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# Detecting multicollinearity using RVIF and graphical methods.

`rvif-package.Rd`

Detecting troubling near-multicollinearity in multiple linear regression models is a classical econometric problem. The purpose of this package is to detect it by using the Redefined Variance Inflation Factor (RVIF) and the scatterplot between the Variance Inflation Factor (VIF) and the Coefficient of Variation (CV).

In addition, the RVIF is used to determine whether the statistical analysis of the model is affected by the degree of multicollinearity in the model.

## Details

This package contains four functions. The first two, `cv_vif` and `plot.cv_vif`, respectively return the values of the Variance Inflation Factor (VIF) and the Coefficient of Variation (CV), as well as their representation in a scatterplot. It should be noted that the VIF is useful for detecting essential multicollinearity, while the CV is useful for detecting non-essential multicollinearity. Thus, the scatterplot of both measures can provide interesting information for determining whether there is a troubling degree of multicollinearity and identifying the type of multicollinearity present and the variables causing it.

On the other hand, the funcion `rvif` calculates the redefined VIF and the percentage of approximate multicollinearity due to each independent variable.

Finally, `multicollinearity` determines whether the degree of multicollinearity in the regression model affects the statistical analysis of the model, i.e., whether the non-rejection of the null hypothesis in the individual significance tests is due to the linear relationships between the independent variables of the model.

## Author

Román Salmerón Gómez (University of Granada) and Catalina B. García García (University of Granada).

Maintainer: Román Salmerón Gómez (romansg@ugr.es)

## References

Salmerón, R., García, C.B. and García, J. (2018). Variance inflation factor and condition number in multiple linear regression. Journal of Statistical Computation and Simulation, 88:2365-2384, doi: doi:10.1080/00949655.2018.1463376 .

Salmerón, R., Rodríguez, A. and García, C.B. (2020). Diagnosis and quantification of the non-essential collinearity. Computational Statistics, 35(2), 647-666, doi: doi:10.1007/s00180-019-00922-x .

Salmerón, R., García, C.B., Rodríguez, A. and García, C. (2022). Limitations in detecting multicollinearity due to scaling issues in the mcvis package. R Journal, 14(4), 264-279, doi: doi:10.32614/RJ-2023-010 .

Salmerón, R., García, C.B. and García, J. (2025). A redefined Variance Inflation Factor: overcoming the limitations of the Variance Inflation Factor. Computational Economics, 65, 337-363, doi: doi:10.1007/s10614-024-10575-8 .

Overcoming the inconsistences of the variance inflation factor: a redefined VIF and a test to detect statistical troubling multicollinearity by Salmerón, R., García, C.B and García, J. (working paper, https://arxiv.org/pdf/2005.02245).