Hi, I'm aware of the importance of standardize or normalize when using Euclidean distances and analysis such as PCA. Is it also necessary to linear models?
So each variable influence over dependent variable is influenced by the scale and range of the other independent variables?
Is it necessary to any GLM distribution?
No. You would actually loose the quantitative meaning of the coefficients.
What can be important is to center variables that are part of interactions (to reduce collinearity and get better numerical stability). Centering can also be helpful to interpret intercepts (as then being the expectation at the mean of the predisctor values).
I agree with Jochen Wilhelm about transforming the variables. But re centering, I have a somewhat different view. Typically, I would center the variables only when numerical instability became an issue using the original variables. Why? Let me illustrate with an example. Suppose I have X1=Age and X2=Age2 in my model. After I estimate the model, I want to display the fitted value of Y at several selected values of age. If I have the original age variable in my model, I just plug in the desired values (e.g., in a -margins- command in Stata, EMMEANS sub-command in SPSS, etc.). But if I have used a centered age variable, I have to plug in each desired age minus the centering value rather than just the desired ages. That may not seem like a big deal, but I see it as an (unnecessary) opportunity for error to creep in. Maybe if I was better at mental arithmetic, I wouldn't see it that way. ;-)
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