crmReg-package {crmReg}

Cellwise Robust M-regression and SPADIMO

Description

Method for fitting a cellwise robust linear M-regression model (CRM, Filzmoser et al. (2020) <DOI:10.1016/j.csda.2020.106944>) that yields both a map of cellwise outliers consistent with the linear model, and a vector of regression coefficients that is robust against vertical outliers and leverage points. As a by-product, the method yields an imputed data set that contains estimates of what the values in cellwise outliers would need to amount to if they had fit the model. The package also provides diagnostic tools for analyzing casewise and cellwise outliers using sparse directions of maximal outlyingness (SPADIMO, Debruyne et al. (2019) <DOI:10.1007/s11222-018-9831-5>).

Details

Package:	crmReg
Type:	Package
Version:	1.0.1
Date:	2020-03-26
License:	GPL (>=2)

The crmReg package provides the implementation of the Cellwise Robust M-regression (CRM) algorithm (Filzmoser et al., 2020) and the SPArse DIrections of Maximal Outlyingness (SPADIMO) algorithm (Debruyne et al., 2019). The package also includes a predict function for fitted CRM regression models, a function for creating heatmaps of cellwise outliers, and a data preprocessing function for centering and scaling the data as used by CRM.

Given an observation that has been detected as an outlier, SPADIMO (Debruyne et al., 2019) finds the subset of variables contributing most the outlier’s outlyingness. Here, the outlyingness of a data point is defined as its robust Mahalanobis distance. The relevant variables are found by checking the direction in which the observation is most outlying. SPADIMO estimates this direction of maximal outlyingness in a sparse manner. Thereby, the method helps to understand in which way an outlier lies out.

The SPADIMO algorithm allows us to introduce the cellwise robust M-regression (CRM) estimator (Filzmoser et al., 2020) as a linear regression estimator that intrinsically yields both a map of cellwise outliers consistent with the linear model, and a vector of regression coefficients that is robust against vertical outliers and leverage points. As a by-product, the method yields a weighted and imputed data set that contains estimates of what the values in cellwise outliers would need to amount to if they had fit the model. The CRM method consists of an iteratively reweighted least squares procedure where SPADIMO is applied at each iteration to detect the cells that contribute most to outlyingness. As such, CRM detects deviating data cells consistent with a linear model.

The package contains five main functions.

The function spadimo computes the sparse directions of maximal outlyings of a given observation and shows diagnostic plots for analyzing that observation.

The function crm fits a cellwise robust M-regression estimator. Besides a vector of regression coefficients, the function returns an imputed data set that contains estimates of what the values in cellwise outliers would need to amount to if they had fit the model. The output of crm is a list object of class "crm".

The function predict.crm obtains predictions from a fitted object of class "crm".

The function cellwiseheatmap makes a heatmap of cellwise outliers which are typically the result of a call to the crm function.

The function daprpr preprocesses the data by classical or robust centering and scaling.

Author(s)

Peter Filzmoser, Sebastiaan Hoppner, Irene Ortner, Sven Serneels, and Tim Verdonck

Maintainer: Sebastiaan Hoppner <[e-mail]>

References

Debruyne, M., Hoppner, S., Serneels, S., and Verdonck, T. (2019). Outlyingness: Which variables contribute most? Statistics and Computing, 29 (4), 707–723. DOI:10.1007/s11222-018-9831-5

Filzmoser, P., Hoppner, S., Ortner, I., Serneels, S., and Verdonck, T. (2020). Cellwise Robust M regression. Computational Statistics and Data Analysis, 147, 106944. DOI:10.1016/j.csda.2020.106944

See Also

crm, spadimo, predict.crm, cellwiseheatmap, daprpr

Examples

library(crmReg)
data(topgear)

# get case weights from a robust estimator (covMCD function in robustbase package):
MCD <- robustbase::covMcd(topgear, alpha = 0.5)

# SPADIMO with diagnostic plots:
# Example 1:
Peugeot <- spadimo(data = topgear,
                   weights = MCD$mcd.wt,
                   obs = which(rownames(topgear) == "Peugeot 107"))
# check the plots!
# individual variable names contributing most to Peugeot 107's outlyingness:
print(Peugeot$outlvars)
# sparse direction of maximal outlyingness with eta = Peugeot$eta:
print(Peugeot$a)
# default SPADIMO control parameters:
print(Peugeot$control)

# Example 2:
Bugatti <- spadimo(data = topgear,
                   weights = MCD$mcd.wt,
                   obs = which(rownames(topgear) == "Bugatti Veyron"),
                   control = list(stopearly = TRUE, trace = TRUE, plot = TRUE))
# check the plots!
# individual variable names contributing most to Bugatti Veyron's outlyingness:
print(Bugatti$outlvars)
# sparse direction of maximal outlyingness with eta = Bugatti$eta:
print(Bugatti$a)

# fit Cellwise Robust M-regression:
crmfit <- crm(formula = MPG ~ ., data = topgear)

# estimated regression coefficients and detected casewise outliers:
print(crmfit$coefficients)
print(rownames(topgear)[which(crmfit$casewiseoutliers)])

# fitted response values (MPG) versus true response values:
plot(topgear$MPG, crmfit$fitted.values, xlab = "True MPG", ylab = "Fitted MPG")
abline(a = 0, b = 1)

# residuals:
plot(crmfit$residuals, ylab = "Residuals")
text(x = which(crmfit$residuals > 30), y = crmfit$residuals[which(crmfit$residuals > 30)],
     labels = rownames(topgear)[which(crmfit$residuals > 30)], pos = 2)

print(cbind.data.frame(car = rownames(topgear),
                       MPG = topgear$MPG)[which(crmfit$residuals > 30), ])

# cellwise heatmap of casewise outliers:
cellwiseheatmap(cellwiseoutliers = crmfit$cellwiseoutliers[which(crmfit$casewiseoutliers), ],
                data = round(topgear[which(crmfit$casewiseoutliers), -7], 2),
                col.scale.factor = 1/4)
# check the plotted heatmap!