Difference between Block and Categorical factors in Custom Design

[#1]

Dear JMP community, 

I have a question regarding the custom design function in JMP. I want to generate a D-optimal design with 12 continuous factors and 2 blocking factors and I have 64 runs at my disposal. I want this design to be able to estimate the 2nd order interaction effects of the 12 continuous factors as well. 

I add a blocking factor in the “Custom Design” menu and I select all 2nd order interaction effects to be estimated if possible. However, JMP does not estimate these blocking effects.

Would you know why this is the case?

A follow-up question: when I select categorical factors instead of blocking factors, I get a different D-, A-, and I-efficiencies. Surely, blocking factors and categorical factors are the same in terms of Ordinary Least Squares estimation. How does JMP handle categorical factors differently from blocking factors? (I can’t seem to find an answer in your manuals)

[#2 · Accepted solution]

We treat categorical and blocking factors differently from a philosophical point of view.

A categorical factor presents two or more levels to be investigated. I can set any level I want. A blocking factor represents a limitation on the experimental units and a restriction on the randomization of the runs.

We do not involve blocking factors in interaction effects because we believe that the fixed or random effect of changing blocks is solely on the mean (intercept) or on the random error (variance), respectively. We do not believe that the effect of the factors changes between blocks. Science and engineering work the same in all blocks but the mean response might shift between blocks in a fixed or random way.

If you believe that there is an interaction, then there is a real factor that changes level when you change blocks. It should be identified and then treated as a factor, not as a block.

[#3]

Mark,

I agree with your answer whole heartedly when designing an experiment. However, I have seen numerous examples where the treatment effects for one or several blocks are outside of random variation, that is, a block-treatment interaction is found in the analysis.  In semiconductor manufacturing, production lots are common blocking factors.  Consider a one factor, multi level experiment, run on 20 lots.  For all but 2 lots, there is a large improvement (> 4 times the random variation) with one level ( the clear winner), but the two deviant lots show no effect.

Further investigation often provides other factors that might influence (interfere with) the "winning" condition. So, block-treatment interactions should always be investigated.   Variability plots are terrific for finding potential problems, especially plotting the adjusted treatment means (result - block average|control average).  Typically, gross deviations, interactions, can be seen visually on block adjusted variability plots. 

So bottom line, it is my opinion that at least a visual analysis of block treatment interactions should be done, if there are more than 3-4 blocks. 

[#4]

I think that we are on the verge of a violent agreement.

[#5]

If you have 12 continuous factors, there are 66 two-factor interactions (2FIs). So, it is impossible to estimate all these interactions with a 64 run design. If you make the 2FIs "If Possible" JMP will create a design that attempts to estimate as many of these effects as possible given the number of runs you specify.

On blocking versus categorical factors...

If you made two designs, one using blocking factors, and the other using categorical factors with the same number of levels as the blocking factors, you will not necessarily get the same design. There are often many designs that have exactly or very nearly the same values of the criterion being optimized. These designs could have differing values for other criteria.

[#6]

@MaartenvM:

I'll just throw in another wild idea...you don't mention how many levels/blocks you are thinking for the two blocking factors...but is there some way you could use your 'blocking' factors as true 2 level categorical factors all rolled up in a definitive screening design? A casual definitive screening design I created with 12 continuous and 2 categorical factors (at 2 levels each) has 34 runs. Well below your full budget.

As @bradleyjones points out there are many, many possible two factor effects...and if effect sparsity holds for your system...most will in all likelihood not be active. Then you can leverage the two stage DSD modeling method to identify active main and 2 factor interaction effects. Then you've still got some resources left over for more experimentation/verification/one off trials etc.

@bradleyjones and @Mark_Bailey please comment if my idea is misguided?