How to force I-Optimal algorithm in Custom Design to choose integers only?

[#1]

Hello,

I am working on a custom I-optimal design with two factors (time and temperature). I would like to force the algorithm to choose an I-optimal design where all temperatures are based on integers (e.g., 0, 50, 75, 100) since I can only set my equipment to whole temperature values. 

I haven't been able to find an option that would force the algorithm to do this. When I simply round the temperature values of the design that has been found to integer values and then look at the average variance of the prediction, it becomes much worse. For this reason, I'd like the optimization algorithm to choose the integers in the first place, in hopes that a better average prediction variance would be reached overall. Please let me know how this is possible, as it really seems like it should be, but I can't figure out how. Thank you!

Alan

[#2]

Define your factors to be Discrete Numeric type.

[#3]

Hi Mark,

If I do that, then I have to tell the software that there are ~130 discrete levels to cover the range, and then I have to manually change each of them, but I can't actually see what each one is since all 130 are crammed into a small space of the GUI. Additionally, if I am using equipment that allows for 0.5 degree increments, that doubles the levels, making things even more difficult and inefficient to enter. One other substantial problem is that I have an irregular experimental region with several linear constraints, and when using discrete numeric factors for temperature, JMP no longer lets me include the temperature factor in my linear constraints. Isn't there another way to do this by keeping temperature set to continuous and just adding an argument somehow that selections must be integers?

[#4]

One possible approach: Make a data table that contains your possible temperature values. It seems like using a sequence would work well. Then in custom design include the temperature as a Covariate. JMP will ask for the data table column to use, so point to the one you made.

That being said, I would be concerned with the design if rounding the temperatures to an integer value drastically changes your prediction variance. With the extra information of the constraints you have in place, that tells me that you have a very unstable design space. You will REALLY need to be careful in validating your model once you have completed your design and analysis.

[#5]

Hi Dan,

Thank you for your input. I'll keep your concerns in mind.

As for solving my immediate problem, as you suggest, I have added the temperature as a covariate based on a table of values, but JMP is now no longer allowing me to create linear constraints that include temperature, but only the continuous factor (time). I need to be able to set constraints based on temp x time combinations. Is there something obvious that I am missing?

[#6]

You misunderstood me. I apologize. I did not mean that your factor must be defined such that it includes all the discrete temperatures that are possible. It should only the ones that you want to test. Maybe four discrete levels?

Alternatively, why not specify temperature as a continuous factor, define the range of temperature with low and high, and then define the model with the potential terms? JMP will find the optimal design but if one of the temperature levels is not achievable, change it to the closest setting that you actually use before the analysis. This way works best if you have some linear constraints, too.

Really sorry about the confusion.

[#7]

Hi Mark,

No worries. I played around with doing things this way at first, and it does avoid most of the problems. However, my concern was that in constraining the possible temperatures that the I-Optimal algorithm would be severly hampered in finding the lowest average prediction variance. Do you suspect that this will not be the case as long as it has the full range of values for the continuous factor (i.e. time)? I'll try to run a couple of tests for comparison to check it out.

[#8]

I would not worry about the optimization. Yes, by definition, adding linear constraints will constrain the optimizer, right? But it is built for such a case.

Not sure what you mean, though, by "severely hamper" but then I do not know what the set of constraints might be.

So, I think that the most straight-forward approach to designing your experiment is to enter both factors as continuous type and define them to have the full range of levels. Define your constraints. Define your model. This way is actually the normal approach. I think that using covariate or discrete numeric factors is 'over thinking' the problem or 'gaming' the optimizer in non-productive ways. It isn't wrong or illegal. It just doesn't work as well.

Let's use custom design as it was intended.

[#9]

Hi Mark,

I added temp as an 8-level categorical factor, but again, JMP will now not let me include linear constraints of time x temp combinations. Advice is welcome.

[#10 · Accepted solution]

My advice is to scrap that approach and jettison the previous ventures. Start over. My previous post suggests that we take a straight-forward approach using custom design as it was intended. Use continuous factors and linear constraints. Specify your linear model. You can always round or change the levels from custom design to suit the practical limitations of your equipment later.