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I would like to fit a non-linear model by doing nonlinear feature transformation first (e.g. exp, log) and then using linear regression (or regularized linear regression). However, I am stuck at whether to do standardization first before nonlinear transformation or vice versa. I know it doesn't matter for polynomial fitting because your final models will be mathematically equivalent no matter you do z-score before polynomial transformation or later.

But when it comes to other types of nonlinear transformation, I am very confused. Because all my variables have physical meaning and also have different magnitude (e.g. concentration measurements/wave numbers/temperatures/mass....). And I am trying to find a relation between the concentration = f(temperature,mass...). So say my final model is $C = exp (T) + m^2*T... $, centering T or not really makes the model different.

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  • $\begingroup$ You can't standardize and center before log transform anyway. Standardization of there either for computational or interpretation convenience, do you need such a convenience? $\endgroup$ – rep_ho Jan 24 '19 at 22:06
  • $\begingroup$ @rep_ho Thanks. I should be more rigorous. I mean before exp and other transformations? Because I don't know the the true underlying relationship but I know a linear model is not suffice, so I would like an interpretable nonlinear model. But I was considering whether I should do zscore first and do the combination of different nonlinear transformation on my data (if possible) or afterwords. I consider zscore because the variables are of different magnitude so I don't want the unit to affect my analysis (e.g. I could use mass in g or kg and they are orders of magnitude different). $\endgroup$ – Vickyyy Jan 24 '19 at 22:10
  • $\begingroup$ I recommend visual inspection of scatterplots for concentration versus each of the other variables to see if any obvious relationship such as log, exp, etc. is suggested. This is easy and fast to perform, and might yield useful insight. $\endgroup$ – James Phillips Jan 25 '19 at 1:36

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