I am working on an experiment using Response Surface Methodology (Design of Experiment). I use StatEase software for the same. During analysis the software shows that CUBIC model for my data is Aliased. However, the cubic model is significant (p 0.05). Moreover R2 value is also very good 0.985.
Can I use this model for prediction of optimized conditions, although the model is aliased, but statistically significant?
All that means is that the 3-way and higher terms are confounded behind lower order terms. Sometimes these aliased terms can be separated from the other terms it is confounded with. The 3-way interactions are usually not significant. So, not being able to see them, or having them aliased, does not hurt your model. What type of Response Surface are you using?
When it comes to prediction from you model, look at the R^2(Pred). That is a better indicator of the prediction ability of your model.
Dear Dr. Andrew, thanks for your answer. But I did not get what do you mean by what TYPE of response surface. I am using response surface plot derived from a central composite model.
I think that you may check whether your predicted R^2 is agreed well with your adjusted R^2. If they were, then your model can be used. However, RSM can only be used in determine the reaction kinetics and stability or evaluate of the kinetic constants when parameters are suitably transformed into second-order equation. It means that RSM is only effective for the variables that can be described with a second-order polynomial equation.
There are many different types of Response Surfaces, Central Composite Designs, Box-Behnken Designs, Optimal Response Surfaces, etc. Some CCDs will let you see 3-way interactions. Most BBDs will not. Some Optimal Designs will let you see a few 3-way interactions.
Helo,
You can use the regression model for optimization if found a mathematical model that predicts your results.
For experimental tests is recommended in the first time to use a screening design to eliminate the less influence factors.
In Design Expert (Stat Easy Software) try letting the software reduce your model by the option "Backwards", which takes in account all variables and interactions, and eliminates the ones that do not are significant. Use the resultant model taking in account that variables aliased in this final model can not be resolved (for example, interactions between variables ABC can be aliased, confounded with A2B or something according to what the analysis of the software says). You can use the resultant model if the main factors (pure variables) are not aliased. Greetings
Dear Luis, awesome! i did that.. Really your suggestion was very helpful to me. Thanks a lot. :)
It sounds like you got the results you were looking for.
Depending upon the type of CCD you used, the 3-way interactions and the weird A2B type interactions might be directly estimateable. You might run into issues where terms are confounded with each other.
Suppose that you use a half-fraction 6-factor CCD. Each 3-way interaction will be confounded with another 3-way interaction So, if you find that interaction ABC is significant, the confounding is really ABC and DEF. DX will say that DEF is aliased with ABC.
You are absolutely right Dr. Andew! Reduced cubic model will neglect all such weird interacations!
I have a question.
I did the experiment based on response surface method (central composite) in design expert software. At the end of the experiment, I had a quadratic regression model that it can used for predicting the response. also using optimizing section of design expert software, can be used for predicting. but there is a problem that I can't understand it: predicted value of response with equation that manually was done (it is 9) is not equal to predicting optimizing section of software (it is 12).why they are different? Also I check some articles and this issue exist in all of them.thanks for guides.
Xia Qin
To employ the backward method of reduction, I recommend checking out this engaging YouTube video. The relevant content begins at the 37th minute. Click here to watch: https://youtu.be/tsUPtEePoIk?si=cYpbd2pnhmYwtMJF.
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