Checking multicollinearity

For the linear model with multiple explanatory variables, we need to also think about multicollinearity - this is when two (or more) of the predictors in our regression model are moderately or highly correlated.

We can assess multicollinearity using the variance inflation factor (VIF), which for a given predictor \(x_j\) is calculated as:

\[ VIF_j = \frac{1}{1-R_j^2} \\ \]

The vif() function from the car package will provide VIF values (or for categorical predictors, GVIF) for each predictor in your model.

vif(INSERT_MODEL_NAME)

Interpretation Guidance:

Suggested cut-offs for VIF are varied. Some suggest 10, others 5. Define what you will consider an acceptable value prior to calculating it. You could loosely interpret VIF values \(>5\) as moderate multicollinearity and values \(>10\) as severe multicollinearity.

Block 3 note: Multicollinearity in interaction models

Interaction terms often result in multicollinearity, because these terms are made up of the product of some ‘main effects’. Mean-centering the variables will help to reduce this source of structural multicollinearity (“structural” here refers to the fact that multicollinearity is due to our model specification, rather than the data itself).