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Blocking by a categorical level

carlosariasq

Dear community,

I am trying to produce a custom design in which I compare different materials performance in an already stablished process.

I included the new 4 materials as categorical factors and I have three continuos factors I would like to measure: time of the process, the time of a pre-treatment stage and the addition of a reagent. My factors are not hard to change and I am looking to fit a Response Surface Model

I expect that each level of my categorical factor behaves more or less the same under the different continuous factor combinations (they are different minerals). So, here is my question: does it make sense to block per categorical factor to compare them later? Or is not really necessary?. I am just afraid that if I do not block, my conclusions after might be biased.

If the blocking is reasonable, how can I do this in my student version JMP Student Edition 19?

Thank you very much to all who read

Kind regards,

Accepted answers

All comments

statman

Sorry, but I do not think there is quite enough information here to give very specific advice, and I may not completely understand your objective. So let me comment more generally.

My first question would be: Are you trying to understand the underlying causal mechanisms, or are you primarily trying to pick a winning material and set of operating conditions? Those can lead to rather different experimental strategies.

As I understand your description, you have one categorical factor, Material, with four levels, plus three continuous factors: process time, pretreatment time, and reagent addition. I am not quite sure what you mean by reagent addition. Is this the amount or concentration of reagent, making it a continuous factor, or simply reagent added/not added, which would make it categorical?

I would also question whether I would start with a response surface design. IMHO, RSM is most useful after you have developed a reasonable understanding of the underlying mechanisms, have identified the important variables, and have some understanding of the relevant noise. In other words, I generally want to have some confidence in a first-order model and know approximately where the interesting design space is before spending runs estimating curvature. Otherwise, you may build a very elegant mathematical model of a region you do not yet understand particularly well.

Now to your blocking question.

I would not block by material if material is one of the factors you want to compare. Blocking is principally a strategy for dealing with noise—variables that affect the response but that you are not willing or able to control as experimental factors. If you make each material a block, you confound the material effect with the block effect. You have then deliberately removed your ability to estimate cleanly the very effect you said you wanted to compare.

Instead, I would treat Material as a design factor.

If your hypothesis is that all four materials respond similarly to changes in the three continuous variables, that is actually an experimentally testable hypothesis. In addition to the main effect of Material, I would be interested in the Material × continuous-factor interactions. For example, does increasing pretreatment time have approximately the same effect for all four minerals? Does reagent amount affect all materials similarly? If those interactions are negligible, then your assumption of common behavior across materials has some experimental support. If they are important, simply comparing overall material averages could be quite misleading.

That distinction is important. Saying beforehand that you expect the materials to behave similarly is a prediction; the experiment gives you an opportunity to challenge that prediction.

This does not mean that you should not block. Blocking can be an excellent strategy, but I would block on a legitimate source of noise—for example, day, batch of raw material, operator, equipment setup, reagent lot, or some other condition under which groups of experimental runs must be performed. I often like blocks because they can also deliberately expand the inference space of the experiment and provide information about the robustness of the conclusions.

For example, if the experiment requires several days, I might deliberately distribute all four materials and the continuous-factor combinations across days rather than running Material 1 on Monday, Material 2 on Tuesday, etc. The latter would completely confound material with day. Randomizing the materials and treatment combinations within appropriate blocks would protect you from exactly the kind of bias you are concerned about.

So before worrying about how to create the block in JMP, I would first ask: What source of noise are you trying to block against? If the answer is simply "the four materials," then I would not call those blocks. They are experimental treatments and belong in the model as such.

frankderuyck

I agree with above, blocking is not necessary. Your Material effect is a 4-level fixed and easy to change categorical factor.

carlosariasq

Thank you very much for this clear reply.

At this moment is clear for me that there is not need for blocking. Here some additional information that might help for new feedback:

What I mean by a very well stablished process, is one that works in a specific type of mineral. I ran experiments at the temperature/time/reagent amount conditions of the stablished process for the new minerals (4 level categorical factor), but none of them was reactive at these standard conditions.

My factor pre-treatment time, is one which I would like to know if there is statistical ground to say whether it improves the reactivity of the minerals or not in the process. However, I need to vary also the time of the reaction and the amount of reagent, because being this a new type of material (after the pre-treatment), it might be that it requires new conditions of time and amount of reagent to see some improvement.

I went for the RSM because we perform some random tests for pre-treatment and we did see some improvement on reactivity, hence, I do not have a quantitative screening, but a previous relevant information. At the moment and after your feedback, I would go for a screening DOE rather than a RSM. For what I have read, Definitive Screening are better, but they only allow two level categorical factors and they require a block to estimate possible quadratic effects.

This being said, here are my current options:

1. A RSM Custom DOE with 24 runs and a 0.738 average variance of prediction

2. Two definitive screening designs (to account for the 4 materials), each with 14 runs and 0.327 average variance of prediction

3. A custom DOE with only intercept, main effects and interaction parameters, which requires a minimum of 19 runs with an average variance of prediction of 0.622 and no center runs

It seems to me that the Custom DOE still holds as the best option, but I would like (if possible) to receive your feedback and opinion on whether going for an RSM with my previous described information is reasonable.

Again, thanks immensely for your reply and help. An amateur like me in this field appreciates it a lot

frankderuyck

Hello, how about the reagent: is this a binary categorical input yes/no or do you want to check a continuous effect like e.g. reagent concentration? As you want to investigate the impact of time I'd propose to investigate your response as a time fuction Y = f(time). So at each DOE setting of your inputs x you measure Y at specified time intervals t; what kind of function f(t) do you expect: linear, exponential..? When you have JMP Pro, using the Functional Data Explorer & functional DOE it is possible to analyse effects of input x on functional response Y(t). When you don't have Pro version there are other methods like PLS, curve fiting,..

Custom DOE is the best option to set up the experiment here. When factor reagent is clear, I propose to set up an I-optimal DOE with 3 input factors: Temperature, Material, Reagent and, for each run, responses Y(t0), Y(t1), Y(t2)...Y(tn) at given time intervals ti.

carlosariasq

Hello Frank,

Thanks for your feedback. The reagent is a continuous factor measured in concentration.
The suggestion is very clever indeed. I would like to ask in that case, would the time then be modelled separately for both time of pre-treatment and time of the process itself? Or would this become a total time? Because is not clear to me how to separate the effect of the time of pre-treatment from the effect that the material would be submitted to the stablished process.

Thanks and have a nice day