# outlier

##### Find and graph Mahalanobis squared distances to detect outliers

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.

- Keywords
- multivariate, models

##### Usage

`outlier(x, plot = TRUE, bad = 5,na.rm = TRUE, xlab, ylab, ...)`

##### Arguments

- x
A data matrix or data.frame

- plot
Plot the resulting QQ graph

- bad
Label the bad worst values

- na.rm
Should missing data be deleted

- xlab
Label for x axis

- ylab
Label for y axis

- …
More graphic parameters, e.g., cex=.8

##### Details

Adapted from the mahalanobis function and help page from stats.

##### Value

The D2 values for each case

##### References

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.

##### See Also

##### Examples

```
# 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)
# }
```

*Documentation reproduced from package psych, version 1.7.5, License: GPL (>= 2)*