As the x-variables become more strongly correlated, it becomes more difficult to determine which of the variables are actually producing the statistical effect on the y-variable. This is a problem of multicollinearity.

One way of assessing problems with multicollinearity is through the estat vif command (vif=variance inflation factor). This tells us how much of the variance that is being inflated by multicollinearity. As a rule of thumb, a vif-value that is near 10 or higher calls for concern.

More information help estat vif

Another way of assessing multicollinearity is using the estat vce command, with the corr (short for correlation) option.

More information help estat vce

Practical example

The first step is re-run the multiple linear regression model. The quietly option is included in the beginning of the command to suppress the output.

quietly reg gpa cognitive bullied ib1.skipped if pop_linear==1

Next, we try the estat vif command.

estat vif

We get a mean vif-value of 1.07, which tells us that we do not seem to have any problems with multicollinearity in this model.

Let us also try the estat vce command. By adding the corr (=correlation) option, we will get a correlation matrix instead of a covariance matrix.

estat vce, corr

The table shows the correlations between the different variables/categories. In line with the earlier sections on correlation analysis (see Correlation analysis), we can conclude that the coefficients suggest (very) weak correlations here.