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Why I cannot get the result of main effect when I choose 2nd interaction with mixture factors?

DaeYun_Kim

Dear All,

Here's our homepage's split plot experiment example.

https://www.jmp.com/support/help/14/split-plot-experiment.shtml

And when I performed custom design of experiments with this automotive thickness example and set the 2nd interaction, then this pop-up window appeared.

캡처.JPG

And the page which I mentioned above said that "Click OK to dismiss the informative message".

I cannot understand why main effect terms removed for non-mixture factors. Could anyone tell me why?

Thanks in advance.

Accepted answers

Mark_Bailey

This result is about a constraint and the parameterization of the linear model.

The mixture factors (A, B, C) are constrained to sum to one. (A+B+C=1) That constraint is the reason that the intercept (I) is removed. Without a constraint, a pure blend of A alone would be modeled as Y=bA+I. With the constraint, the model is Y=b'A.The Y is the same and the Y prediction is the same but the parameter b and b' are different. So is there interpretation. The average response is implicitly modelled already by the 'main effect' terms. Adding an explicit term for the intercept would cause a singularity during the estimation of the model parameters.

Similarly, the cross terms that you added implicitly represent the main effect of the non-mixture factor (D), so the explicitly term for it must be removed.

All comments

Mark_Bailey

This result is about a constraint and the parameterization of the linear model.

Similarly, the cross terms that you added implicitly represent the main effect of the non-mixture factor (D), so the explicitly term for it must be removed.

DaeYun_Kim

Thanks Mark.

I can understand because of the constraint there sholud be removed main effect terms.
But what canI do if I want to get the estimates of main effect terms?

In this case(Split plot design via custom design) when I have adjusted 2nd interaction, then runs are 21.

After that, I click the main effect of two extrusion rate and temperature by force, then the rus are 20 less than above experiment.

My queston is...

1. When I want to see the main factors' effect with mixture factors, can I adjust the main effects by force after appplying 2nd interaction? Of course when I apply 2nd interaction, the main effect terms are removed already.

2. If #1 is right(adjust main effects after applying 2nd interactions) why the runs are less than 21?

Best

Mark_Bailey

You are missing the point. The linear model is one way to model the response. It is a linear combination of features or variables. The mixture constraint changes the terms that are explicitly entered into the linear combination. The intercept is no longer linearly independent and cannot be explicitly entered into the model for estimation.

LIkewise, the 'main effect' of the process factor is a concept from the linear model but the polynomial cannot explicitly contain the first-order term for this factor when other terms include the crossing to represent the interaction.. So there are no explicit estimates for this non-existent term.

I suggest using the Prediction Profiler to understand the 'main effect' of the process factor.

Dan_Obermiller

You cannot separate the main effects from the mixture design. Think of how the experiment was conducted. You cannot just change the non-mixture factors. You must also specify the mixture factors as well. Put another way, suppose you had 3 mixture factors with no constraints. Do you want the main effect for the (1,0,0) combination or the (0,1,0) combination? They will likely be different. Easiest way to assess a "main effect" is to look at the prediction profiler. But remember, as whenever there is an interaction, the profiler will change when other factors change.

louv

Hi DaeYun,

I have created a Journal for Mixture DOE's that is stored in the Community

https://community.jmp.com/t5/Technical-Reference-Library/J05-JMP-for-Mixture-DOE/ta-p/21546

This Journal has examples and references from various sources including John Cornell, Wendell F Smith, Ron Snee among others.

I think you may find this useful.

Lou

DaeYun_Kim

Thanks Mark, Dan and Lou

It was one of questions from my customer and I had not answered clearly at that time.

It would be very helpful to me and my customers in Korea.

Thanks again to all of you.

Best