Mixture Design Containing SumTotal as a Factor

Question

Hello!

I am wondering what the most appropriate way to include the sum total of mixtures within an mixture design is.  For example, I have a 5 factor mixture, but I also want to include their total amount as a discrete or continuous factor;

A: 10-50%

B:10-50%

C:10-50%

D:10-50%

E:10-50%

Total: 1g-3g

Is there a better way to do this than simply including the non-mixture factor as an additional term?  Does it matter that this 6th term is related to the first 5 etc.

Thank you,

Max

MaxLloyd · Answer

Thank you @Dan_Obermiller , I believe this answers my question, I just didn't know if there was a special way of incorporating the total amount of components into a mixture designother than simply adding a continuous factor.  In my case the 5 factors account for everything in the mixture, and I have reason to believe that the effect of the factors will differ depending on the total amount.  Specifically I am mixing 5 different DNA sequences together and performing a cell culture transfection with the blend.

Thanks again,

Max

Dan_Obermiller · Answer

The percentages for the 5 mixture components are a percentage of the weight? In other words, if the total is 1 gram, and you want 50% of A and 50% of B, then there is 0.5 grams of A and 0.5 grams of B.

If that is the case, there would not really be an issue with adding the amount as a continuous factor to the design. I would strongly recommend including all two-way terms in the model as I would expect the effects of the components may change based on the amount.

Finally, if you think the total amount matters, I am led to believe that those 5 components are not the only components. The blend is then added to something else where the total amount makes a difference. Knowing more about the situation would likely be beneficial here.

statman · Answer

Max, I'll share my thoughts, and I'm sure others will too.

Mixture designs are a special case where the response variables are dependent on proportions of components rather than the amount of each component. You can also run designs where the proportions remain constant and the amounts vary.  There is also a third strategy where factors are manipulated in a factorial and the mixture components are simplex designs around each factorial point.

I consider mixture designs to be optimization designs, so the screening of unimportant factors has already been accomplished and you already understand the effects of NOISE.  Typically, mixture designs are done with ≤4 variables (it is a challenge to visualize the surfaces).