Optimal design and quantitative factorial variables

[sarah123]

Hi all, I'm trying to create a d-optimal main effects design with quantitative variables (e.g. price) that have 3+ levels. In my candidate runs, I observe runs with the intermediate levels of the quantitative variables, however, in all the output for my test designs, I have not seen any runs with intermediate levels of the quantitative variables. Only the largest and the smallest values of those variables.

Has anyone encountered this before, and is there a reason that the d-optimal designs are not selecting runs with the intermediate levels?

Thank you for any advice.

[WarrenKuhfeld · Accepted solution]

Yes.  That is correct.  Two points define a line.  If you want a linear (quantitative) effect, then the correct behavior is to pick the extreme points.  That is most efficient.  If you want intermediate points (the middle point for a quadratic effect) then treat the factor as qualitative.

[sarah123]

Thank you! I had a suspicion but this is new to me and I didn't see it written in any of the examples I worked through 🙂