A Redefined Variance Inflation Factor: Overcoming the Limitations of the Variance Inflation Factor

The variance inflation factor is one the most applied tools for diagnosing the possible existence of multicollinearity in a multiple linear regression model. However, the VIF can detect only the relationships between independent variables without considering the intercept and is not appropriate to use with binary variables. In addition, the orthogonal model from which is calculated is also controversial. All these limitations are not usually considered when the VIF is calculated which may lead to misleading conclusions. This paper parts from an alternative orthogonal model to present a redefined variance inflation factor (RVIF) which overcomes the above limitations. This method was implemented in the rvif R package (Salmerón and García in rvif: collinearity detection using redefined variance inflation factor and graphical methods [Computer software manual]. https://cran.r-project.org/package=rvif , 2022). A Monte Carlo simulation is performed to provide threshold for this new measure. The contribution of this paper is illustrated with different examples. It is also compared with the vif command from the car R package to calculate the VIF, concluding that it could be recommendable to warn non-statisticians of its controversial use.