The Mahalanobis distance is \(D^2 = (x-\mu)' \Sigma^-1 (x-\mu)\) where \(\Sigma\) is the covariance of the x matrix. D2 may be used as a way of detecting outliers in distribution. Large D2 values, compared to the expected Chi Square values indicate an unusual response pattern. The mahalanobis function in stats does not handle missing data.
outlier(x, plot = TRUE, bad = 5,na.rm = TRUE, xlab, ylab, ...)A data matrix or data.frame
Plot the resulting QQ graph
Label the bad worst values
Should missing data be deleted
Label for x axis
Label for y axis
More graphic parameters, e.g., cex=.8
The D2 values for each case
Adapted from the mahalanobis function and help page from stats.
Yuan, Ke-Hai and Zhong, Xiaoling, (2008) Outliers, Leverage Observations, and Influential Cases in Factor Analysis: Using Robust Procedures to Minimize Their Effect, Sociological Methodology, 38, 329-368.
# NOT RUN {
#first, just find and graph the outliers
d2 <- outlier(sat.act)
#combine with the data frame and plot it with the outliers highlighted in blue
sat.d2 <- data.frame(sat.act,d2)
pairs.panels(sat.d2,bg=c("yellow","blue")[(d2 > 25)+1],pch=21)
# }