Guidance on Data Analysis for a 4-Factor Mixture Design with 4 Responses

[#1]

I am working on a mixture design in JMP with four continuous factors and four responses. While I have made progress in modeling and evaluating individual responses, I am finding it challenging to analyze all responses collectively. Specifically:

• The ternary plots are limited to visualizing only three mixture components at a time, which makes it difficult to understand the behavior of all four factors simultaneously.
• Some of my responses suggest conflicting trends, requiring a "middle ground" approach for optimization.
• The prediction profiler, though helpful, doesn't fully address the complexity of combining all responses for a comprehensive analysis.
• Instead of identifying a single optimal value for each factor, I aim to define smaller, practical ranges for each compound. These ranges will be used in subsequent analyses where evaluation will consider additional responses.

Here is what I have already done:

1. For each response, I retained only the significant effects that reduced RMSE.
2. I examined the residuals and lack of fit, finding no evident trends or issues.

I am looking for the best approach or tools within JMP to analyze this mixture design effectively, particularly in synthesizing insights across all responses and identifying meaningful ranges for each factor. If you could point me toward relevant strategies or documentation, I would greatly appreciate it.

Thank you in advance!

[#2]

Hi @K_JMP,

It seems you already have done a lot of work to analyze your results. Here are some additional suggestions related to some of your points :

• Instead of ternary plot, you could also use contour plot matrix ("Multiple Contour frames" in the red triangle options of the Contour Profiler) to display all your factors by pairs.
• What is the difficulty you're facing with Prediction Profiler ? If you have categorical responses, there is a way to include them through the use of probabilities formula.
• If you want to define acceptable factors ranges, the Design Space Profiler might be helpful.
• Concerning the analysis approach, since Mixture designs are optimization designs, it's a good idea to refine your model based on a predictive metric. Make sure you do respect effects heredity. If you have JMP Pro, you could try using other estimation methods in the Generalized Regression models, such as SVEM, Pruned Forward or Backward Selection, ... with different  validation methods options. Depending on your mixture design and the repartition of points, you could also try simple Machine Learning that are effective at interpolating without big risks of overfitting (SVM and Random Forest are good candidates).

I hope these few suggestions might help you,

[#3]

Here are my thoughts.  First do a correlation of the response variables.  Do any correlate.  Look for outliers (Mahalonobis). Use different graphing techniques to look at the mixture response surfaces.  Unfortunately, we can't see in 4 dimensions, so try getting multiple graphs for each possible set of 3.  Be practical in your analysis, there is no "magic" analysis that does the interpretation for you.