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Aug 29, 2016 7:18 AM
(958 views)

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Solution

If I understand your response, the discrete numeric is actually a mixture, but the issue is that you cannot specify it as mixture?

If so, there are two ways to go about it. Let's say we have a 5-level discrete numeric mixture (X1), and 2 other mixture factors (X2 & X3). The cleanest way is to create the design for just X1 (as discrete numeric) & X2 (continuous for the purposes of creating the design), since X3 will just be 1 - X1 - X2. We need to use disallowed combination to make sure X1 + X2 doesn't go below 0 or above 1. If you run the first piece of jsl in the attached as an example, it should give you an idea.

The other option is to have all 3 factors, X1 as discrete numeric, and X2 & X3 as continuous, but use the disallowed combinations to have their sum "close to 1". The numbers won't look as nice, since the custom designer has to work much harder to optimize it, and you would have to "X2" or "X3" after to make sure the sum is 1 (since the sum will be not quite 1). This is the second example of code, but please note that in this case, you'll want to manually remove the intercept from the model terms.

In either case, you'll need to change the type to mixture afterwards. Sometimes for myself, I just create a separate design with mixture factors, and copy the new design into it, so it has the right column properties.

Hope this helps,

Ryan

6 REPLIES

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Aug 29, 2016 8:44 AM
(780 views)

Hello,

Here is one option for you. You can use the Custom Design platform under DOE to designate the factor types you want for your Mixture Design. Below is an example of a 3 level discrete factor and two mixture factors. You can have upwards of 8 different levels for your discrete factor.

If on the the other hand you want keep one factor as a constant amount in the mixture and vary the others from low to high you can use a mixture sum to limit the mixture components to specified percentage and use the constant amount to make up the difference.

Hope this helps.

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Aug 29, 2016 11:10 PM
(780 views)

Hello billw,

thank you very much for your instant help. However, I did try this solution before but when doing it like this, I can't add constraints of mixture for all three factors. Since one factore is not flagged as "mixture" but as "discrete numeric" it will not be considered in the mixing rules by jmp. Do you have an idea, what my mistake might be?

Thank you again in advance!

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Aug 30, 2016 7:06 AM
(780 views)

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If I understand your response, the discrete numeric is actually a mixture, but the issue is that you cannot specify it as mixture?

If so, there are two ways to go about it. Let's say we have a 5-level discrete numeric mixture (X1), and 2 other mixture factors (X2 & X3). The cleanest way is to create the design for just X1 (as discrete numeric) & X2 (continuous for the purposes of creating the design), since X3 will just be 1 - X1 - X2. We need to use disallowed combination to make sure X1 + X2 doesn't go below 0 or above 1. If you run the first piece of jsl in the attached as an example, it should give you an idea.

The other option is to have all 3 factors, X1 as discrete numeric, and X2 & X3 as continuous, but use the disallowed combinations to have their sum "close to 1". The numbers won't look as nice, since the custom designer has to work much harder to optimize it, and you would have to "X2" or "X3" after to make sure the sum is 1 (since the sum will be not quite 1). This is the second example of code, but please note that in this case, you'll want to manually remove the intercept from the model terms.

In either case, you'll need to change the type to mixture afterwards. Sometimes for myself, I just create a separate design with mixture factors, and copy the new design into it, so it has the right column properties.

Hope this helps,

Ryan

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Aug 31, 2016 6:12 AM
(780 views)

Thank you Ryan.lekivetz for your feedback.

From my current point of view, your first recommendation seems to fit my demands the most. I guess I will need more time to think about that, but as I said, this looks promising to me. Thanks again!

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Aug 31, 2016 8:35 AM
(780 views)

Ryan's approach is a great way to approach this problem as the optimal designs give you the most flexibility, but you may have some difficulties specifying the model in terms of the continuous variables. That can lead to problems getting interior points of your design space (if desired).

Another possible option, if you have an unconstrained mixture design OR the constrained space is a smaller simplex, is to go with a "classic" mixture design: the simplex lattice. When choosing that design in JMP, just remember to state that the number of levels is 4 rather than 5. That will put EVERY component at 5 levels and gives you a grid over the entire design space.

Dan Obermiller