In regression analysis, multicollinearity occurs when two or more predictor variables are highly correlated with each other, such that they do not provide unique or independent information in the regression model.
If the degree of correlation is high enough between predictor variables, it can cause problems when fitting and interpreting the regression model.
The most straightforward way to detect multicollinearity in a regression model is by calculating a metric known as the variance inflation factor, often abbreviated VIF.
VIF measures the strength of correlation between predictor variables in a model. It takes on a value between 1 and positive infinity.
We use the following rules of thumb for interpreting VIF values:
- VIF = 1: There is no correlation between a given predictor variable and any other predictor variables in the model.
- VIF between 1 and 5: There is moderate correlation between a given predictor variable and other predictor variables in the model.
- VIF > 5: There is severe correlation between a given predictor variable and other predictor variables in the model.
The following example shows how to detect multicollinearity in a regression model in R by calculating VIF values for each predictor variable in the model.
Example: Testing for Multicollinearity in R
Suppose we have the following data frame that contains information about various basketball players:
#create data frame df = data.frame(rating = c(90, 85, 82, 88, 94, 90, 76, 75, 87, 86), points=c(25, 20, 14, 16, 27, 20, 12, 15, 14, 19), assists=c(5, 7, 7, 8, 5, 7, 6, 9, 9, 5), rebounds=c(11, 8, 10, 6, 6, 9, 6, 10, 10, 7)) #view data frame df rating points assists rebounds 1 90 25 5 11 2 85 20 7 8 3 82 14 7 10 4 88 16 8 6 5 94 27 5 6 6 90 20 7 9 7 76 12 6 6 8 75 15 9 10 9 87 14 9 10 10 86 19 5 7
Suppose we would like to fit a multiple linear regression model using rating as the response variable and points, assists, and rebounds as the predictor variables.
To calculate the VIF for each predictor variable in the model, we can use the vif() function from the car package:
library(car) #define multiple linear regression model model <- lm(rating ~ points + assists + rebounds, data=df) #calculate the VIF for each predictor variable in the model vif(model) points assists rebounds 1.763977 1.959104 1.175030
We can see the VIF values for each of the predictor variables:
- points: 1.76
- assists: 1.96
- rebounds: 1.18
Since each of the VIF values for the predictor variables in the model are close to 1, multicollinearity is not a problem in the model.
Note: If multicollinearity does turn out to be a problem in your model, the quickest fix in most cases is to remove one or more of the highly correlated variables.
This is often an acceptable solution because the variables you’re removing are redundant anyway and add little unique or independent information in the model.
The following tutorials explain how to perform other common tasks in R:
How to Perform Multiple Linear Regression in R
How to Create a Q-Q Plot in R
How to Create a Residual Plot in R