DDC: Detect Deviating Cells

Description

This function aims to detect cellwise outliers in the data. These are entries in the data matrix which are substantially higher or lower than what could be expected based on the other cells in its column as well as the other cells in its row, taking the relations between the columns into account. Note that this function first calls checkDataSet and analyzes the remaining cleaned data.

Usage

DDC(X, DDCpars = list())

Arguments

X is the input data, and must be an \(n\) by \(d\) matrix or a data frame.

DDCpars

A list of available options:

fracNA Only consider columns and rows with fewer NAs (missing values) than this fraction (percentage). Defaults to \(0.5\).
numDiscrete A column that takes on numDiscrete or fewer values will be considered discrete and not used in the analysis. Defaults to \(3\).
precScale Only consider columns whose scale is larger than precScale. Here scale is measured by the median absolute deviation. Defaults to \(1e-12\).
cleanNAfirst If "columns", first columns then rows are checked for NAs. If "rows", first rows then columns are checked for NAs. "automatic" checks columns first if \(d \geq 5n\) and rows first otherwise. Defaults to "automatic".
tolProb Tolerance probability, with default \(0.99\), which determines the cutoff values for flagging outliers in several steps of the algorithm.
corrlim When trying to estimate \(z_{ij}\) from other variables \(h\), we will only use variables \(h\) with \(|\rho_{j,h}| \ge corrlim\). Variables \(j\) without any correlated variables \(h\) satisfying this are considered standalone, and treated on their own. Defaults to \(0.5\).
combinRule The operation to combine estimates of \(z_{ij}\) coming from other variables \(h\): can be "mean", "median", "wmean" (weighted mean) or "wmedian" (weighted median). Defaults to wmean.
returnBigXimp If TRUE, the imputed data matrix Ximp in the output will include the rows and columns that were not part of the analysis (and can still contain NAs). Defaults to FALSE.
silent If TRUE, statements tracking the algorithm's progress will not be printed. Defaults to FALSE.
nLocScale When estimating location or scale from more than nLocScale data values, the computation is based on a random sample of size nLocScale to save time. When nLocScale = 0 all values are used. Defaults to 25000.
fastDDC Whether to use the fastDDC option or not. The fastDDC algorithm uses approximations to allow to deal with high dimensions. Defaults to TRUE for \(d > 750\) and FALSE otherwise.
standType The location and scale estimators used for robust standardization. Should be one of "1stepM", "mcd" or "wrap". See estLocScale for more info. Only used when fastDDC = FALSE. Defaults to "1stepM".
corrType The correlation estimator used to find the neighboring variables. Must be one of "wrap" (wrapping correlation), "rank" (Spearman correlation) or "gkwls" (Gnanadesikan-Kettenring correlation followed by weighting). Only used when fastDDC = FALSE. Defaults to "gkwls".
transFun The transformation function used to compute the robust correlations when fastDDC = TRUE. Can be "wrap" or "rank". Defaults to "wrap".
nbngbrs When fastDDC = TRUE, each column is predicted from at most nbngbrs columns correlated to it. Defaults to 100.

Value

A list with components:

DDCpars The list of options used.
colInAnalysis The column indices of the columns used in the analysis.
rowInAnalysis The row indices of the rows used in the analysis.
namesNotNumeric The names of the variables which are not numeric.
namesCaseNumber The name of the variable(s) which contained the case numbers and was therefore removed.
namesNAcol Names of the columns left out due to too many NA's.
namesNArow Names of the rows left out due to too many NA's.
namesDiscrete Names of the discrete variables.
namesZeroScale Names of the variables with zero scale.
remX Cleaned data after checkDataSet.
locX Estimated location of X.
scaleX Estimated scales of X.
Z Standardized remX.
nbngbrs Number of neighbors used in estimation.
ngbrs Indicates neighbors of each column, i.e. the columns most correlated with it.
robcors Robust correlations.
robslopes Robust slopes.
deshrinkage The deshrinkage factor used for every connected (i.e. non-standalone) column of X.
Xest Predicted X.
scalestres Scale estimate of the residuals X - Xest.
stdResid Residuals of orginal X minus the estimated Xest, standardized by column.
indcells Indices of the cells which were flagged in the analysis.
Ti Outlyingness (test) value of each row.
medTi Median of the Ti values.
madTi Mad of the Ti values.
indrows Indices of the rows which were flagged in the analysis.
indNAs Indices of all NA cells.
indall Indices of all cells which were flagged in the analysis plus all cells in flagged rows plus the indices of the NA cells.
Ximp Imputed X.

References

Rousseeuw, P.J., Van den Bossche W. (2018). Detecting Deviating Data Cells. Technometrics, 60(2), 135-145. (link to open access pdf)

Raymaekers, J., Rousseeuw P.J. (2019). Fast robust correlation for high dimensional data. Technometrics, published online. (link to open access pdf)

Examples

Run this code

# NOT RUN {
library(MASS); set.seed(12345)
n <- 50; d <- 20
A <- matrix(0.9, d, d); diag(A) = 1
x <- mvrnorm(n, rep(0,d), A)
x[sample(1:(n * d), 50, FALSE)] <- NA
x[sample(1:(n * d), 50, FALSE)] <- 10
x[sample(1:(n * d), 50, FALSE)] <- -10
x <- cbind(1:n, x)
DDCx <- DDC(x)
cellMap(DDCx$remX, DDCx$stdResid,
columnlabels = 1:d, rowlabels = 1:n)

# For more examples, we refer to the vignette:
vignette("DDC_examples")
# }