I have three responses for a 2-level 3-factor BBD, a quadratic model was selected for all. How do I explain the significant lack of fit for one response? Is there anything that can be done to make the model fit?
Your number of data points is too small for any kind of statistical inference, please increase it first!
Oyetola -
Are you saying that you have selected a model, but two out of three new data points are outside of reasonable prediction intervals? That isn't a lot of data. That could just be bad luck. If you continue to see this for new data, then you may have overfit your model to the sample data. Perhaps you could collect additional data and select a new model, trying not to make it more complex than necessary.
If you are saying that is all the data you have in a sample and you want to use a complex model, then I don't think that that is really possible.
By the way, I do not know what you mean by BDD. Perhaps B is for bayesian?
Sorry if I did not guess correctly what your question is about. Perhaps you could clarify.
Cheers - Jim
James R Knaub I would guess that BBD is Box-Behnken desiign, but I don't know that for sure. Best wishes, David Booth
James R Knaub BBD stands for Box-Behnken design just as David Eugene Booth stated. This is a design popularly used in scientific experiments because of its few generated runs. Maybe you're correct that the data isn't much. which led to overfitting of my model. I can't increase the number of my experimental runs now because that would mean having a new design entirely. A new design would require new experiments.
How large is your sample size? The three responses you noted were just new ones, obtained after model selection, right?
Can you use a less complex version of your model? (Statistical Learning says less complex models tend to be more biased, but I think that is assuming plenty of data.) Without enough data, I think a too complex model will likely overfit, which means that the wrong general population is assumed. Perhaps if you could use a less complex model, the data you have could be used better. You apparently do not have enough data for a formal cross-validation, but perhaps if you include the three new data points in the sample, and leave out some others to use in a prediction check after you select a new model, things may go better.
Lack of fit is one of the problems of statistical techniques. However, to solve this problem, the use of AI techniques for sparse data learning could be a solution. These models learns a randomized version of your data runs and fit a black box model to your data.
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