Analysis of a Mixture DOE with stepwise regression

[#1]

In Mixture case studies (webcast & JMP documentation library) I notice that backward regression is used to analyse the results. Why is stepwise regression not used with forward regression or all possible models in regualr (non Pro) JMP? Is stepwise not possble because of the special nature of mixture models?

[#2]

If the higher-order model is 'correct,' then the space-filling design is not necessarily 'better.' Think of a simpler situation: a first-order effect only of a single continuous factor. What is the best 10-run design? Five runs at the low setting and five runs at the high setting. A 'space-filling' design would distribute the runs over more than two levels, which is not statistically efficient.

A space-filling design for mixtures is advantageous when the response changes rapidly in a narrow region of the simplex, and the region is unknown. It is a screening design with a twist for mixture experiments.

[#3]

Suppose you are testing a mixture with 5 components and want to know which components have an effect on the response, how do you screen out these effective ingredients? Is this possible due to the confounding? 

[#4]

I suppose that even with space filling designs screening will be very difficult?

Remark: I have a wide experience in non mixture DOE so my questions above may look naive for mixture experts.  So far my conclusion is that mixture DOE requires experience and as analysis methods are less clear cut than non-mixture, for scientists it looks little artificial. I'm preparing for a lot of questions in a coming DOE training where formulations are important. Thanks all for you inputs, is a great help!

[#5]

Space-Filling designs tend to focus a little more on the interior than on the borders of the experimental space, and on optimization (fitting the best predictive model thanks to the uniformly distributed design points and a large variety of modeling/algorithms options).

Mixture designs are more used in an optimization strategy to find the best formulation ratios for specific performances/responses, but there are designs that can help you "screen" mixture factors (or at least evaluate the relative importance of the mixture factors between each others, since statistical significance is not appropriate to screen effects here, due to the multicollinearity). 

• In JMP, ABCD designs may be helpful to compare the influence of the mixture factors (and the example is quite close to the case suty you mentioned with 5 mixture factors) : JMP-Example of an ABCD design
• You may also use Simplex Centroïd design with a relatively low centroïd degree (2 or 3 for example) : JMP-Example of Simplex Centroid design 

In general, if you're not familiar with Mixture designs, there are a lot of available ressources on internet. Here are a few examples to help you :

https://reliawiki.org/index.php/Mixture_Design

https://online.stat.psu.edu/stat503/lesson/11/11.3

https://www.lexjansen.com/sugi/sugi21/iv/138-21.pdf

I hope this answer will help you,

[#6]

Thanks Victor!

[#7]

IMHO, before you train others in a methodology, you should be proficient with many applications under your belt. I suggest you read Cornell (Cornell is one of the leading experts on Mixtures) to start your journey into understanding mixtures.

Cornell, John (1990) “Experiments with Mixtures, Designs, Models, and the Analysis”, Wiley (SBN: 047152221X)

Some favorite papers:

Snee, Ronald D., Design and Analysis of Mixture Experiments, Journal of Quality Technology, Vol. 3, No. 4, October 1971

Cornell, John, Embedding Mixture Experiments Inside Factorial Experiments, Journal of Quality Technology, Vol. 22, No. 4, October 1990

Snee, Ronald D., Donald Marquardt, Screening Concepts and Designs for Experiments with Mixtures, Technometrics, Vol. 18, No. 1, February 1976

and our own Dan Obermiller's: Tips on JMPing into Mixture Experiments

[#8]

The Cox mixture model is an attempt to help an experimenter answer this question. It requires specifying a reference blend. The model is used to determine unique effects of each component.

[#9]

Sinerely thanks for these refefence-mix! I will go and dig into this challenging subject

[#10]

I saw in a presentation of Louis Valente a great way to label and color the mixture design points by a Point Type column, see below. How do you create this Point Type Column? 

[#11 · Accepted solution]

There is a script in the Sample Scripts folder (in the JMP folder under \Samples\Scripts) that does this.  The name of the script is "LabelMixturePoints.jsl".