What is a Variance Inflation Factor (VIF)?
The variance inflation factor (VIF) in regression analysis is a metric for multicollinearity. In a multivariate regression model, multicollinearity occurs when there is a correlation between many independent variables. The regression findings may suffer as a consequence of this. As a result, the variance inflation factor may be used to calculate the extent to which multicollinearity has inflated the variance of a regression coefficient.
The Variance Inflation Factor (VIF): An Understanding
One method to determine the multicollinearity level is the variance inflation factor. Multiple regression analysis examines the impact of many factors on a particular result. The result that the independent variables—the model’s inputs—have an impact on is known as the dependent variable. When one or more independent variables or inputs have a linear connection or correlation, this is known as multicollinearity.
The Multicollinearity Problem
Due to the inputs’ mutual influence, multicollinearity challenges the multiple regression model. Because of this, it is challenging to determine the extent to which the independent variables’ combination influences the dependent variable, or outcome, in the regression model. As a result, they could be more independent.
Multicollinearity may result in estimates of the regression coefficients that are not statistically significant, but it does not lower a model’s overall predictive power. It may be seen as double-counting inside the model.
In statistical terms, estimating the link between each independent and dependent variable will be more challenging in a multiple regression model with significant multicollinearity. Unless stated otherwise, the underlying impact measured by two or more independent variables that measure almost the same thing is accounted for twice (or more) across the variables when they are strongly connected. Determining which independent factors impact the dependent variables when they are strongly correlated is difficult.
Significant and unpredictable variations in the predicted coefficients on the independent variables might result from little adjustments to the model equation’s structure or the data employed. This is problematic since testing precisely this kind of statistical link between the independent and dependent variables is the aim of many econometric models.
Methods for Testing Multicollinearity
Multicollinearity tests may be performed to make sure the model is appropriately stated and operating. One of these measurement instruments is the variance inflation factor. Modifying the model helps determine the severity of multicollinearity problems using variance inflation factors. The degree to which an independent variable’s behavior (variance) is inflated or impacted by its interaction or connection with other independent variables is measured by the variance inflation factor.
Variance inflation factors provide a rapid assessment of how much a variable contributes to the regression’s standard error. The variance inflation factor for the variables involved will be substantial when significant multicollinearity difficulties exist. Once these variables are found, the multicollinearity problem may be resolved by combining or removing collinear variables using various techniques.
VIF Formula and Calculation
What Is There to Tell From VIF?
Multicollinearity does not occur when Ri2 = 0 and, therefore, when VIF or tolerance = 1. This is because the independent variable is not associated with the other variables.
- VIF equal to 1 means the variables are not correlated
- VIF between 1 and 5 = variables are moderately correlated
- VIF is more significant than 5, which means the variables are highly correlated
More studies are necessary for the VIF, which indicates a more substantial likelihood of multicollinearity. There is severe multicollinearity that has to be adjusted when the VIF is greater than 10.One Instance of Using VIF
For example, an economist wishes to determine whether the unemployment rate (an independent variable) and the inflation rate (a dependent variable) have a statistically significant connection. The model will likely introduce multicollinearity by including extra independent variables relevant to the unemployment rate, such as new initial jobless claims.
The entire model may exhibit robust and statistically significant explanatory power; nevertheless, it may not be able to distinguish between the impact of the unemployment rate and the new initial jobless claims. The VIF would identify this, and depending on the particular hypothesis the researcher is interested in testing, it suggests either eliminating one of the variables from the model or finding a method to combine them to capture their combined influence.
A Good VIF Value: What Is It?
Generally speaking, a VIF of three or fewer is not the reason for alarm. Your regression findings will become less trustworthy as VIF rises.
What does a VIF of 1 suggest?
A VIF of one indicates that the regression model’s variables are not correlated and do not exhibit multicollinearity.
Why is VIF employed?
In regression analysis, VIF quantifies the degree of correlation between the independent variables. Regression models may encounter issues due to multicollinearity, a correlation like this.
The Final Word
Higher multicollinearity in a regression model may be cause for concern. However, a low level of multicollinearity is acceptable.
There are two ways to address excessive multicollinearity: First, because the data these strongly linked variables offer is redundant, one or more of them may be eliminated. As an alternative to OLS regression, one may use principle components analysis or partial least squares regression, which can be used to either generate new uncorrelated variables or decrease the collection of variables to a smaller size with no association. This will increase a model’s predictability.
Conclusion
- In a multiple regression model, a variance inflation factor (VIF) indicates how multicollinear the independent variables are.
- Finding multicollinearity is crucial because it doesn’t lessen the model’s ability to explain phenomena but alleviates the independent variables’ statistical significance.
- When picking independent variables and setting up the model, a significant difference in the coefficient of determination (VIF) for one variable means it is strongly connected to the other variables and needs to be fixed or considered.
