How to calculate the standard value of Mahalanobis distance to check multivariate outliers?

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Gerhard Nachtmann

If you use R, have a look at `mahalanobis` function:

https://stat.ethz.ch/R-manual/R-devel/library/stats/html/mahalanobis.html

To detect multivariate outliers in a robust way see package `mvoutlier`:

https://CRAN.R-project.org/package=mvoutlier

Stephen J. Walsh

Hi - do you have given multivariate mean and covariance? or are you estimating them from the data? (these parameters are required for computing Mahalanobis distance).

If the parameters are given, Mahalanobis distance is Chi-square distributed, and this knowledge can be used to identify outliers.

If you have to estimate the parameters, then suggest Minimum Determinant Covariance, such as here: http://svitsrv25.epfl.ch/R-doc/library/robustbase/html/covMcd.html. Then, you compute the Mahalnobis distance of each point in robust and non-robust way, plot these distances in an Y vs. X plot and those points not falling on Y = X are clear outliers.

@Stephen: covMcd is fine, yes.

As Stephen mentioned the Chi-square distribution, you can use mvoutlier::chisq.plot() directly.

Bhuvanesh Kumar Sharma

Respected Gerhard Nachtmann sir & Stephen J. Walsh sir..Thanks for your responses....I have calculated mahalanobis distance for individual items. I have studied in SEM assumptions that the values above a particular value considered to be outliers so how to calculate that value? Is there any formula in excel? as I have seen in one of the video in YouTube. I am ok with SPSS not R.

Tegegne Haile

Dear all,

Can someone help me if you have an excel file to calculate the mahalanobis distance critical value.

Thanks!

Alaba T. Owoseni

Please use R. Using R to me is simpler as you have the opportunity of importing your data set that you have contained in excel file into R. All you need to do is to call function Mahalanobis() contained in package "stats"

Muhammmad Abbas

Can you please help me and mention the acceptable range of values for Mahalanobis test. Which values should be accepted from the result and which to be deleted.

Note: I am using SPSS to calculate Mahalanobis distance values.