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I am planning to do simulation for parametric study and there are 9 parameters in total. I was suggested to use DoE to reduce the number of simulations that I need to do. I studied the basic of DoE but I am still confused about the adoption of DoE in simulation. Should I do a preliminary study first by setting 2 values for each parameter first?

Also, would factorial design be influenced by multicollinearity issue of the parameters?

Thirdly, each parameter may of different unit and their ranges would also be different. Would this affect the interpretation of the significance of the parameters?

Finally, what is the difference between DoE and regression (ANOVA)? It seems that ANOVA can tell you the significance of the parameters and you can do VIF for multicollinearity test. Please advise.

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  1. Factorial design (also fractional factorial) is orthogonal so multicollinearity is definitely not a problem. That is the beauty of design: you can choose to avoid such problems. In a fractional design, some effects will be aliased, but you can choose which.

  2. ANOVA is about analyzing the results of the experiment, design is about planning the experiment before implementing it. But in reality, they become mixed up because you need to think about possible analysis to make a good plan.

  3. Different units and different ranges is not a problem. But you need to think hard about the ranges: too short and the experiment will not give conclusions (effects too small), too long and it will not work!

  4. If this is deterministic computer experiments, without randomness, the situation is quite different from classical DoE. But is still useful, often called surrogate modeling. See Best DoE method to fit Gaussian Process Regressor. With 9 parameters you could start with two values for each parameter (add a centerpoint), with a full factorial that is $2^9$, quite a lot of runs ... so a fractional factorial is preferred. A $2^{9-5}$ plus a centerpoint (16+1 runs) should do, as a preliminary investigation.

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    $\begingroup$ Thanks much for answering. DoE is usually described in the textbooks as an important step for optimization model building. Is it appropriate to use DoE for predictive model building, i.e. using it to find out the most influential parameters before building a predictive model by regression or other machine learning technique? $\endgroup$
    – the terrible
    Commented Nov 7, 2018 at 12:35
  • $\begingroup$ Well, you cannot really use it to find "the most influential parameters", for that you need to do the experiment and estimate the parameters. You use it too choose values for the experimentally manipulated variables so that the estimation can be maximally informative. $\endgroup$
    – kjetil b halvorsen ♦
    Commented Nov 7, 2018 at 12:58

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