Correct model selection for mixture factors + process factor

[#1]

Dear all

I made a custom design with JMP18 on biomass pyrolysis and conducted a total of 30 experiments. The experimental design consists of the following factors (Screenshot attached):

Mixture factors:

(1) Cellulose content

(2) Hemicellulose content

(3) Lignin content

(4) Ash content

(5) Others (e.g., proteins)

Process factors:

(6) Pyrolysis temperature

The mixture factors (1)-(5) add up to 100%. I also considered interactions between all factors, including second order interactions.

There is a high multicollinearity between factors (1)-(5). I learned that in this case, the Standard Least Square model would not be suitable to identify the relevant factors for my model, since it is not robust in case of multicollinearity between factors. Which model approach would you choose? 

From a technical documentation (please find it attached) authored by Bernd Heinen from SAS, I conclude that the Elastic Net model approach could be suitable, as it is robust for multicollinearity of factors. What do you think?

Thanks a lot for your help!

Best regards Jannis

[#2]

Hi @jgrafmu2,

Mixture designs are optimization designs, that means you have built it with an assumed model that you're able to fit with the experiments you have done. The goal is to have a useful and predictive model that can help you optimize your formulation factors and process parameter, not filter/select factors or effects in the model based on p-values or other statistical criterion (like LASSO or penalized regression methods can provide). 

It's completely normal to have multicollinearity between your mixture factors, you have a relationship between these factors by design : X1+X2+X3+X4+X5 = 100% (or any constant value), due to the mixture situation. Since these factors are not independant but linked through this mixture constraint, there will be multicollinearity between them, no matter the analysis chosen.

The Least Squares model is appropriate for Mixture design if you fit a model with no intercept : Elements in the Fit Model Launch Window. If you use the "Fit Model" script already present in your datatable once you have generated the design, the option "No Intercept" should already be checked by default :

You should start with the assumed model, and depending on your objective and decision criterion (predictive performance with RMSE, good model complexity with information criterion like AICc and BIC, good explanative performance with R² and R² adjusted, etc...), you can refine your model. You can read this example in the JMP Help documentation, it could help you figure out how to proceed with the analysis : Example of a Mixture Design with Analysis

You might be interested in the following discussions :
How to use the effect summary effectively for a mixture DOE? 
Custom Design: Mixture with Process Variables. How to Evaluate Design? 
Mixture-Process Design or Response Surface Design 

Related to the differences in the ranges of variations of your factors and the presence of a "Others" mixture factor, you might also be interested in this presentation When Not to Run a Mixture Experiment. 

Please find attached the datatable recreated with your capture (please add the JMP table next time, it's easier to understand your topic and answer your questions),