Basic usage
Suppose that we have a simple scenario that one predictor \(X_1\) is almost linearly dependent on another two predictors \(X_2\) and \(X_3\), thus \(X_1\) is strongly correlated with these two predictors. The dependence among these three variables is a sufficient cause for collinearity which can be shown through large variances of estimated model parameters in linear regression. We illustrate this with a simple example:
## Simulating some data
set.seed(1)
p = 6
n = 100
X = matrix(rnorm(n*p), ncol = p)
X[,1] = X[,2] + X[,3] + rnorm(n, 0, 0.01)
y = rnorm(n)
summary(lm(y ~ X))
#>
#> Call:
#> lm(formula = y ~ X)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -2.56042 -0.73579 -0.05585 0.86967 2.20334
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 0.02084 0.11157 0.187 0.852
#> X1 10.14768 10.34285 0.981 0.329
#> X2 -10.08175 10.33068 -0.976 0.332
#> X3 -10.30688 10.34038 -0.997 0.321
#> X4 0.04175 0.11321 0.369 0.713
#> X5 0.07191 0.09563 0.752 0.454
#> X6 -0.16951 0.11482 -1.476 0.143
#>
#> Residual standard error: 1.094 on 93 degrees of freedom
#> Multiple R-squared: 0.06683, Adjusted R-squared: 0.006628
#> F-statistic: 1.11 on 6 and 93 DF, p-value: 0.3625The mcvis method highlights the major collinearity-causing variables on a bipartite graph. There are three major components of this graph: + the top row renders the “tau” statistics and by default, only one tau statistic is shown (\(\tau_p\), where \(p\) is the number of predictors). This tau statistic measures the extent of collinearity in the data and relates to the eigenvalues of the correlation matrix in \(X\). + the bottom row renders all original predictors. + the two rows are linked through the MC-indices that we have developed, which are represented as lines of different shades and thickness. Darker lines implies larger values of the MC-index indicate what predictor contribute more to causing collinearity.
If you are interested in how the tau statistics and the resampling-based MC-index are calculated, our paper is published as Lin, C., Wang, K. Y. X., & Mueller, S. (2020). mcvis: A new framework for collinearity discovery, diagnostic and visualization. Journal of Computational and Graphical Statistics
library(mcvis)
mcvis_result = mcvis(X = X)
mcvis_result
#> X1 X2 X3 X4 X5 X6
#> tau6 0.51 0.25 0.24 0 0 0This matrix of MC-indices is the main numeric output of mcvis and our visualisation techniques are focused on visualising this matrix. Below is a bipartite graph visualising the last row of this matrix, which is the main visualisation plot of mcvis.
plot(mcvis_result)
We also provide a igraph version of the mcvis bipartite graph.
plot(mcvis_result, type = "igraph")
