MVN: An R Package for Assessing Multivariate Normality

MVN: An R Package for Assessing Multivariate Normality

2016-11-30 | Selcuk Korkmaz, Dincer GoksuIuk and Gokmen Zararsiz
The MVN R package is designed to assess multivariate normality (MVN) for statistical methods that require this assumption, such as MANOVA, discriminant analysis, and principal component analysis. It includes three widely used MVN tests: Mardia's, Henze-Zirkler's, and Royston's, along with graphical methods like chi-square Q-Q, perspective, and contour plots. The package also provides functions for univariate normality checks and multivariate outlier detection using robust Mahalanobis distances. Additionally, a user-friendly web application is available for non-R users. MVN tests evaluate whether data follow a multivariate normal distribution by analyzing skewness and kurtosis. Mardia's test uses multivariate extensions of skewness and kurtosis measures, while Henze-Zirkler's test employs a non-negative functional distance. Royston's test uses the Shapiro-Wilk/Shapiro-Francia statistic, adapting based on data kurtosis. These tests may yield different results, so combining them with graphical methods enhances decision-making. The package also includes univariate normality tests and plots, which help identify deviations from MVN. For example, in the Iris dataset, Mardia's and Henze-Zirkler's tests suggested multivariate normality, while Royston's test rejected it. The chi-square Q-Q plot showed deviations from normality, indicating potential issues with the data. Removing the skewed Petal.Width variable improved MVN results. The MVN package supports bivariate data through perspective and contour plots, which visually assess normality. These plots confirmed bivariate normality in the setosa2 dataset. Multivariate outlier detection using robust Mahalanobis distances identified outliers in the versicolor dataset. The package is available as an R package and a web application, making it accessible to both R users and non-R users. It provides comprehensive tools for assessing MVN, including statistical tests, graphical methods, and outlier detection. The package is regularly updated and offers flexibility for various statistical analyses. Overall, the MVN package is a valuable resource for researchers to evaluate multivariate normality and ensure the validity of statistical methods that depend on this assumption.The MVN R package is designed to assess multivariate normality (MVN) for statistical methods that require this assumption, such as MANOVA, discriminant analysis, and principal component analysis. It includes three widely used MVN tests: Mardia's, Henze-Zirkler's, and Royston's, along with graphical methods like chi-square Q-Q, perspective, and contour plots. The package also provides functions for univariate normality checks and multivariate outlier detection using robust Mahalanobis distances. Additionally, a user-friendly web application is available for non-R users. MVN tests evaluate whether data follow a multivariate normal distribution by analyzing skewness and kurtosis. Mardia's test uses multivariate extensions of skewness and kurtosis measures, while Henze-Zirkler's test employs a non-negative functional distance. Royston's test uses the Shapiro-Wilk/Shapiro-Francia statistic, adapting based on data kurtosis. These tests may yield different results, so combining them with graphical methods enhances decision-making. The package also includes univariate normality tests and plots, which help identify deviations from MVN. For example, in the Iris dataset, Mardia's and Henze-Zirkler's tests suggested multivariate normality, while Royston's test rejected it. The chi-square Q-Q plot showed deviations from normality, indicating potential issues with the data. Removing the skewed Petal.Width variable improved MVN results. The MVN package supports bivariate data through perspective and contour plots, which visually assess normality. These plots confirmed bivariate normality in the setosa2 dataset. Multivariate outlier detection using robust Mahalanobis distances identified outliers in the versicolor dataset. The package is available as an R package and a web application, making it accessible to both R users and non-R users. It provides comprehensive tools for assessing MVN, including statistical tests, graphical methods, and outlier detection. The package is regularly updated and offers flexibility for various statistical analyses. Overall, the MVN package is a valuable resource for researchers to evaluate multivariate normality and ensure the validity of statistical methods that depend on this assumption.
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