I am doing weighted linear regression (W-OLS) with and without standardization (centering and scaling). The results are not identical and in many cases normalization is making the results worse. Can you please help me to figure out why this is happening? I suppose, normalization should not hurt. Is there any better way for normalization, e.g. subtracting min and dividing by (max-min)?
The coefficients should be different when you standardize (otherwise, why would you standardize?); data is standardized because you want to change the results. The t-statistics, p-values, and various goodness-of-fit measures should be unchanged. If they are changed, this means either:
- You are doing something wrong. That is, you are making a mistake of some kind.
- The independent variables have really large values (e.g., are in the thousands or greater), and you have numerical precision results. In this case, the understandardized values are incorrect.