freedom in choosing how many products/tasks/attributes to show. FYI: there are no prohibition to worry about.
Given that we are only collecting data on some of the attributes/levels per respondent, it stands to reason that the more products we show (or the more attributes, or the more tasks or any combination of the three) the better the data we collect and the better our results. After reading the technical paper on CBC advanced design module, I was left with the impression that one way to understand which combination would provide better data is to look at the "Strength of design for this model" score after I run an "Advanced test".
After generating several possible designs and running tests for everything, I can see that there are a number of options. For instance I can show 3 products per task, 7 attribute per product and include 15 tasks and have roughly the same design strength as if I showed 4 products per task, 7 attributes in 13 or even 14 tasks.
Another thing to look at is the estimated standard errors; assuming that for all these possibilities the standard error is less than 0.05.
How do I choose which design to use? When do I stop adding attributes/tasks/products in my design?