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I have a dataset that has high collinearity among variables. When I created the linear regression model, I could not include more than five variables ( I eliminated the feature whenever VIF>5). But I need to have all the variables in the model and find their relative importance. Is there any way around it?. I was thinking about doing PCA and creating models on principal components. Does it help?.

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  • $\begingroup$ Why can’t you include more than five variables? $\endgroup$
    – Dave
    Oct 31, 2021 at 2:30
  • $\begingroup$ Because VIF increases beyond 5 when I use more than 5 features. $\endgroup$
    – NAS_2339
    Oct 31, 2021 at 17:50
  • $\begingroup$ So VIF exceeds $5$…how does that impact your analysis? $\endgroup$
    – Dave
    Oct 31, 2021 at 20:24
  • $\begingroup$ Doesn't it mean high collinearity in the data? So that I can't keep those features $\endgroup$
    – NAS_2339
    Nov 1, 2021 at 1:17
  • $\begingroup$ But VIF of 4.5 also means that there is (multi)collinearity. How does VIF $>5$ impact your analysis? $\endgroup$
    – Dave
    Nov 1, 2021 at 3:05

2 Answers 2

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PCA will generate „new“ (transformed) features which are orthogonal (non-correlated). However, since the original features are transformed, you can hardly claim to say a lot about the importance of (original) features based on PCA.

One obvious alternative would be to use a random forest (RF) to determine feature importance. Using tree based models (like RF or tree based boosting) you do not need to care about collinearity in the feature space.

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  • $\begingroup$ But my principal components are still a linear combination of the original variables, right?. Can I distribute the feature importance of the principal components to the original variables somehow? $\endgroup$
    – NAS_2339
    Oct 26, 2021 at 5:49
  • $\begingroup$ Not sure about this. Tend to say it is not a good idea… $\endgroup$
    – Peter
    Oct 26, 2021 at 19:18
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When using PCA, you should not try to interpret the single features anymore. The principal components are multiple linear combinations of your variables that should not be related to the original features.

When you want to work on feature importance, you can use random forests or decision trees instead, as described before. You can do it with neural networks as well by randomizing or shuffling one feature, re-train the network, and comparing the performance.

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