# Decomposing R squared or VIF

In the context of multi-regression, I am wondering if there is a way to decompose $$VIF_i = 1/(1-R_i^2)$$ where $R_i^2$ is the r squared obtained from the regression of dependent variable = i and independent variables are all other factors.

I want to decompose $VIF_i$ or $R_i^2$ into individual factors to see how much each individual factor contributes to the $VIF_i$ or $R_i^2$

Someone recommended using the square of partial correlation coefficient and that value is linearly related to $R_i^2$. My undestanding is that partial correlation coefficient measures the correlation between two variables, holding the other variables constant. Is this a viable option?

• Decomposing the R-squared (e.g. by looking at squared semi-partial correlations) and gain the information you are interested in is difficult. Imagine e.g. a situation with three highly correlated covariables $z_1$, $z_2$, $z_3$. How would you want to decompose the R-squared corresponding to the VIF of $z_1$ in contributions of $z_2$ and $z_3$? – Michael M Aug 29 '18 at 16:27
• @MichaelM well.. I do not know how to decompose the R-squared corresponding to the VIF of z1 in contributions of z2 and z3 and that's why I posted the question to get an answer. – Jun Jang Aug 29 '18 at 16:47