A method to simulate multivariate outliers with known mahalanobis distances for normal and non-normal data
Monte Carlo simulations and theoretical analyses have repeatedly demonstrated the impact of outliers on statistical analysis. Most simulation studies generate outliers using one of two general approaches: by multiplying an arbitrary point by a constant or through a finite mixture. The latter can be...
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Elsevier
2024-12-01
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| Series: | Methods in Psychology |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590260124000237 |
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| author | Oscar L. Olvera Astivia |
| author_facet | Oscar L. Olvera Astivia |
| author_sort | Oscar L. Olvera Astivia |
| collection | DOAJ |
| description | Monte Carlo simulations and theoretical analyses have repeatedly demonstrated the impact of outliers on statistical analysis. Most simulation studies generate outliers using one of two general approaches: by multiplying an arbitrary point by a constant or through a finite mixture. The latter can be extended to multivariate settings by defining the Mahalanobis distance between the centroids of two clusters of points. Nevertheless, when researchers aim to simulate individual data points with population-level Mahalanobis distances, the number of available procedures is very limited. This article generalizes one of the few existing methods to simulate an arbitrary number of outliers in an arbitrary number of dimensions, for both multivariate normal and non-normal data. A small simulation demonstration showcases how this methodology enables new simulation designs that were either unpopular or not possible due to the lack of a data-generating algorithm. A discussion of potential implications highlights the importance of considering multivariate outliers in simulation settings. |
| format | Article |
| id | doaj-art-4cf94d25006048088be5c2d3ffe3ef4f |
| institution | OA Journals |
| issn | 2590-2601 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Methods in Psychology |
| spelling | doaj-art-4cf94d25006048088be5c2d3ffe3ef4f2025-08-20T01:57:52ZengElsevierMethods in Psychology2590-26012024-12-011110015710.1016/j.metip.2024.100157A method to simulate multivariate outliers with known mahalanobis distances for normal and non-normal dataOscar L. Olvera Astivia0College of Education, University of Washington, 2012 Skagit Ln, Seattle, WA 98105, United StatesMonte Carlo simulations and theoretical analyses have repeatedly demonstrated the impact of outliers on statistical analysis. Most simulation studies generate outliers using one of two general approaches: by multiplying an arbitrary point by a constant or through a finite mixture. The latter can be extended to multivariate settings by defining the Mahalanobis distance between the centroids of two clusters of points. Nevertheless, when researchers aim to simulate individual data points with population-level Mahalanobis distances, the number of available procedures is very limited. This article generalizes one of the few existing methods to simulate an arbitrary number of outliers in an arbitrary number of dimensions, for both multivariate normal and non-normal data. A small simulation demonstration showcases how this methodology enables new simulation designs that were either unpopular or not possible due to the lack of a data-generating algorithm. A discussion of potential implications highlights the importance of considering multivariate outliers in simulation settings.http://www.sciencedirect.com/science/article/pii/S2590260124000237OutlierMultivariateMahalanobis distanceSkewnessKurtosis |
| spellingShingle | Oscar L. Olvera Astivia A method to simulate multivariate outliers with known mahalanobis distances for normal and non-normal data Methods in Psychology Outlier Multivariate Mahalanobis distance Skewness Kurtosis |
| title | A method to simulate multivariate outliers with known mahalanobis distances for normal and non-normal data |
| title_full | A method to simulate multivariate outliers with known mahalanobis distances for normal and non-normal data |
| title_fullStr | A method to simulate multivariate outliers with known mahalanobis distances for normal and non-normal data |
| title_full_unstemmed | A method to simulate multivariate outliers with known mahalanobis distances for normal and non-normal data |
| title_short | A method to simulate multivariate outliers with known mahalanobis distances for normal and non-normal data |
| title_sort | method to simulate multivariate outliers with known mahalanobis distances for normal and non normal data |
| topic | Outlier Multivariate Mahalanobis distance Skewness Kurtosis |
| url | http://www.sciencedirect.com/science/article/pii/S2590260124000237 |
| work_keys_str_mv | AT oscarlolveraastivia amethodtosimulatemultivariateoutlierswithknownmahalanobisdistancesfornormalandnonnormaldata AT oscarlolveraastivia methodtosimulatemultivariateoutlierswithknownmahalanobisdistancesfornormalandnonnormaldata |