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I've seen that by standardizing variables with subtracting their means, the VIF drops significantly below threshold of 5. But originally they were >10. What's the mathematical proves that standardization eliminate structural multi-collinearity problem?

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    $\begingroup$ stats.stackexchange.com/questions/16710/… $\endgroup$ – mlofton Jun 27 '20 at 3:08
  • $\begingroup$ Standardizing is a type of transformation and other types of transformations also help in reducing/eliminating Multi-collinearity. For example, taking first order differences may help in some situation, although it will create another problem- Autocorrelation or we may do ratio transformation- Dividing the equation by some correlated explanatory variable. This will also reduce multicollinearity but will now cause hetroscedasticity. $\endgroup$ – napoleon Jun 27 '20 at 4:37
  • $\begingroup$ I guess the model itself is changed from retraining. There might be a correlation between residuals and variables. And this might introduce a non-proportional reduction in residual to the variables. $\endgroup$ – hbadger19042 Jun 27 '20 at 4:40
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I'm relatively new here, so I can't put this as a comment. The answer to the question that mlofton linked is great, and I believe it is line with this paper:

Iacobucci, D., Schneider, M. J., Popovich, D. L., & Bakamitsos, G. A. (2016). Mean centering helps alleviate “micro” but not “macro” multicollinearity. Behavior research methods, 48(4), 1308-1317.

Basically, standardizing variable doesn't help the model as a whole, but it can reduce VIF.

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