More about Mahalanobis distance in R

There are several Mahalanobis distance post in this blog, and this post show a new way to find outliers with a library in R called "mvoutlier".

 

Mahalanobis ellipses can only be shown in 2 dimensions with a cutoff value as we have seen, so we show the maps of scores 2 by 2 for the different combinations of PCs, like in this case for PC1 and PC2 and we can mark the outliers in the plot by the identify function: 

In this case I mark some of the samples out of the Mahalanobis distance cutoff. Anyway the Mahalanobis distance is univariate and in this case where we have a certain number of PCs, we have to see not just a map of two of them or all at the same time, we need a unique Mahalanobis distance value and to check if that value is over or into the cutoff value that we assign.

 

For that reason we use the Moutlier function of the "chemometrics" package and show a real Mahalanobis outlier plot which can be Robust or Classical:

 

We can see the classical plot and identify the samples over the cutoff:

 

We can see the list of all the distances in the output list for the function. I will continue with more options to check the Mahalanobis distances in the next post.