Question about augmenting a DOE design

[#1]

I have a question about augmenting an interaction design to allow adding a 3rd level to a 2 level categorical factor.  With that in mind, is it reasonable to do the following?

1) Run an interaction design with two continuous factors defined as continuous and one factor that's actually categorical, but is defined as continuous.  All levels would be either -1 or 1.   See attachment 01.

2) After collecting the response data, augment the design with 4 center points (0,0,0) to allow adding a 3rd level (0) to the categorical factor.  See attachment 02.

3) Collect the response data for the 4 center points.

4) Fit model

5) Use the Prediction Profiler to get predictions but take care that the categorical factor is set only to -1, 0 or 1.

[#2 · Accepted solution]

Hi @SteveCz,

There might be an easier workaround to add a new level to a categorical factor when augmenting your design.
On your original design datable, simply add a new row with the new level value for your categorical factor (all the other factors values stay empty/missing).
When augmenting the design, JMP should recognize that there is three levels for your categorical factor, but since all the other factors values are empty for the last row, it won't consider the last row added as part of the design and will recommend new runs with the desired third level of your categorical factor.

See Add new levels to a design for more info.

Hope this workaround may help you,

[#3]

Many thanks for the detailed reply Victor. 

I'll try the interesting workaround you indicated and see if it works for the application.  If not, I'll post some additional questions.

Steve

[#4]

You're asking a theoretical question that requires a much better understanding of the situation.  The answer to your question is it depends.  In some cases it would not be advisable to do what you are asking, in others it might be interesting to try.  Why would you presume the 3rd level of the categorical factor is at the center of that categorical space? You must also always keep in mind, when augmenting, you are confounding block effects (changing inference space) with the new effects.  This can lead to erroneous conclusions.

[#5]

Thanks for the sage advice Mr. Statman.  I definitely understand your point about block effects, but in this case, we're trying to work around some difficult economic constraints and accept there are some compromises as a result.

I asked this question because as far as I can see, there's no way to add a 3rd categorical level (in this case a third type of tooling) to a factor originally declared as a 2-level categorical.  But when I declared it initially as 2-level continuous (even though in reality it's categorical) I could add the center points to get exactly what we wanted.  Design Diagnostics all look reasonable and I was able to fit model to some fake data as well.

But thanks for pointing out the concerns with our approach and we'll keep them in mind as we wrestle with our economic constraints.

Steve

[#6 · Accepted solution]

No worries.  Why don't you pretend you were designing the experiment with the appropriate levels for the categorical, create that design and compare it to the one you ran?  It might be as easy as adding the additional treatments using just the third level categorical.