DoE custom designs - include factors that are mutually exclusive

[#1]

Hi JMP community.

I just started my DoE journey on JMP recently. Sorry if I am missing anything obvious here. 

I am trying to work out a DOE design of a biological process that have 4-5 factors. Factor A, B and C are mutually exclusive e.g. if factor A is present then B and C are not, vice versa.

I have found a previous discussion here in the community Defining Factor Constraints in Custom Design DOE  that described the use of additional categorical factor to describe the use of A or B in combination with a factor "AorB" that "shared" by A and B to set up the constrains. I can see how this can be applicable to my case if all the value range of A, B and C are the same. In my case, each individual factor A, B, C will likely have a different value range, what should I do additionally to make this also recognized in the model?  

Thanks so much in advance for any help and guidance!

[#2 · Accepted solution]

Hi,

I think you can do this with disallowed combinations. The simplest way is using the Disallowed Combinations Filter.

I set up a design with a categorical factor for ingredient (A, B, C) and a continuous factor for Amount (0 to 2).

Then I set up 2 disallowed combinations, as below. (I select OR after creating the first one)

For B, amounts between 1 and 2 are disallowed.

For C, amounts between 0 and 0.5 are disallowed.

You should find that the resulting design (attached)  obeys these constraints.

You can also use Disallowed Combinations Script to do the same things.

phil_kay_0-1621333388940.png

These are the same disallowed combinations defined in a script:

X1 == "B" & (X2 >= 1 & X2 <= 2) | X1 == "C" & (X2 >= 0 & X2 <= 0.5)

[#3]

Hi @Phil_Kay  thank you a lot for the solution! I have implemented the constraints you mentioned and worked very well for my scenario. I would also like to ask a follow-up question on how to define the value of zero. From example, continuous factor for amount (X2) can be zero in my case as well as the example you gave, which is still meaningful with other factors constantly present. How should I define categorical factor for ingredient (X1) in such case? It seems to me it is technically cannot be categorized into neither A or B or C. Does this even matter to the model? if it does, how could we define this? I was thinking an additional level can be added to the ingredient categorical factor (e.g. "blank") to define X2 == 0. Does this make sense? I was trying to define it in script but seemed it won't reflect to the design. Any hints would be appreciated!

[#4]

Good point. For our example, if X2=0, then it should not matter what X1 is.

The model that I specified for the design had the terms X1, X2, X1*X2, and X2*X2.

X1 is a term for modelling the difference in intercept between the category levels of X1. That is, to capture variation in the response due to changing the ingredient type when X2 is 0. We know that there should be no difference in the response due to X1 when X2 = 0. Therefore we should remove this effect from the model.

X2 will model the simple linear effect of changing the amount. X2*X2 captures the curvilinear effect of changing the amount (you may or may not expect this to be important). And X1*X2 will model the interaction between X1 and X2, that is, the different effect of changing amount for each ingredient type.

An appropriate model would therefore include X2, X2*X2, and X1*X2. (You could also consider including X1*X2*X2)

JMP will show a warning when you try to fit this model because it is unusual to fit an interaction effect that includes a factor for which you are not fitting the main effect.

There are 2 other things that you will need to do. By default JMP will recode continuous factors such that the intercept is in the centre of the factor range. And Fit Model will also centre quadratic and interaction effects to the centre of the range. You can turn these settings off.

This is what you need to do then:
1. Remove the main effect, X1, from the model when creating the design and do not include it when fitting the model.
2. Remove the Coding column property from the X2 column in the design data table.
3. Uncheck Center Polynomials from the main red triangle menu in the Fit Model dialog.

You should then have a design and a model that makes sense for the situation that you have.

[#5]

I have included a new version of the design table that was designed without the X1 main effect. The Coding for X2 has been removed. There is simulated Y data. And a model that has been fit without X1 and without centering the polynomial.

This is the column property to remove:

Coding column property.png

This is showing that the intercept of the model (where X2=0) is the same for all levels of X1, as it should be:

Regression plot no X1 main effect.png