Variance Inflation Factor (VIF) measures the intercorrelation among independent variables in a multiple regression model. In mathematical terms, the variance inflation factor for a regression model variable would be the ratio of the overall model variance to the variance of the model with a single independent variable. A high VIF indicates a high correlation between variables.
Understanding Variance Inflation Factor
A multiple regression model is used in a situation where a person wants to examine the effect of multiple variables on an outcome. Here, the dependent variable would be the outcome that is tested with the independent variables. The independent variables would form inputs into the model.
The existence of high intercorrelation between variables makes them less independent. Thus, intercorrelation between variables in a multiple regression model creates problems in testing the variables. It makes it difficult to determine how much the combination of independent variables impacts the dependent variable or the outcome of the regression model.
Even small changes in the data or in the structure of the regression model can lead to large and, sometimes, erratic changes in the coefficients of variables.
VIF is a statistical tool which helps in testing a regression model for correctness. It tests how the behaviour of an independent variable is altered due to a correlation with other independent variables. Thus, it helps in identifying the severity of the issues to facilitate adjustment to the model.
High intercorrelation between variables may produce results which are not significant statistically. It may also lead to double counting of variables. However, VIF can be used for testing economic data variables.
Explained with an Illustration
VIF, as a statistical tool, has practical applications for determining the effect of an independent variable on the dependent variable. For example, a person can use the statistical tool of VIF to determine the relationship between the unemployment rate (independent variable) and inflation rate (dependent variable). Here, the person can introduce additional independent variables, such as new initial jobless claims and test the dependence among variables.