Prediction Profiler with Mixtures

[#1]

I found out something intringuing, which can be easily seen by using the jmp file called "Donev mixture data.jmp".

Any Mixture DOE table can be used as well.

The thing is that Prediction Profiler curves are different depending on whether your ingredient factors are defined as "Mixture" in column settings dialog box, or not.

Image 1 shows the column settings dialog box, in where you can indicate whether your factor is an ingredient of a mixture:

 

Image 2 shows the Prediction Profiler for Linear Fit Model with "Damping" as the response, and "CuSO4" ; "Na2S2O3" ; "Glyoxal" as factors. "Mixture" was specified in column settings for these three factors:

 

And image 3 is the Prediction Profiler we get for the same model, but "Mixture" was not specified in "CuSO4", "Na2S2O3" and "Glyoxal" column settings:

Prediction Profilers look totally different, which could possibly lead to wrong interpretation of the results...

Any explanation ?

[#2]

There is an explanation.

In order to match your pictures I needed to do more than just remove the Mixture column property. In the Fit Model window I also had to remove the "&Mixture" from the main effects. When I tried to run a model, JMP warned that I was missing an effect (Wavelength).This then gives a clue as to what is happening.

With the mixture properties and the tag on the mixture effects, JMP will fit what is called a Scheffe mixture model. Without these things, JMP is not fitting a Scheffe model, but is fitting a no-intercept model. The two models are different.

Easiest way to see the problem with removing the Mixture column property and Mixture attributes from the model is to start using the profiler. With the Mixture attributes, changing one component of the mixture will automatically change the others so that they always add to 1, which they should in a mixture setting. Once they are removed, changing one of the sliders does NOT change the others leading to impossible situations. such as 60% Glyoxal, 80% NaSO4, and 80% CuSO4.

Bottom line: there should never be a reason to remove those properties from true mixture components.

[#3]

Thank you Dan for this useful explanation.

You are absolutely right about the fact that there should never be a reason to remove the "Mixture" property in the Column settings. But in some cases I have been faced with, I had to build predictive models on (mixture) external data that were not coming from a DOE, and for which the "Mixture" property was not specified in the tables.

By the way, there are in fact two options in the Column settings: "Mixture" and "Design Role / Mixture" (see picture below). I am not sure what is the effect of selecting only one or both of these two options before generating the Fit model.

Lastly, is there a statistical difference between:

- a no-intercept model, without XiXj nor Xi² terms, using non-mixture factors, and a specified linear constraint on the Xi to add to 1

and:

- a Scheffé model, using mixture factors, without XiXj term ? 

Thanks again for your help.

[#4 · Accepted solution]

Now that I understand where the question came from, let me try to answer a bit more directly. For a data table that did NOT come from a DOE and has mixture factors, you will only need to turn on the Mixture column property. If the mixture factors truly add to 1 (with no round-off error), when fitting the model a Scheffe model will be fit.

You can see that the Scheffe model is fit correctly when you look at the Analysis of Variance report. You should see a line that states "Tested against reduced model Y=mean". If it is not fitting a Scheffe model you will likely get singularity details or the ANOVA table will state "Tested against reduced model Y=0".

So the Mixture column property is what allows JMP to use pseudocomponent coding in the analysis and fit a Scheffe model properly and give you the proper prediction profiler.

The Mixture design role is needed for creating a designed experiment with a mixture factor. It really has nothing to do with the analysis, and comes into play if using that column in the design creation.

Now to your question about the two models.

The answer is YES, there is a difference. A no-intercept model says that the overall mean response is equal to 0 so it does not need to be estimated, while the Scheffe model actually has a mean. It is just included in with the parameter estimates. Remember the line in the ANOVA table output that I mentioned earlier? That is the difference.However, in that first scenario with the no-intercept model, JMP will actually see that the factors add up to 1 with the no-intercept box being checked and will then fit the Scheffe model for you (again, look at the ANOVA table report to verify this). I am not even sure how to get JMP to fit that first model in this question.

I hope this helps.