Good morning,
is there any way to check for multivariate outliers when data is not only composed by continuous variables? My dataset includes categorical variables (with 2 and 3 levels) and continuous variables. I guess whether exists any modification from Mahalanobis distances or any other test.
I know that at least there is one, developed by Leon & Carriere for looking for outliers in data including nominal and ordinal variables (reference below). But i did not find any software including it.
Leon, A.R. y K.C., Carriere. 2005. A generalized Mahalanobis distance for mixed data. Journal of Multivariate Analysis. 2005. 92, 174-185.
I work mainly in R and MPlus, so it would be great if you can give a solution within tghis software.
Thanks!
I think mvoutlier package in R (https://cran.r-project.org/web/packages/mvoutlier/mvoutlier.pdf) can help you for this purpose. Take a glance at link.
Thanks Abdullah,
I know this package, but there is no vignette or tutorial and I did not find an answer to my question there. Also, for Mahalanobis distance, the package MVN is useful for continuous data
In addition, I updated my question after the new insights
Mario, what is your very aim of finding multivariate outliers of mixed data (as it is named in that article)? The article seems interesting but I don't think there exists a software that implements the proposed method.
Hi Mehmet,
in general, the presence of outliers can be a big a problem when analyse the data both in univariate and multivariate contexts. Also, the choice of a particular estimation method, for example in SEM, depends on MVN and so on the presence of outliers.
Multivariate outliers are easy to detect with different methods when variables are continuous. What I do not know is whether it have sense to include also the categorical or ordinal variables when checking for these outliers. If the answer is yes, whet method is the adequate one?
The answer to this question should lie in the article you pointed.
Multivariate outliers are different from univariate outliers. So the discussion should separate them.
For SEM you can use some more robust methods like WLS, GLS instead of OLS or ML. About MVN, ordinal and categorical variables cannot be normal. So that assumption already fails. It might be written somewhere that SEM requires MVN, but how realistically this assumption is satisfied with real data is still questionable.
I can recommend Ronan's answer in the following thread.
https://www.researchgate.net/post/Does_removing_multivariate_outliers_Mahalanobis_d_square_method_leads_to_better_model_fit_in_case_of_Structure_Equation_ModelingAMOS
Hi Mehmet, thanks.
Yes, I know that in case I have no MVN I should choose other estimation methods apart from the classical ML or GLS. And also it is not anymore assumed that SEM requires MVN, is just a knowledge needed to choose the estimator to fit a SEM. I also know that when checking for univariare normality, it has no sense to check for normality in ordinal and categorical variables.
My worries are related with the potential contribution of. e.g. the categorical variables to the Multivariate distribution of the continuous variables in the same dataset. Imagine, and this is an invention, that the categorical variables works as a blocking factors of the continuous variables when computing Mahalanobis distance or any other index which serves to detect outliers. This example is an invention, but I do not know if this or something similar can occur.
Yes it can. The logic in the article you pointed and another article* that is referred by that article seems related to what you describe. Namely, joint distributions of mixed variables are considered in those articles and Mahalanobis distance (which is a sum of those distances for continuous and discrete data) is defined accordingly. You can consider the articles referenced by your pointed article.
* A. Bar-Hen, J.J. Daudin, Generalization of the Mahalanobis distance in the mixed case, J.Multivariate Anal. 53 (1995) 332–342.
Hi Mario. Did you manage to work anything out for this? I'm also trying to find something in R to do the same, but no luck yet.
Hi Margaret,
I was confused since I read that there was some methods for including categorical but, of course, It is not logic to look for normality when variables are not continuous
For example, if you have binary, categorical variables, do not go for MVN, what you have to do is to select the proper estimator.
Look at the package MVN, but is only applicable to numerical continuous variables, not categorical ones. there is the Mardia's test and also allows you to check for MV outliers using Mahalanobis distance.
Hope it helps
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