Interpreting a Mixture of Mixtures Study

[#1]

Can I get some help interpreting the results of my mixture of mixtures study? I'm studying the friction of asphalt, specifically the effects of aggregate type, aggregate blend ratios at coarse and fine fractions, and asphalt gradation type.

Aggregate Types, 6 total:
- Class A (high quality): A1, A2, A3
- Class B (low quality): B1, B2, B3

Aggregate Blending (Coarse and Fine portions)
- Blend percent of Coarse Class A and B aggregate in total mix: 0 to 50%
- Blend percent of Fine Class A to B aggregate in total mix: 0 to 50%
- Total of Coarse and Fine = 100%

Gradation Type, 2 types
- Type C
- Type D

Attached is my study .jmp file. I feel comfortable with multivariate regression analysis, but this mixture stuff is tripping me up. Any direction to get started is welcome. Thanks! 

[#2]

There is just not enough information provided about the experimental situation to give sound advice (e.g., Do you know measurement system error?  How much of a change in friction matters?  What is an experimental unit?  How was it measured?...). I'm not sure I understand why you are calling this a mixture design?  Two factors (it doesn't appear Aggregate and gradation type are mixture factors) and since you did ratios rather than the independent amounts of fine and coarse.  You actually have an alternate to a mixture design (not good or bad).  Analyze as typical fractional factorial design starting with the model you used to design the experiment and use fit model.

OK, I had a look at the data table, I'm still confused.  It seems you  have the aggregate types included in your 4 component mixture design?  It appears you have confounded those Aggregate types with the mixture components?

[#3]

Thanks for your comments. My study has both factorial and mixture components.

There are three categorical factors:

• Agg Type-Class A (Levels: A1, A2, A3)
• Agg Type-Class B (Levels: B1, B2, B3)
• Gradation Type (Levels: Type C, Type D)

Then there are two mixtures, where each is a two-component mixture.

• AggBlend, Coarse (A_Coarse + B_Course = 0.5)
• AggBlend, Fine (A_Fine + B_Fine = 0.5)

Can you clarify what you mean by "you did ratios rather than the independent amounts of coarse and fine?" I think I did not do ratios. 

• Coarse (A=0.2, B=0.3) + Fine (A=0, B=0.5) = 1.0

Because it's just two components, are you saying I could have changed the 4 mixture variables to 2 continuous ratio variables? (Ratio of A/B_Coarse, and Ratio of A/B_Fine). When I've done this in the past, I ran into problems with the analysis of AggType * AggRatio interactions. (I can expound on those problems if needed).

Here's what the DOE dialogue looked like.

I don't know how I got here with the model, but I think there are problems. (1) I am missing the AggType main effects. (2) Some interaction terms don't make logical sense.

• The first interaction, AggType, Class A * AggBlend, Coarse_Class A, would show how the Class A Agg type varies by it's amount in the mixture. And for test runs where Class A is not in the mixture (Blend Class A=0), it's effect wouldn't be considered. But the next interaction, AggType, Class A * AggBlend, Coarse_Class B, seems to be looking at the exact same thing, but the inverse. The mixture constraints mean that B Blend = 0.5 - A Blend. 
• The interaction, AggBlend, Coarse_Class A * AggBlend, Coarse_Class B, doesn't seem helpful at all. This is just the interaction of A Blend and 0.5-A Blend.

If I build the model intuitively, I end up with the following. Does this seem valid?

[#4]

This might be helpful a Case Study in the JMP Library by Marie Guadard

https://community.jmp.com/t5/JMP-Sample-Data/Design-of-Experiments-Example-A-Mixture-of-Mixtures-Des...

[#5]

Thanks. A good read. The example is strictly mixtures, whereas my situation is both categorical and mixture variables. This is where I'm tripping up.