CV_VIF {rvif}

VIF, CV and its scatter plot

Description

This function provides the values for the Variance Inflation Factor (VIF) and the Coefficient of Variation (CV), as well as its representation in a scatter plot.

Usage

CV_VIF(X, size=NULL, top=82.64, limit=40, dummy=FALSE, pos=NULL, intercept=TRUE)

Arguments

X

A numeric design matrix that should contain more than one regressor (intercept included).

size

A numeric vector containing the percentage of multicollinearity due to each variable. By default size=NULL.

top

A real number that indicates the threshold from which the percentage of multicollinearity due to each variable is considered troubling. By default top=82.64.

limit

A real number that indicates the lower limit of the vertical axis. By default limit=40.

dummy

A logical value that indicates if there are dummy variables in the design matrix X. By default dummy=FALSE.

pos

A numeric vector that indicates the position of the dummy variables, if these exist, in the design matrix X. By default pos=NULL.

intercept

A logical value used only by the function RVIF. By default intercept=TRUE.

Details

It is interesting to note the distinction between essential (near-linear relationship between at least two independent variables excluding the intercept) and non-essential multicollinearity (near-linear relationship between the intercept and at least one of the remaining independent variables), due to the VIF is not an appropriate measure to detect non-essential collinearity (only detects essential collinearity), while the CV is useful to detect only non-essential collinearity.

Then, this distinction between essential and non-essential multicollinearity and the limitations of each measure for detecting the different kinds of multicollinearity, can be very useful for detecting whether there is a troubling degree of multicollinearity, what kind of multicollinearity it is and which variables are causing the multicollinearity.

For this it is important include in the figures the lines corresponding to the established thresholds for each measure (CV and VIF): dashed vertical line for 0.1002506 (CV) and dotted horizontal line for 10 (VIF). These lines determine four regions (see Example 1) that can be interpreted as follows: A, existence of troubling non-essential and non-troubling essential multicollinearity; B, existence of troubling essential and non-essential multicollinearity; C, existence of non-troubling non-essential and troubling essential multicollinearity; D: non-troubling degree of existing multicollinearity (essential and non-essential).

Value

CV

Coefficient of Variation of each independent variable.

VIF

Variance Inflation Factor of each independent variable.

Author(s)

R. Salmerón ([e-mail]) and C. García ([e-mail]).

References

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

R. Salmerón, A. Rodríguez, and C. García. Diagnosis and quantification of the non-essential collinearity. Computational Statistics, 35:647-666, 2020.

Limitations in Detecting Multicollinearity due to Scaling Issues in the mcvis Package by Salmerón, R., García, C.B, Rodríguez, A. and García, C. (working paper).

Examples

## Example 1
plot(-2:20, -2:20, type = "n", xlab="Coefficient of Variation", ylab="Variance Inflation Factor")
abline(h=10, col="black", lwd=3, lty=2)
abline(v=0.1002506, col="black", lwd=3, lty=3)
text(-1.25, 2, "A", pos=3, col="red")
text(-1.25, 12, "B", pos=3, col="red")
text(10, 12, "C", pos=3, col="red")
text(10, 2, "D", pos=3, col="red")

## Example 2
library(multiColl)
set.seed(2022)
obs = 100
cte = rep(1, obs)
x2 = rnorm(obs, 5, 0.01)
x3 = rnorm(obs, 5, 10)
x4 = x3 + rnorm(obs, 5, 1)
x5 = rnorm(obs, -1, 30)
x = cbind(cte, x2, x3, x4, x5)
CV_VIF(x, size = c(1, 1, 1, 1))