1 - Are there any good examples or any option in JMP Pro to run compositional data analysis before I run PCA and modeling with the compositional data to predict some responses? Let's say I have 20 variables (powder oxides found by X-ray fluorescence, some of which can be zero that need to be imputed, if I use, for example, R, before centered log-ratio transformation), and the summation of these 20 is 100%. I also have a response. Any idea how to run all these in JMP?
2 - In the above example, let's say I have additional variables 21, 22, etc. which are not part of the compositional data. Let's say they are the powder fineness, density, etc. How to include this in the analysis? Assuming no tools are available in JMP, should I first transform the compositional data, and then run PCA with all 22 variables?
I'm not sure what you are looking for. The compositional variables would be called "mixture" components in JMP. You can build a model with them, but the type of model would be called a Scheffe model. It looks like a no-intercept model, but really the intercept would be included with the main effects. Your model could also include non-compositional factors, too.
As for PCA, you could do that at any time. Of course if you have 20 compositional variables, you will only end up with 19 PCs because of the sum to 100%.
You should look up information on mixture analysis. There are some free webinars from jmp.com that might get you started. There is also a full course on the design and analysis of mixture experiments that would be of benefit.
Thank @Dan_Obermiller. The predictions are very inaccurate for all 3 responses I have when I use Scheffe model or Mixture response surface. I feel the predictors may need to be transformed but I am not sure if JMP is taking care of the centered log-ratio (clr) transformation suggested by John Aitchison for compositional data ??