OUTLIERS: OUTLIERS
In DFA.CANCOR: Linear Discriminant Function and Canonical Correlation Analysis
OUTLIERS R Documentation
OUTLIERS
Description
Provides tests and qqplots for multivariate outliers.
Usage
OUTLIERS(data, variables, ID=NULL, iterate=TRUE,
alpha_univ=.05, plot_univariates=TRUE,
MCD=TRUE, MCD.quantile = .75, alpha=0.025, cutoff_type = 'adjusted',
qqplot=TRUE, plot_iters=NULL,
verbose=TRUE)
Arguments
data
A dataframe where the rows are cases & the columns are the variables.
variables
The names of the continuous variables in the dataframe for the analyses,
e.g., variables = c('varA', 'varB', 'varC').
ID
(optional) The names of the case identification variable in data, if
there is one. If ID is not specified, then the sequence of row numbers will
be used as the case IDs.
iterate
(optional) Should multiple iterations be conducted when searching for
outliers?
The options are: TRUE (default) or FALSE.
alpha_univ
(optional) The p (alpha) level for univariate outliers.
The default = .05.
plot_univariates
(optional) Should univariate plots be provided?
The options are: TRUE (default) or FALSE.
MCD
(optional) Should the Minimum Covariance Determinant method be used
to compute the means and covariances?
The options are: TRUE (default) or FALSE.
MCD.quantile
(optional) The MCD quantile, which is the the minimum
number of the data points regarded as good points (MASS package).
The default = .75, as recommended by Leys et al. (2018).
alpha
(optional) alpha
cutoff_type
(optional) The kind of cutoff to be computed. The options are
adjusted' (the default) or 'quan'.
qqplot
(optional) Should qqplots be provided?
The options are: TRUE (default) or FALSE.
plot_iters
(optional) A vector with the iterations for the qqplot. For example,
"plot_iters = c(1,2,6,7)" will produce a qqplot for each of iterations 1, 2, 6, and 7
on the output figure. The default is "plot_iters = c(1,2,3,4)".
verbose
(optional) Should detailed results be displayed in console? TRUE (default) or FALSE
Details
This function provides both statistical and graphical methods of
identifying multivariate outliers. Both methods are based on
Mahalanobis distances.
A Mahalanobis distance is an estimate of how far each case is from the
center of the joint distribution of the variables in multivariate
space. Cases that are distant from the swarm of most other cases may
be multivariate outliers.
Squared Mahalanobis distances have an approximate chi-squared
distribution (when there is multivariate normality). Statistically, a
multivariate outlier is said to exist when the squared Mahalanobis
distance for a case is greater than a specified cut-off value that is
derived from the chi-square distribution.
The computations for Mahalanobis distances are based on estimates of
the means and covariances for the dataset. However, the means and
covariances that are based on all of the data are affected by the
existence of multivariate outliers. This renders the simple,
whole-sample estimates of Mahalanobis distances, and thus the
identification of outliers, problematic.
Better estimates of the means and covariances are obtained using the
Minimum Covariance Determinant (MCD) method, which identifies the most
central subset of the data. Mahalanobis distances are considered more
"robust" when they are computed using the MCD means and covariances.
The default for the MCD argument for this function is set to TRUE
for this reason. Setting it to FALSE will result in the procedure
using the whole-sample based means and covariances, which is not
recommended.
Once obtained, Mahalanobis distances (robust or not) are assessed for
statistical significance by comparing them with a specified quantile
from the chi-squared distribution. There are two options for
determining the specified quantile cutoff value. The simple,
traditional approach is to use the alpha quantile of the chi-squared
distribution with the degrees of freedom equal to the number of
variables. In the present function, the default alpha threshold is
0.025.
A modern, alternative method of determining cutoff values is to use the
adaptive reweighted estimator procedure (Filzmoser, Garrett, &
Reimann, 2005), which derives a cutoff value that is appropriate for
each specific dataset and sample size. These threshold values are
called "adjusted quantiles".
The cutoff_type argument for this function can be set to "adjusted"
for an adjusted quantile, or to "quan" for the traditional alpha
quantile.
A "qqplot" of the squared Mahalanobis distances can be used to
graphically assess multivariate normality and the existence of
outliers. In this case, the (sorted) squared Mahalanobis distances are
plotted against the corresponding quantiles of the chi-square
distribution. When the the squared Mahalanobis distances fit the
hypothesized distribution, the points in the Q-Q plot will fall on a
straight, y = x line (chi-squared values are squared z scores).
Deviations from the straight line suggest violations of multivariate
normality and the possible existence of multivariate outliers.
The search for multivariate outliers can be conducted more than once
for a given dataset. If outliers are identified on the first step
(iteration), they can be removed from the dataset and another search
for outliers can be conducted on the remaining data. It is not
uncommon for multiple iterations to be required before no further
outliers are found. Bigger outliers can mask smaller but still
possibly important outliers. It is probably best to run the analyses
for multiple iterations. In the present function, multiple iterations
are conducted when the iterate argument is set to TRUE.
The present function provides up to four possible qqplots in the
one-page output figure for a data analysis. By default, these plots
will be for the first four interations that produced outliers. Use
the plot_iters argument to produce plots from alternative iterations.
For example, "plot_iters = c(1,2,6,7)" will place the qqplots from
iterations 1, 2, 6, and 7 on the output figure.
Value
The returned output is a list with the outliers.
Author(s)
Brian P. O'Connor
References
Filzmoser, P., Garrett, R. G., & Reimann, C. (2005). Multivariate outlier
detection in exploration geochemistry. Computers & Geosciences,
31, 579-587.
Leys, C., Klein, O., Dominicy, Y., & Ley, C. (2018). Detecting
multivariate outliers: Use a robust variant of the Mahalanobis distance.
Journal of Experimental Social Psychology, 74, 150-156.
Rodrigues, I. M., & Boente, G. (2011). Multivariate outliers.
International Encyclopedia of Statistical Science (pp. 910-912).
Berlin:Springer-Verlag.
Rousseeuw, P. J., & Leroy, A. M. (1987). Robust Regression and Outlier
Detection. New York, NY: John Wiley & Sons.
Examples
OUTLIERS(data = iris, variables = c('Sepal.Length','Sepal.Width','Petal.Length'),
ID=NULL, iterate=TRUE,
alpha_univ=.05, plot_univariates=TRUE,
MCD=TRUE, MCD.quantile = .75, alpha=0.025, cutoff_type = 'adjusted',
qqplot=TRUE, plot_iters=c(1,2,5,6),
verbose=TRUE)
DFA.CANCOR documentation built on June 8, 2025, 11:12 a.m.
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| OUTLIERS | R Documentation |
OUTLIERS
Description
Provides tests and qqplots for multivariate outliers.
Usage
OUTLIERS(data, variables, ID=NULL, iterate=TRUE,
alpha_univ=.05, plot_univariates=TRUE,
MCD=TRUE, MCD.quantile = .75, alpha=0.025, cutoff_type = 'adjusted',
qqplot=TRUE, plot_iters=NULL,
verbose=TRUE)
Arguments
data |
A dataframe where the rows are cases & the columns are the variables. |
variables |
The names of the continuous variables in the dataframe for the analyses, e.g., variables = c('varA', 'varB', 'varC'). |
ID |
(optional) The names of the case identification variable in data, if there is one. If ID is not specified, then the sequence of row numbers will be used as the case IDs. |
iterate |
(optional) Should multiple iterations be conducted when searching for
outliers? |
alpha_univ |
(optional) The p (alpha) level for univariate outliers. The default = .05. |
plot_univariates |
(optional) Should univariate plots be provided?
|
MCD |
(optional) Should the Minimum Covariance Determinant method be used
to compute the means and covariances?
|
MCD.quantile |
(optional) The MCD quantile, which is the the minimum number of the data points regarded as good points (MASS package). The default = .75, as recommended by Leys et al. (2018). |
alpha |
(optional) alpha |
cutoff_type |
(optional) The kind of cutoff to be computed. The options are adjusted' (the default) or 'quan'. |
qqplot |
(optional) Should qqplots be provided?
|
plot_iters |
(optional) A vector with the iterations for the qqplot. For example, "plot_iters = c(1,2,6,7)" will produce a qqplot for each of iterations 1, 2, 6, and 7 on the output figure. The default is "plot_iters = c(1,2,3,4)". |
verbose |
(optional) Should detailed results be displayed in console? TRUE (default) or FALSE |
Details
This function provides both statistical and graphical methods of identifying multivariate outliers. Both methods are based on Mahalanobis distances.
A Mahalanobis distance is an estimate of how far each case is from the center of the joint distribution of the variables in multivariate space. Cases that are distant from the swarm of most other cases may be multivariate outliers.
Squared Mahalanobis distances have an approximate chi-squared distribution (when there is multivariate normality). Statistically, a multivariate outlier is said to exist when the squared Mahalanobis distance for a case is greater than a specified cut-off value that is derived from the chi-square distribution.
The computations for Mahalanobis distances are based on estimates of the means and covariances for the dataset. However, the means and covariances that are based on all of the data are affected by the existence of multivariate outliers. This renders the simple, whole-sample estimates of Mahalanobis distances, and thus the identification of outliers, problematic.
Better estimates of the means and covariances are obtained using the Minimum Covariance Determinant (MCD) method, which identifies the most central subset of the data. Mahalanobis distances are considered more "robust" when they are computed using the MCD means and covariances. The default for the MCD argument for this function is set to TRUE for this reason. Setting it to FALSE will result in the procedure using the whole-sample based means and covariances, which is not recommended.
Once obtained, Mahalanobis distances (robust or not) are assessed for statistical significance by comparing them with a specified quantile from the chi-squared distribution. There are two options for determining the specified quantile cutoff value. The simple, traditional approach is to use the alpha quantile of the chi-squared distribution with the degrees of freedom equal to the number of variables. In the present function, the default alpha threshold is 0.025.
A modern, alternative method of determining cutoff values is to use the adaptive reweighted estimator procedure (Filzmoser, Garrett, & Reimann, 2005), which derives a cutoff value that is appropriate for each specific dataset and sample size. These threshold values are called "adjusted quantiles".
The cutoff_type argument for this function can be set to "adjusted" for an adjusted quantile, or to "quan" for the traditional alpha quantile.
A "qqplot" of the squared Mahalanobis distances can be used to graphically assess multivariate normality and the existence of outliers. In this case, the (sorted) squared Mahalanobis distances are plotted against the corresponding quantiles of the chi-square distribution. When the the squared Mahalanobis distances fit the hypothesized distribution, the points in the Q-Q plot will fall on a straight, y = x line (chi-squared values are squared z scores). Deviations from the straight line suggest violations of multivariate normality and the possible existence of multivariate outliers.
The search for multivariate outliers can be conducted more than once for a given dataset. If outliers are identified on the first step (iteration), they can be removed from the dataset and another search for outliers can be conducted on the remaining data. It is not uncommon for multiple iterations to be required before no further outliers are found. Bigger outliers can mask smaller but still possibly important outliers. It is probably best to run the analyses for multiple iterations. In the present function, multiple iterations are conducted when the iterate argument is set to TRUE.
The present function provides up to four possible qqplots in the one-page output figure for a data analysis. By default, these plots will be for the first four interations that produced outliers. Use the plot_iters argument to produce plots from alternative iterations. For example, "plot_iters = c(1,2,6,7)" will place the qqplots from iterations 1, 2, 6, and 7 on the output figure.
Value
The returned output is a list with the outliers.
Author(s)
Brian P. O'Connor
References
Filzmoser, P., Garrett, R. G., & Reimann, C. (2005). Multivariate outlier
detection in exploration geochemistry. Computers & Geosciences,
31, 579-587.
Leys, C., Klein, O., Dominicy, Y., & Ley, C. (2018). Detecting
multivariate outliers: Use a robust variant of the Mahalanobis distance.
Journal of Experimental Social Psychology, 74, 150-156.
Rodrigues, I. M., & Boente, G. (2011). Multivariate outliers.
International Encyclopedia of Statistical Science (pp. 910-912).
Berlin:Springer-Verlag.
Rousseeuw, P. J., & Leroy, A. M. (1987). Robust Regression and Outlier
Detection. New York, NY: John Wiley & Sons.
Examples
OUTLIERS(data = iris, variables = c('Sepal.Length','Sepal.Width','Petal.Length'),
ID=NULL, iterate=TRUE,
alpha_univ=.05, plot_univariates=TRUE,
MCD=TRUE, MCD.quantile = .75, alpha=0.025, cutoff_type = 'adjusted',
qqplot=TRUE, plot_iters=c(1,2,5,6),
verbose=TRUE)
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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