Package 'crmReg' reference manual

Title:	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>).
Authors:	Peter Filzmoser [aut], Sebastiaan Hoppner [aut, cre], Irene Ortner [aut], Sven Serneels [aut], Tim Verdonck [aut]
Maintainer:	Sebastiaan Hoppner <[email protected]>
License:	GPL (>= 2)
Version:	1.0.2
Built:	2024-11-15 04:36:27 UTC
Source:	https://github.com/cran/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 <[email protected]>

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

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!
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!

Heatmap of cellwise outliers

Description

Makes a heatmap of cellwise outliers.

Usage

cellwiseheatmap(cellwiseoutliers, data,
                col = c("blue", "lightgray", "red"), col.scale.factor = 1,
                notecol.outlier = "white", notecol.clean = "black", notecex = 1,
                margins = c(9.5, 14), lhei = c(0.5, 15), lwid = c(0.1, 3.5),
                sepcolor = "white", sepwidth = c(0.01, 0.01))
cellwiseheatmap(cellwiseoutliers, data,
                col = c("blue", "lightgray", "red"), col.scale.factor = 1,
                notecol.outlier = "white", notecol.clean = "black", notecex = 1,
                margins = c(9.5, 14), lhei = c(0.5, 15), lwid = c(0.1, 3.5),
                sepcolor = "white", sepwidth = c(0.01, 0.01))

Arguments

`cellwiseoutliers`	a matrix that indicates the cellwise outliers as the (scaled) difference between the original data and imputed data, both scaled and centered. Typically the result of a call to the `crm` function.
`data`	the data as a data frame that is shown in the cells, including row and column names.
`col`	vector of colors used for downward outliers, clean cells and upward outliers respectively (default is `c("blue", "lightgray", "red")`).
`col.scale.factor`	numeric factor for scaling the colors of the cells (default is `1`). Usually a value between 0 and 1, e.g. 1/2, 1/3, etc.
`notecol.outlier`	character string specifying the color for cellnote text of cellwise outliers (default is `"white"`).
`notecol.clean`	character string specifying the color for cellnote text of clean cells (default is `"black"`).
`notecex`	numeric scaling factor for cellnotes (default is `1`).
`margins`	numeric vector of length 2 containing the margins (see `par(mar= *)`) for column and row names, respectively (default is `c(9.5, 14)`).
`lhei`	numeric vector of length 2 containing the row height (default is `c(1, 15)`).
`lwid`	numeric vector of length 2 containing the row width (default is `c(0.7, 3.5)`).
`sepcolor`	character string specifying the color between the cells (default is `"white"`).
`sepwidth`	vector of length 2 giving the width and height of the separator box drawn between the cells (default is `c(0.01, 0.01)`).

Details

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

Author(s)

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

References

Examples

library(crmReg)
data(topgear)

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

# 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!
library(crmReg)
data(topgear)

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

# 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!

Cellwise Robust M-regression

Description

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.

Usage

crm(formula, data, maxiter = 100, tolerance = 0.01, outlyingness.factor = 1,
    spadieta = seq(0.9, 0.1, -0.1), center = "median", scale = "qn",
    regtype = "MM", alphaLTS = NULL, seed = NULL, verbose = TRUE)crm(formula, data, maxiter = 100, tolerance = 0.01, outlyingness.factor = 1,
    spadieta = seq(0.9, 0.1, -0.1), center = "median", scale = "qn",
    regtype = "MM", alphaLTS = NULL, seed = NULL, verbose = TRUE)

Arguments

`formula`	an lm-style formula object specifying which relationship to estimate.
`data`	the data as a data frame.
`maxiter`	maximum number of iterations (default is `100`).
`tolerance`	obtain optimal regression coefficients to within a certain tolerance (default is `0.01`).
`outlyingness.factor`	numeric value, larger or equal to 1 (default). Only cells are altered of cases for which the original outlyingness (before SPADIMO) is larger than outlyingness.factor * outlyingness AFTER SPADIMO. The larger this factor, the fewer cells are imputed.
`spadieta`	the sparsity parameter to start internal outlying cell detection with, must be in the range [0,1] (default is `seq(0.9, 0.1, -0.1)`).
`center`	how to center the data. A string that matches the R function to be used for centering (default is `"median"`).
`scale`	how to scale the data. Choices are "no" (no scaling) or a string matching the R function to be used for scaling (default is `"qn"`).
`regtype`	type of robust regression. Choices are `"MM"` (default) or `"LTS"`.
`alphaLTS`	parameter used by LTS regression. The percentage (roughly) of squared residuals whose sum will be minimized (default is `0.5`).
`seed`	initial seed for random generator, like .Random.seed (default is `NULL`).
`verbose`	should output be shown during the process (default is `TRUE`).

Details

The cellwise robust M-regression (CRM) estimator (Filzmoser et al., 2020) is 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.

Value

crm returns a list object of class "crm" containing the following elements:

`coefficients`	a named vector of fitted coefficients.
`fitted.values`	the fitted response values.
`residuals`	the residuals, that is response minus fitted values.
`weights`	the (case) weights of the residuals.
`data.imputed`	the data as imputed by CRM.
`casewiseoutliers`	a vector that indicates the casewise outliers with `TRUE` or `FALSE`.
`cellwiseoutliers`	a matrix that indicates the cellwise outliers as the (scaled) difference between the original data and imputed data, both scaled and centered.
`terms`	the terms object used.
`call`	the matched call.
`inputs`	the list of supplied input arguments.
`numloops`	the number of iterations.
`time`	the number of seconds passed to execute the CRM algorithm.

Author(s)

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

References

Examples

library(crmReg)
data(topgear)

# 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!
library(crmReg)
data(topgear)

# 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!

Data Preprocessing

Description

Data preprocessing, classical and robust centering and scaling.

Usage

daprpr(Data, center.type, scale.type)daprpr(Data, center.type, scale.type)

Arguments

`Data`	the data.
`center.type`	type of centering as R function name (e.g. `"mean"`, `"median"`, `"l1median"`).
`scale.type`	type of scaling as R function name (e.g. `"sd"`, `"qn"`, `"Sn"`, `"scaleTau2"`).

Details

daprpr preprocesses the data by classical or robust centering and scaling. Given center.type = "mean" and scale.type = "sd", function daprpr is equivalent to scale(Data, center = TRUE, scale = TRUE).

Value

daprpr returns the scaled data with attributes "Center", "Scale" and "Type".

Author(s)

Sven Serneels

Examples

library(crmReg)
data(topgear)

topgear_centered_scaled <- daprpr(topgear, center.type = "median", scale.type = "qn")

boxplot(topgear_centered_scaled)
attributes(topgear_centered_scaled)$Type
attributes(topgear_centered_scaled)$Center
attributes(topgear_centered_scaled)$Scale
library(crmReg)
data(topgear)

topgear_centered_scaled <- daprpr(topgear, center.type = "median", scale.type = "qn")

boxplot(topgear_centered_scaled)
attributes(topgear_centered_scaled)$Type
attributes(topgear_centered_scaled)$Center
attributes(topgear_centered_scaled)$Scale

Predict method for CRM fits

Description

Obtains predictions from a fitted crm object.

Usage

## S3 method for class 'crm'
predict(object, newdata = NULL, ...)
## S3 method for class 'crm'
predict(object, newdata = NULL, ...)

Arguments

`object`	a fitted object of class "`crm`".
`newdata`	optionally, a data frame in which to look for variables with which to predict. If omitted, the fitted coefficients are used.
`...`	further arguments passed to or from other methods.

Details

predict.crm produces predicted values, obtained by evaluating the fitted crm object on the data frame newdata.

Value

predict.crm returns a vector of predicted response values.

Author(s)

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

References

Examples

library(crmReg)
data(topgear)

train <- topgear[1:200, ]
test <- topgear[201:245, ]

crmfit <- crm(formula = MPG ~ ., data = train, seed = 2020)

estimated_MPG_test <- predict(crmfit, newdata = test)

plot(test$MPG, estimated_MPG_test, xlab = "True MPG", ylab = "Estimated MPG")
abline(a = 0, b = 1)
library(crmReg)
data(topgear)

train <- topgear[1:200, ]
test <- topgear[201:245, ]

crmfit <- crm(formula = MPG ~ ., data = train, seed = 2020)

estimated_MPG_test <- predict(crmfit, newdata = test)

plot(test$MPG, estimated_MPG_test, xlab = "True MPG", ylab = "Estimated MPG")
abline(a = 0, b = 1)

SPArse DIrections of Maximal Outlyingness

Description

Computes the sparse directions of maximal outlyings of a given observation and shows diagnostic plots for analyzing that observation.

Usage

spadimo(data, weights, obs,
        control = list(scaleFun = Qn, nlatent = 1, etas = NULL, csqcritv  = 0.975,
                       stopearly = FALSE, trace = FALSE, plot = TRUE))spadimo(data, weights, obs,
        control = list(scaleFun = Qn, nlatent = 1, etas = NULL, csqcritv  = 0.975,
                       stopearly = FALSE, trace = FALSE, plot = TRUE))

Arguments

`data`	the data as a data frame.
`weights`	a numeric vector containing the case weights from a robust estimator.
`obs`	the (integer) case number under consideration.
`control`	a list of options that control details of the `crm` algorithm. The following options are available: `scaleFun` function used for robust scaling the variables (e.g. `Qn`, `mad`, etc.). `nlatent` integer number of latent variables for sparse PLS regression (via SNIPLS) (default is `1`). `etas` vector of decreasing sparsity parameters (default is `NULL` in which case `etas = seq(0.9, 0.1, -0.05)` if n > p, otherwise `etas = seq(0.6, 0.1, -0.05)`). `csqcritv` probability level for internal chi-squared quantile (used when n > p) (default is `0.975`). `stopearly` if `TRUE`, method stops as soon as the reduced case is no longer outlying, else if `FALSE` (default) it loops through all values of eta. `trace` should intermediate results be printed (default is `FALSE`). `plot` should heatmaps and graph of the results be shown (default is `TRUE`).

Details

Value

spadimo returns a list containing the following elements:

`outlvars`	vector containing individual variable names contributing most to `obs`'s outlyingness.
`outlvarslist`	list of variables contributing to `obs`'s outlyingness for different values of `eta`.
`a`	vector, the sparse direction of maximal outlyingness.
`alist`	list of sparse directions of maximal outlyingness for different values of `eta`.
`o.before`	outlyingness of original case (n < p) or PCA outlier flag (n >= p) before removing outlying variables.
`o.after`	outlyingness of reduced case (n > p) or PCA outlier flag (n >= p) after removing outlying variables.
`eta`	cutoff where `obs` is no longer outlying.
`time`	time to execute the SPADIMO algorithm.
`control`	a list with control parameters that are used.

Author(s)

Michiel Debruyne, Sebastiaan Hoppner, Sven Serneels, and Tim Verdonck

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

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)
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)

Top Gear car data

Description

The data set contains information on cars featured on the website of the popular BBC television show Top Gear. The original, full data set is available in the package robustHD.

Usage

data(topgear)data(topgear)

Format

A data frame containing 245 observations and 11 variables.

log(Price): the natural logarithm of the list price (in UK pounds)
log(Displacement): the natural logarithm of the displacement of the engine (in cc).
log(BHP): the natural logrithm of the power of the engine (in bhp).
log(Torque): the natural logarithm of the torque of the engine (in lb/ft).
Acceleration: the time it takes the car to get from 0 to 62 mph (in seconds).
log(TopSpeed): the natural logarithm of the car's top speed (in mph).
MPG: the combined fuel consuption (urban + extra urban; in miles per gallon).
Weight: the car's curb weight (in kg).
Length: the car's length (in mm).
Width: the car's width (in mm).
Height: the car's height (in mm).

Source

The original data set is available in the package robustHD. The data were scraped from http://www.topgear.com/uk/ on 2014-02-24.

Examples

data(topgear)
str(topgear)
head(topgear)
summary(topgear)
data(topgear)
str(topgear)
head(topgear)
summary(topgear)

Package 'crmReg'

Help Index

Cellwise Robust M-regression and SPADIMO

Description

Details

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Heatmap of cellwise outliers

Description

Usage

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Cellwise Robust M-regression

Description

Usage

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Value

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Data Preprocessing

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Predict method for CRM fits

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SPArse DIrections of Maximal Outlyingness

Description

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Examples

Top Gear car data

Description

Usage

Format

Source

Examples