R: Calculate and plot Mahalanobis distances

acc_multivariate_outlier {dataquieR}

R Documentation

Calculate and plot Mahalanobis distances

Description

A standard tool to detect multivariate outliers is the Mahalanobis distance. This approach is very helpful for the interpretation of the plausibility of a measurement given the value of another. In this approach the Mahalanobis distance is used as a univariate measure itself. We apply the same rules for the identification of outliers as in univariate outliers:

the classical approach from Tukey: 1.5 * IQR from the 1st (Q_{25}) or 3rd (Q_{75}) quartile.
the 3SD approach, i.e. any measurement of the Mahalanobis distance not in the interval of \bar{x} \pm 3*\sigma is considered an outlier.
the approach from Hubert for skewed distributions which is embedded in the R package robustbase
a completely heuristic approach named \sigma-gap.

For further details, please see the vignette for univariate outlier.

Indicator

Usage

acc_multivariate_outlier(
  variable_group = NULL,
  id_vars = NULL,
  label_col,
  n_rules = 4,
  max_non_outliers_plot = 10000,
  criteria = c("tukey", "3sd", "hubert", "sigmagap"),
  study_data,
  meta_data
)

Arguments

`variable_group`	variable list the names of the continuous measurement variables building a group, for that multivariate outliers make sense.
`id_vars`	variable optional, an ID variable of the study data. If not specified row numbers are used.
`label_col`	variable attribute the name of the column in the metadata with labels of variables
`n_rules`	numeric from=1 to=4. the no. of rules that must be violated to classify as outlier
`max_non_outliers_plot`	integer from=0. Maximum number of non-outlier points to be plot. If more points exist, a subsample will be plotted only. Note, that sampling is not deterministic.
`criteria`	set tukey \| 3SD \| hubert \| sigmagap. a vector with methods to be used for detecting outliers.
`study_data`	data.frame the data frame that contains the measurements
`meta_data`	data.frame the data frame that contains metadata attributes of study data

Value

a list with:

SummaryTable: data.frame underlying the plot
SummaryPlot: ggplot2 outlier plot
FlaggedStudyData data.frame contains the original data frame with the additional columns tukey, ⁠3SD⁠, hubert, and sigmagap. Every observation is coded 0 if no outlier was detected in the respective column and 1 if an outlier was detected. This can be used to exclude observations with outliers.

ALGORITHM OF THIS IMPLEMENTATION:

Implementation is restricted to variables of type float
Remove missing codes from the study data (if defined in the metadata)
The covariance matrix is estimated for all variables from variable_group
The Mahalanobis distance of each observation is calculated MD^2_i = (x_i - \mu)^T \Sigma^{-1} (x_i - \mu)
The four rules mentioned above are applied on this distance for each observation in the study data
An output data frame is generated that flags each outlier
A parallel coordinate plot indicates respective outliers