Covariates and Definitive Screening Design

[#1]

Hello,

Can covariates also be used in connection with a Definitive Screening Design, or is that only possible, for example, in a Custom Design?

Regards

Klaus

[#2]

Hi @NominalGemsbok3,

Definitive Screening Designs can only handle numeric continuous factors or 2-levels categorical factors.
Read more about Definitive Screening Designs in JMP Help.

Custom designs can handle many types of factors.

Hope this answer will help you,

[#3]

It seems, however, that there is a workaround in which you can add the covariate as a continuous variable directly in Construct Model Effects.

[#4]

Covariates are a specific type of Factor : "The values of a covariate factor are measurements on experimental units that are known in advance of an experiment."

Unless the covariates levels and factor levels combinations do match with the ones needed for a Definitive Screening Design (in which case, you can only specify them as continuous factors), else you'll have to use the Custom Designs platform.

You can use a Bayesian D-Optimal design with covariates and get similar performances as DSD : https://www.linkedin.com/posts/victorguiller_doe-experimentaldesign-datascience-activity-72543860324...

Hope this clarify the answer,

[#5]

Thank you very much — this is a very interesting approach. But I hope you’ll forgive me for needing some further clarification; the experiment is very important, time-consuming, and also expensive.

a) What do you mean by: “Unless the combinations of covariate levels and factor levels match those required for a Definitive Screening Design (DSD)…”?
In our example, it would look like this: we have the following factors and factor levels in our DSD:

1 0 1 1 1 1 No
1 0 -1 -1 -1 -1 Yes
2 1 0 1 1 -1 No
2 -1 0 -1 -1 1 Yes
1 1 -1 0 1 1 Yes
1 -1 1 0 -1 -1 No
2 1 -1 -1 0 1 No
2 -1 1 1 0 -1 Yes
1 1 1 -1 -1 0 No
1 -1 -1 1 1 0 Yes
2 1 -1 1 -1 -1 No
2 -1 1 -1 1 1 Yes
1 1 1 -1 1 -1 Yes
1 -1 -1 1 -1 1 No
2 1 1 1 -1 1 Yes
2 -1 -1 -1 1 -1 No
1 0 0 0 0 0 Yes
1 0 0 0 0 0 No
2 0 0 0 0 0 Yes
2 0 0 0 0 0 No

The first column represents a block, and the last one a categorical variable.
For each row — that is, for each experimental run — we have a corresponding measured value, say a frequency, which clearly and uniquely belongs to that specific run and which we would like to use as a covariate.
Would that be acceptable?

b) I had the impression that in a Bayesian design, there are more and different correlations present. Are the results obtained from both methods still comparable or equivalent?

[#6]

Hi @NominalGemsbok3,

a) Short answer: you can.

Long answer: It depends what this "covariate" represents, regarding the context of you study:

• If this "covariate" can only be measured or known after the run is prepared with its specific factor levels, it's similar to a response (not a covariate), so the approach seems acceptable. You could add this measure as an "Uncontrolled" factor in your model, but you may have to take care about multicollinearity or correlations between factors and "covariate" for example, in your model.
• If you can evaluate/calculate this covariate value based on the factor levels (a "true" covariate according to the definition in JMP Help), so before the run is prepared, I would consider using this covariate factor directly in the design (so using Custom design), to make sure the covariate values are balanced across all other factor levels combinations/runs.

Hope this answer your first question (difficult without any context, more information and/or a toy dataset to visualize the problem).

b) There is some flexibility in Bayesian design depending on the number of runs you can afford, and the Optimality Criterion chosen. The more constraint on the number of runs (less runs), the more correlations between effects terms.
Concerning the possible correlation between main effects and interaction effects, I tried a D- and Alias-Optimal design for 5 continuous factors, 1 two-levels categorical factor, and 1 blocking effect (2 runs per block) with 30 runs (all interaction effects estimability set to "If Possible") and the correlation map shows no correlation between main effects and interaction effects :

There are still some minor correlations between block effects and main effects or block effects and interaction effects.
Note that in this situation, a design for main effects only would have required a minimum of 14 runs, and for main effects + interactions a minimum of 44 runs. Bayesian D-Optimal design enable to have this flexibility in run size, while conserving the possibility to detect interaction effects.

Hope this answer will clarify your question,

[#7]

Okay, let me put it a bit more precisely. We have five continuous factors and one categorical factor, and 20 experimental runs — that is, 20 different combinations of factor levels (we can’t conduct more runs in this first step). For each of these combinations — meaning for each of the 20 experimental runs — we determine a certain quantity in a preliminary test (the natural frequency of the object). This value cannot be controlled; we simply take it as it is. It is not controllable, but somehow results from the combination of factor levels, and therefore must be assigned to that specific combination. So, for combination 1, the corresponding natural frequency is X1 (and only that one); for combination 2, it’s frequency X2, and so on.Therefore, since these values must be uniquely assigned to a specific combination, I don’t understand what JMP could still balance here. Could you possibly explain that to me again?

[#8 · Accepted solution]

Ok, with this context, you're in the first situation described in point a) of my answer. You won't be able to balance these values in the design because you don't know in advance these values, so this factor is uncontrolled, like ambiant température recorded during experiments, not a covariate.

You can create any design you want and record these values after, and adding this uncontrollable factor effect in the model.

[#9]

Sorry, but where did you get your definition of covariate?  The values don't have to be known before the experiment.  The covariate is a measurable independent noise variable (a factor one is not willing to control) that varies over the course of the experiment.  It covaries with the Y. Since it is a random variable, to analyze it, you must add it to the model.  This requires you create a mixed model (both fixed and random effects in the model).

[#10]

Hi @statman,

I have listed the source of the covariate definition in my response, see JMP Help related to Factor type definitions : https://www.jmp.com/support/help/en/18.2/#page/jmp/factors.shtml

The situation you describe is referred to an Uncontrolled factor in JMP. I just used the same terms to avoid any confusion or misunderstanding, hope you'll understand.

Best,