EVOP/Mixture Design/Frankenstein Design QuestionI don't have lots of experience with mixture designs so I'm looking for some personal guidance for 'next time this happens' with a prospect/customer. I've got a prospect that uses extreme vertices mixture designs quite often. Their thinking was, if one region of the design factor space looks promising, but it's on the edge of the space, what about moving the design space ala an EVOP kind of approach in the direction of promise for a second design. So second design overlaps a relatively large portion of the first design space. First analyze the second design as it's own distinct single design. Then bolt the two designs together and analyze the entire mess.
My first thought is if nothing else the second design can serve as a means to confirm predictions coming from the first design since the space overlaps. Are there other 'gotchas' I just haven't considered from an analysis point of view for the Frankenstein design as it builds...maybe into EVOPlike iterations, 3 and 4?
Something tells me the Fit Model/Standard Least Squares platform might not be the best place to analyze the Frankenstein design? Maybe Generalized Regression, penalized methods?
I'd love to hear people's thougths.
Re: EVOP/Mixture Design/Frankenstein Design QuestionMixture designs have built-in correlation due to the fact that the percentages of the ingredients must add to 1. Further constraining the ingredients by adding upper and lower bounds or linear inequality constraints makes for still more correlation in the parameter estimates. Finally, adding more and more model terms (2nd and 3rd order effects) makes for still more correlation.
As a result, I believe that mixture designs should almost always be viewed as response surface designs. The most important design diagnostic is the variance of prediction within the region of experimentation.
For model selection, I would recommend removing higher order terms in groups to see whether each group makes substantial differences in the predicted responses. You can also add up the sums of squares for a group and do a multiple degree of freedom hypothesis test to see the significance of including that group of terms.
Re: EVOP/Mixture Design/Frankenstein Design QuestionI agree the Augment Design platform is the way to go to build the second, third, and on designs. That's pretty straightforward to me. What I was mostly unclear on is thoughts on best pathways to analyze the Frankenstein design. I'm just thinking the optimality criteria of the Frankenstein design is probably not what you look for compared to if they ran one design with I optimality say, for 3 mixture factors. And the factor correlations are going to be pretty messed up...leading to high VIFs and unstable parameter estimates? Or is my thinking misguided?
That leads me to trying say the Gen Reg penalized regression space? I'm thinking the parameter estimates will have little to no interpretability...but that's OK for this particular problem...the primary objective is prediction for the response.
Re: EVOP/Mixture Design/Frankenstein Design QuestionI agree with Mike that the Augment Designer is the tool to use here. Once you click the Augment button in that designer, you can change the ranges of the factors to move to a new region. You should also click the check box to make the new runs a separate block. If that effect is significant, it is an indication that the intercept has shifted between the two sets of runs.
Re: EVOP/Mixture Design/Frankenstein Design QuestionI think that the workflow you described is the essence of why we have the Augment platform. Maybe @bradleyjones could throw some wisdom our way on this one.
best,
M
