Coding and intercept in mixture DoE models

[#1]

Hello Community,

I have a question concerning the models found for Mixture DoE when the default L PseudoComponent Coding is activated (default conditions).

When this is activated, my main effects have strange forms like in the picture below:

I prefer when they have a cleaner view, just Oil, water and vinegar (not in the form of ratio). Apart from the visual aesthetics preferences, there is something that confuses me even more. When I export ththe equation for this case and I simplify it, it looks like:

The number in the green circle seems to me like an intercept and in mixture doe, the model normally does not have intercept.

My first question would be: If I want a more visually aesthetic model, I know I can just uncheck the L PseudoComponent coding. However, what is the danger of doing so?

My second question is: Why I’m seeing an intercept in my model in this mixture case?

Thank you,

Julian

[#2]

Regarding your model, did you check the "No Intercept" box when you ran the fit model?

 

[#3]

Thank you  @statman  for your answer,

Yes I had that option checked.

[#4]

Pseudocomponent coding is used to lower the correlation between model terms.  The "danger" of turning this off is that you will likely increase that correlation which leads to an inflation in the variance of the parameter estimates. This in turn could lead to incorrectly declaring terms as insignificant. But if you are using your mixture model for prediction only (which is what most people are using mixture models for), then there really is no danger in turning off the pseudocomponent coding.

As for your question #2, mixture models actually have an intercept, but it is incorporated into each of the main effects. It cannot be explicitly estimated. In fact, if you add this intercept to each of the main effect parameters, you will have the true Scheffe model main effect parameters. The intercept is not really estimated, it is just an artifact of the scale changes required for the pseudocomponent coding.

[#5]

Thank you @Dan_Obermiller  for your answer.

I saw indeed that turning off Pseudocomponent coding increases VIF values.

There is something that confuses me from your 1st paragraph: what else you can use your model for than for trying to predict ? I'm asking this because in your answer you say that for prediction, no danger in turning Pseudocomponent coding off. What would be a case in which there is actually a danger in turning this off ?

Concerning the second part of your answer. I can clarify that this apparent "intercept" in the equation appears either I have Pseudocomponent coding on or off. I'm therefore not sure it is just an artefact of changing scale since it also appears when Pseudocomponent coding is off.  Am I missing something ? or did I not undestand very well your point ?

[#6]

Some people like to understand what effects are significant from a designed experiment. So they don't care about the predictive ability of the model, only which terms are statistically significant. I personally do not typically care about effect significance in a mixture experiment. However, some of the cross-terms are actually modeling curvature, so I might be interested in the results of those statistical tests to determine if the curvature is significant or not. If I have turned off the pseudocomponent coding, I might be led to believe that the curvature is not significant, but it really is. The increased variance might "hide" the significance of that curvature term. So if I am interested in the statistical tests associated with the parameters, then the pseudocomponent coding is helpful as it will reduce that variance of the parameter estimate. It does NOT alter the prediction though. That is why pseudocomponent coding is often recommended: it does no harm and can only help.

Now for the second part about the mysterious intercept. You should NOT have an intercept if you have turned off the pseudocomponent coding. I am guessing that you are not really fitting a mixture model. To verify this, in your model output go to the red triangle and go to Regression Reports > Analysis of Variance. Look at the Analysis of Variance table. At the bottom of that table you should have a message of "Tested against reduced model: Y=mean" like this:

This indicates that you are fitting a Scheffe model. If it says "Tested against reduced model: Y=0" then you are NOT fitting the Scheffe model. More than likely there are some row(s) in your table where the mixture components do not add up exactly to 1.

If you are truly fitting the Scheffe mixture model and are still getting an intercept, could you post your table or at least the full model output? There is something else that is going on that is not correct as you should not have an intercept when pseudocomponents are not used.