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I am currently fitting models that are intended to be used for extrapolating from a limited sample to a large population. For a specific example, one model is predicting water temperature in rivers based on attributes of the river. The sample includes data from approximately 1,000 river segments (a river segment is a unique length of a river), which will be used to extrapolate to over 100,000 river segments. This is a neural network model, but I have the same question for a different model using hierarchical logistic regression models, so the question is not statistical method specific.

I have read and have found through experience that normalizing my modeling dataset can improve model fit. However, I am unsure in this instance because the goal is extrapolating to the population. Should the predictors be normalized [(y - mean)/stdev] based on their mean and sdev in the sample or in the population of river segments?

I have taken the opinion that I should normalize based on the population to help ensure that the population variability is represented adequately in the modeling dataset.

I apologize if there is a cross posting, as I have searched for this answer thoroughly and have not seen a similar question or discussion anywhere. So I am asking this here. Please point me to an answer if one exists elsewhere.

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  • $\begingroup$ Thank you for the point - I'll remember that in the future. $\endgroup$ – user2532704 Mar 24 '14 at 15:46
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I assume that you are scaling the data in order to improve convergence of the training algorithm. If so, it doesn't make much difference what values you use, except that you have to consistently apply the same scaling to non-training data as to training data.

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  • $\begingroup$ This was my general impression, but I wanted to be sure as I am a trained fish ecologist and not a statistician - though I fit models more than I see fish. $\endgroup$ – user2532704 Mar 24 '14 at 15:47

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