DOE Regression Equation

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    David A Merritt


    If I have two DoE’s with some factors in common, but not all, can I take a term from the regression equation from one of them and insert it as a term in the regression equation of the other?


    Andrew Parr

    @MBBinWI your turn?


    Robert Butler

    Short answer – No.

    Reason: For any given design you are constructing experiments and running them in a way such that two things occur.
    1. The terms in the model are independent of one another
    2. You randomize the runs to guarantee that the effect of any uncontrolled terms (known or unknown) contributes only to the random error associated with the measurement.

    Thus, if you have a term in one design but not in another you have no way of knowing how that term might have impacted the result had it been included in the design where it was absent and you have no way of knowing how it DID vary from experiment to experiment in the design where it was absent.

    If you have the very unusual case where you took the time to record the levels of the variables which were NOT included in the respective designs (this would have to be on an experiment-by-experiment basis) then you could combine the two designs, fill in the blanks for the ignored variables in each design, run a full diagnostic on the matrix of “independent” variables (VIF’s and condition indices) to see if the combination of the two designs is such that you could construct a model based on all of the experiments.

    I’ve never known anyone who would run an analysis in this manner (that is record on an experiment-by experiment basis the levels of various known uncontrolled variables) but I suppose there’s always the chance that someone somewhere might have done so.

    The other option is to construct the reduced models for each of the designs, test the coefficients of similar model terms to see if they are significantly different and, if they are not, freeze those variables as some chosen level and run what-if analysis using only the variables that are different to generate outcome predictions. You could then contrast the differences in predicted outcomes, run confirming experiments, and use the results to guide your choice of predictive equation.

    The best thing to do would be to look at the reduced models for both of the designs and use those results to build a third design incorporating those variables which remained in the reduced models for both designs and analyze the results of that design to generate a predictive equation.



    David – I’ll give you a more graphical answer. You have a tennis ball. You play tennis with that tennis ball. That tennis ball has certain responses. You take that tennis ball home and use it to play catch with your puppy. The movement of the ball has very different behavior (if you merely track the ball) when the puppy plays with it than when you smack it back and forth on the tennis court. Same ball, different behavior. As @rbutler says, if you tracked every variable, then you could conceivably use one for the other, but as you might guess from my scenario, it would incredibly complex and most likely not worth it. Just my humble opinion.

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