Sometimes, it is crucial to investigate the relationship between dependent variable and independent variables in dataset. Unfortunately, in some cases you may meet collinearity among independent variables. you can detect this by using corr command in stata or vif and you realize that the collinearity is present. Then how to remove this collinearity and analyze data with a high possible accuracy in the results? Thank you.
You can choose to keep one among the collinear variables and drop other variables. The decision is entirely based on your judgment: (1) which one fits well within your theoretical framework, and (2) which one is measured with less error.
The issue of collinearity is a bit more nuanced. Some degree of collinearity will always be present, but we typically want to avoid extreme collinearity among variables. For prediction, the issue may not matter but I assume this is for causal inference, and ideally we would know more about the causal structure and relationship between the included variables. It is typically not a good idea to drop variables from the model if they are known to have an important effect on the dependent variable. Better solutions are likely dimensionality reduction (e.g., principal components analysis), regularization (e.g., ridge regression), or generating a composite variable. There are times when dropping variables is relatively harmless, but usually not desirable
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