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- VIF values with int vs. noint REG model

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01-22-2016 02:56 PM - edited 01-22-2016 03:13 PM

We get different values of VIF while doing linear regression model with intercept vs. no intercept. A model with noint yields a higher Vif than one with int. I understand it is because of different rsquare value. Theoretically, model with no intercept makes sense but the values are very high. If i use the thumb rule - variables having VIF >10 should be checked for collinearity, i would have to drop a lot of variables. My interest area is to correct collinearity for a logistic regression model. Hence i am least interested for r square of linear regression model. Which method is correct?

proc reg data=sashelp.cars;

model MPG_City = weight Horsepower EngineSize Wheelbase Cylinders / vif noint;

ods output parameterestimates=parest2;

run;

quit;

proc reg data=sashelp.cars;

model MPG_City = weight Horsepower EngineSize Wheelbase Cylinders / vif;

ods output parameterestimates=parest2;

run;

quit;

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01-23-2016 12:35 AM

When you choose no intercept, you are essentially forcing it to zero. Therefore, you are saying "when my x's are all 0, I expect my Y to be 0." That is the only situation that you should use that option.

The reason you get high VIF's in a no-intercept situation, is because VIF is a ratio that is related to R2. And when you choose no intercept, you can get much higher R2 values. Why? Thats a long one, but here's a great article on it.

Now that you've learned why R2 goes up, look back at the VIF equation: VIF = 1 / (1 - R2) So its easy to see that as VIF goes up, the denominator goes down, which makes overall VIF go up.

tl;dr Using noint is for a specific scenario, which R2 is measured differently and is often higher. Since VIF is related to R2, it also goes up.