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Solution in RS (D-optimal)

FactorAlligator

Hello everybody,

I've successfully run my first RS design but I struggle to understand the solution provided after fitting the model. My design includes 5 continous factors with 4 axial points and 2 center points. I did 1 replicate and fitted the model. There is no significant lack of fit.

The goal is to minimized the response and but the solution is higher than all of my measured values. I included a range check for my factors but for the solution 3 of the 5 factors are negative, which is impossible in reality. How do I get a solution that only considers positive factors?

Thanks!

Best regards,

FactorAlligator

Accepted answers

All comments

Dan_Obermiller

I'm not quite sure what you are seeing or asking. It is impossible for a model to always predict values that are higher than all of your data. What do you mean by a positive factor? Are your factors coded between -1 and +1 or did you leave them in their natural units? Would it be possible for you to share your JMP data table? You could anonymize the data, if necessary.

statman

I agree with Dan. You haven't provided enough information for an answer to your query. In your analysis, did you look at the surface?

Models can easily be extrapolated beyond reasonable conditions (they are simply a model of the data). It is you that must interpret the model.

FactorAlligator

Thank you for your response. The data table is attached. In the mean time I reanalyzed two outliers and this solved the issue with values being negative. By that I meant that my factor is coded between -1 and +1 and in reality it can go down to -2.5 (at this point the concentration of the factor is 0) but my solution was at -3 which cannot be. I would still be interested on how to handle this case if it happens again.

As you can see from my model the best values within the design space yield a min Y response of 162. The lowest response I got in the pattern 00A00 at 213. But the calculated solution is at Y=296. If my goal is to minimize the response I would expect a limit solution of the design space (like when I maximize the desirability).

@statman Also thank you for your response. I checked the surface also in the model view but I cannot gain anything from that unfortunately since some surfaces show a maximum and some a minimum.

statman

I ran the model you had saved to the data table. Not sure if this is the model you are evaluating, so if not some of my comments be inappropriate.

The model needs work. The residuals are suggesting non-constant variance and you have insignificant terms in the model. The statistical significance seems to be based on the center point replicates and higher order quadratic interactions (your error is not based on randomized replicates). Not sure what you mean by your comment about response surfaces? You should get something like the following (though this is using your model):

Screen Shot 2022-05-02 at 7.51.50 AM.jpg

FactorAlligator

Thank you for your input. I am trying to understand your suggestions and hope you could give me further feedback on my thoughts.

The residuals are suggesting non-constant variance and you have insignificant terms in the model.

Do you state that because of the "Residual by Prediceted Plot" that shows a decrease in Y Residual the higher Y Predicted is? Do I understand correctly that I should reduce the model by removing all insignificant terms? If yes, how would I treat main effects that are insignificant like factor X1 while the 2 way interaction X1*X5 is significant?

The statistical significance seems to be based on the center point replicates and higher order quadratic interactions (your error is not based on randomized replicates).

Is this seen in the "Analysis of Variance" where majority of my variance comes from the model and only a small amount from random error? I thought having little unexplained error is desirable.