Multicollinearity Testing in Stata

Introduction

One of the standard post-regression diagnostic tests is a test for multicollinearity. In this blog, we’ll show you to test for multicollinearity after a regression using Stata’s vif command. We’ll show you to run and interpret vif, then adjust your model to eliminate multicollinearity.

Load Data

Let’s load Stata’s prebuilt auto dataset:

sysuse auto
describe

Run the Regression

Try:

regress mpg weight length i.foreign

Here’s what you get:

Test VIF

Next, test the multicollinearity of this regression model with the vif command:

vif

Here’s what you get:

A variance inflation factor (VIF) of over 5 strongly suggests multicollinearity. In this context of this regression, multicollinearity simply means that the two predictors with high VIFs (weight and length) are likely to be highly correlated with each other, which we can check as follows:

pwcorr weight length, sig

Weight and length are highly positively correlated, r = .946, p < .0001.

Rerun the Model with Only One High-VIF Variable

Now, because weight and length are highly positively correlated with each other, we can remove one and retest for multicollinearity. Try:

regress mpg weight i.foreign
vif

And, as you can confirm, the regression remains significant:

However, this time, multicollinearity is not a problem:

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