How do I indicate that a mixture factor can take a number of categorical levels (types of component)

[#1]

Hello,

I am trying to design and then analyse a mixture design with non-mixture factors and am having some trouble understanding how to do it properly. Briefly I am running an experiment on a blend of components under different temperature conditions. The samples are a blend of component 1 with component 2, where component 2 is one of three related materials. What I am having trouble with is encoding the fact that when component 2 = 0 the material of component 2 obviously has no effect on the result as it is completely absent. Using the below factors for the design and restricting factors such that when component 2 = 0, component 2 is not allowed to be A or B for example produces a reasonable design matrix. However when trying to analyse I run into the problem that the model assumes that the type of component 2 (A, B, or C) has an effect on the response even when Component 2 = 0 (i.e is absent).

Component 1: 0-1 (continuous, mixture)

Component 2: 0-1 (continuous, mixture)

Component 2 Type: A, B, C (categorical)

Temperature: 40-150 (continuous)

Can anybody help me with a better way to either generate the design matrix or perform the analysis.

Thanks,

David Gillespie

[#2 · Accepted solution]

Hi,

This same question came up in a thread earlier this week. Basically you need to define the model without the main effect for the categorial factor but with the interaction between the amount factor and the categorical factor. You will likely also need to change the factor coding and settings in Fit Model. Hopefully that helps. You will have to let me know if it works for your mixture problem as the example in the previous thread was not a mixture design.

Regards,

Phil

[#3]

Hi Phil, Thanks very much for the help. As the mixture was only a two component mixture I initially simply modelled it as a single continuous factor and used the solution you referred to, which seemed to produce a sensible model. It did work also work when modelled as a mixture and the predictions are almost identical, which gives me confidence that a similar approach may work for a more complex 3+ component mixture.

It did take me a while to work out how to put all of the factors into the model when modelling as a mixture. One interesting this is that whilst component 1 (mixture) and component 2 (mixture) both appeared in the model independently and component 2 also appeared in a number of higher order and interaction terms, when component 1 was included in higher order or interaction terms the model encountered a singularity and appeared to become unstable. Is this because as only a two component mixture the level of one component is simply 1 minus the other? Hence the following two terms would be inversely correlated as component 1 = (1 - component 2)?

component 1*Temperature

component 2*Temperature

I suppose I could potentially have component 1 throughout instead but in this instance I am using the interaction between component 2 and the categorical factor and so am locked to using component 2 throughout?

Thanks

Dave

[#4]

Just to add that you can also do this with proper Mixture factors.

In the attached example I created a Custom Design with 3 Mixture factors and 3 Categorical “type” factors.

In Custom Design I specified a model that includes:

• Mixture main effects
• 2-way interaction effects between all Mixture factors
• 2-way interactions between each Mixture factor and the corresponding Type factor

This seems to work when I model the simulated Y data. When one of the Mixture factors is 0, the corresponding Type factor has no difference between L1 and L2. E.g. when Monomer is set to 0, Monomer Type shows no difference between L1 and L2:

[#5]

And my colleague, @flo_kussener , added...

Note that if you have a mixture component which has its lower value >0 (in this example X1>0.3 and X2>0.1) JMP automatically checks the L pseudo Component Coding option and in this situation, it considers that the low value has the same behavior than a 0 and removes the effect of the Type. For example, you can see that the X1 is at 0.3 and the X1 type has no effect.

If you uncheck the box