Type:	Package
Title:	Weighted BACON Algorithms
Version:	0.6-3
Description:	The BACON algorithms are methods for multivariate outlier nomination (detection) and robust linear regression by Billor, Hadi, and Velleman (2000) <doi:10.1016/S0167-9473(99)00101-2>. The extension to weighted problems is due to Beguin and Hulliger (2008) https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X200800110616; see also <doi:10.21105/joss.03238>.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
NeedsCompilation:	yes
LazyData:	true
URL:	https://github.com/tobiasschoch/wbacon
BugReports:	https://github.com/tobiasschoch/wbacon/issues
Encoding:	UTF-8
Depends:	R (≥ 3.5.0)
Imports:	stats, graphics, grDevices, hexbin
Suggests:	modi, robustbase, robustX (≥ 1.2-5), knitr, rmarkdown
VignetteBuilder:	knitr, rmarkdown
Packaged:	2025-05-03 21:11:57 UTC; tobias
Author:	Tobias Schoch [aut, cre], R-core [cph] (plot.wbaconlm derives from plot.lm)
Maintainer:	Tobias Schoch <tobias.schoch@gmail.com>
Repository:	CRAN
Date/Publication:	2025-05-03 21:30:01 UTC

Weighted BACON Algorithms for Multivariate Outlier Nomination (Detection) and Robust Linear Regression

Description

The package wbacon implements the BACON algorithms of Billor et al. (2000) and some of the extensions proposed by Béguin and Hulliger (2008).

Details

See wBACON to learn more on the BACON method for multivariate outlier nomination (detection).

See wBACON_reg to learn more on the BACON method for robust linear regression.

Author(s)

Tobias Schoch

References

Billor N., Hadi A.S. and Vellemann P.F. (2000). BACON: Blocked Adaptive Computationally efficient Outlier Nominators. Computational Statistics and Data Analysis, 34, pp. 279–298. doi:10.1016/S0167-9473(99)00101-2

Béguin C. and Hulliger B. (2008). The BACON-EEM Algorithm for Multivariate Outlier Detection in Incomplete Survey Data. Survey Methodology, 34, pp. 91–103. https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X200800110616

Schoch, T. (2021). wbacon: Weighted BACON algorithms for multivariate outlier nomination (detection) and robust linear regression, Journal of Open Source Software, 6 (62), 3238 doi:10.21105/joss.03238

Flag Outliers

Description

By default the function returns a logical vector that indicates which observations were identified or declared as (potential) outliers by the method; if names = TRUE is set in the function call, the row names of the (potential) outliers are returned.

Usage

is_outlier(object, ...)
## S3 method for class 'wbaconmv'
is_outlier(object, names = FALSE, ...)
## S3 method for class 'wbaconlm'
is_outlier(object, names = FALSE, ...)

Arguments

Value

A logical vector or vector with row names.

See Also

wBACON_reg and wBACON

Examples

data(swiss)
m <- wBACON(swiss)

# indicator vector of potential outliers
is_outlier(m)

# names of the potential outliers
is_outlier(m, names = TRUE)

Weighted Median

Description

median_w computes the weighted population median.

Usage

median_w(x, w, na.rm = FALSE)

Arguments

Details

Weighted sample median; see quantile_w for more information.

Value

Weighted estimate of the population median.

See Also

quantile_w

Philips data

Description

The data set consists of 677 observations on 9 variables/characteristics of diaphragm parts for television sets.

Usage

data(philips)

Format

A data.frame with 677 observations on the following variables:

X1

[double], characteristic 1.

X2

[double], characteristic 2.

X3

[double], characteristic 3.

X4

[double], characteristic 4.

X5

[double], characteristic 5.

X6

[double], characteristic 6.

X7

[double], characteristic 7.

X8

[double], characteristic 8.

X9

[double], characteristic 9.

Details

The data have been studied in Rousseeuw and van Driessen (1999) and Billor et al. (2000). They have been published in Raymaekers and Rousseeuw (2023).

Source

Billor, N., A. S. Hadi, and P. F. Vellemann (2000). BACON: Blocked Adaptive Computationally-efficient Outlier Nominators. Computational Statistics and Data Analysis, 34, 279–298. doi:10.1016/S0167-9473(99)00101-2

Raymaekers, J. and P. Rousseeuw (2023). cellWise: Analyzing Data with Cellwise Outliers. R package version 2.5.3, https://CRAN.R-project.org/package=cellWise

Rousseeuw, P. J. and K. van Driessen (1999). A fast algorithm for the Minimum Covariance Determinant estimator. Technometrics, 41, 212–223. doi:10.2307/1270566

Examples

head(philips)

Plot Diagnostics for an Object of Class wbaconlm

Description

Four plots (selectable by which) are available for an object of class wbaconlm (see wBACON_reg): A plot of residuals against fitted values, a scale-location plot of \sqrt{| residuals |} against fitted values, a Normal Q-Q plot, and a plot of the standardized residuals versus the robust Mahalanobis distances.

Usage

## S3 method for class 'wbaconlm'
plot(x, which = c(1, 2, 3, 4), hex = FALSE,
	caption = c("Residuals vs Fitted", "Normal Q-Q", "Scale-Location",
		"Standardized Residuals vs Robust Mahalanobis Distance"),
	panel = if (add.smooth) function(x, y, ...)
		panel.smooth(x, y, iter = iter.smooth, ...) else points,
    sub.caption = NULL, main = "",
	ask = prod(par("mfcol")) < length(which) && dev.interactive(),
	...,
	id.n = 3, labels.id = names(residuals(x)), cex.id = 0.75,
	qqline = TRUE,
	add.smooth = getOption("add.smooth"), iter.smooth = 3,
	label.pos = c(4, 2), cex.caption = 1, cex.oma.main = 1.25)

Arguments

Details

The plots for which %in% 1:3 are identical with the plot method for linear models (see plot.lm). There you can find details on the implementation and references.

The standardized residuals vs. robust Mahalanobis distance plot (which = 4) has been proposed by Rousseeuw and van Zomeren (1990).

Value

[no return value]

References

Rousseeuw, P.J. and B.C. van Zomeren (1990). Unmasking Multivariate Outliers and Leverage Points, Journal of the American Statistical Association, 411, 633–639. doi:10.2307/2289995

See Also

wBACON_reg

Plot Diagnostics for an Object of Class wbaconmv

Description

Two plots (selectable by which) are available for an object of class wbaconmv: (1) Robust distance vs. Index and (2) Robust distance vs. Univariate projection.

Usage

## S3 method for class 'wbaconmv'
plot(x, which = 1:2,
    caption = c("Robust distance vs. Index",
    "Robust distance vs. Univariate projection"), hex = FALSE, col = 2,
    pch = 19, ask = prod(par("mfcol")) < length(which) && dev.interactive(),
    alpha = 0.05, maxiter = 20, tol = 1e-5, ...)
SeparationIndex(object, alpha = 0.05, tol = 1e-5, maxiter = 20)

Arguments

Details

The first plot (which = 1) is a standard diagnostic tool which plots the observations' index (1:n) against.the robust (Mahalanobis) distances; see. e.g., Rousseeuw and van Driessen (1999).

The second plot (which = 2) plots the univariate projection of the data which maximizes the separation criterion for clusters of Qui and Joe (2006) against.the robust (Mahalanobis) distances. This plot is due to Willems et al. (2009).

For large data sets, it is recommended to specify the argument hex = TRUE. This option shows a hexagonally binned scatterplot in place of the classical scatterplot.

Value

[no return value]

References

Rousseeuw, P.J. and K. van Driessen (1999). A Fast Algorithm for the Minimum Covariance Determinant, Technometrics, 41, 212–223. doi:10.2307/1270566

Qiu, W. and H. Joe (2006). Separation index and partial membership for clustering, Computational Statistics and Data Analysis, 50, 585–603. doi:10.1016/j.csda.2004.09.009

Willems, G., H. Joe, and R. Zamar (2009). Diagnosing Multivariate Outliers Detected by Robust Estimators, Journal of Computational and Graphical Statistics, 18, 73–91. doi:10.1198/jcgs.2009.0005

See Also

wBACON

Predicted Values Based on the Weighted BACON Linear Regression

Description

This function does exactly what predict does for the linear model lm; see predict.lm for more details.

Usage

## S3 method for class 'wbaconlm'
predict(object, newdata, se.fit = FALSE, scale = NULL,
    df = Inf, interval = c("none", "confidence", "prediction"), level = 0.95,
    type = c("response", "terms"), terms = NULL, na.action = na.pass, ...)

Arguments

Value

predict.wbaconlm produces a vector of predictions or a matrix of predictions and bounds with column names fit, lwr, and upr if interval is set. For type = "terms" this is a matrix with a column per term and may have an attribute "constant".

If se.fit is TRUE, a list with the following components is returned:

See Also

wBACON_reg

Examples

data(iris)
m <- wBACON_reg(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width,
    data = iris)
predict(m, newdata = data.frame(Sepal.Width = 1, Petal.Length = 1,
    Petal.Width = 1))

Weighted Sample Quantiles

Description

quantile_w computes the weighted population quantiles.

Usage

quantile_w(x, w, probs, na.rm = FALSE)

Arguments

Details

Overview.

quantile_w computes the weighted sample quantiles; argument probs allows vector inputs.

Implementation.

The function is based on a weighted version of the quickselect algorithm with the Bentley and McIlroy (1993) 3-way partitioning scheme. For very small arrays, we use insertion sort.

Compatibility.

For equal weighting, i.e. when all elements in w are equal, quantile_w computes quantiles that are identical with type = 2 in stats::quantile; see also Hyndman and Fan (1996).

Value

Weighted estimate of the population quantiles.

References

Bentley, J.L. and D.M. McIlroy (1993). Engineering a Sort Function, Software - Practice and Experience, 23, 1249–1265. doi:10.1002/spe.4380231105

Hyndman, R.J. and Y. Fan (1996). Sample Quantiles in Statistical Packages, The American Statistician, 50, 361–365.doi:10.2307/2684934

See Also

median_w

Weighted BACON Algorithm for Multivariate Outlier Detection

Description

wBACON is an iterative method for the computation of multivariate location and scatter (under the assumption of a Gaussian distribution).

Usage

wBACON(x, weights = NULL, alpha = 0.05, collect = 4, version = c("V2", "V1"),
    na.rm = FALSE, maxiter = 50, verbose = FALSE, n_threads = 2)
distance(x)
## S3 method for class 'wbaconmv'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
## S3 method for class 'wbaconmv'
summary(object, ...)
center(object)
## S3 method for class 'wbaconmv'
vcov(object, ...)

Arguments

Details

The algorithm is initialized from a set of uncontaminated data. Then the subset is iteratively refined; i.e., additional observations are included into the subset if their Mahalanobis distance is below some threshold (likewise, observations are removed from the subset if their distance larger than the threshold). This process iterates until the set of good data remain stable. Observations not among the good data are outliers; see Billor et al. (2000). The weighted Bacon algorithm is due to Béguin and Hulliger (2008).

The threshold for the (squared) Mahalanobis distances is defined as the standardized chi-square 1 - \alpha quantile. All observations whose squared Mahalanobis distances is larger than the threshold are regarded as outliers.

If the sampling weights weights are not explicitly specified (i.e., weights = NULL), they are taken to be 1.0.

Incomplete/missing data

The wBACON cannot deal with missing values. In contrast, function BEM in package modi implements the BACON-EEM algorithm of Béguin and Hulliger (2008), which is tailored to work with outlying and missing values.

If the argument na.rm is set to TRUE the method behaves like na.omit.

Assumptions

The BACON algorithm assumes that the non-outlying data have (roughly) an elliptically contoured distribution (this includes the Gaussian distribution as a special case). "Although the algorithms will often do something reasonable even when these assumptions are violated, it is hard to say what the results mean." (Billor et al., 2000, p. 289)

In line with Billor et al. (2000, p. 290), we use the term outlier "nomination" rather than "detection" to highlight that algorithms should not go beyond nominating observations as potential outliers; see also Béguin and Hulliger (2008). It is left to the analyst to finally label outlying observations as such.

Utility functions and tools

Diagnostic plots are available by the plot method.

The method center and vcov return, respectively, the estimated center/location and covariance matrix.

The distance method returns the robust Mahalanobis distances.

The function is_outlier returns a vector of logicals that flags the nominated outliers.

Value

An object of class wbaconmv with slots

References

Billor N., Hadi A.S. and Vellemann P.F. (2000). BACON: Blocked Adaptive Computationally efficient Outlier Nominators. Computational Statistics and Data Analysis, 34, pp. 279–298. doi:10.1016/S0167-9473(99)00101-2

Béguin C. and Hulliger B. (2008). The BACON-EEM Algorithm for Multivariate Outlier Detection in Incomplete Survey Data. Survey Methodology, 34, pp. 91–103. https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X200800110616

Schoch, T. (2021). wbacon: Weighted BACON algorithms for multivariate outlier nomination (detection) and robust linear regression, Journal of Open Source Software, 6 (62), 3238 doi:10.21105/joss.03238

See Also

plot and is_outlier

Examples

data(swiss)
dt <- swiss[, c("Fertility", "Agriculture", "Examination", "Education",
    "Infant.Mortality")]
m <- wBACON(dt)
m

# indicator vector of potential outliers
is_outlier(m)

# names of the potential outliers
is_outlier(m, names = TRUE)

Robust Fitting Linear Regression Models by the BACON Algorithm

Description

The weighted BACON algorithm is a robust method to fit weighted linear regression models. The method is robust against outlier in the response variable and the design matrix (leverage observation).

Usage

wBACON_reg(formula, weights = NULL, data, collect = 4, na.rm = FALSE,
    alpha = 0.05, version = c("V2", "V1"), maxiter = 50, verbose = FALSE,
    original = FALSE, n_threads = 2)

## S3 method for class 'wbaconlm'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
## S3 method for class 'wbaconlm'
summary(object, ...)
## S3 method for class 'wbaconlm'
fitted(object, ...)
## S3 method for class 'wbaconlm'
residuals(object, ...)
## S3 method for class 'wbaconlm'
coef(object, ...)
## S3 method for class 'wbaconlm'
vcov(object, ...)

Arguments

Details

First, the wBACON method is applied to the model's design matrix (having removed the regression intercept/constant, if there is a constant) to establish a subset of observations which is supposed to be free of outliers. Second, the so generated subset is regressed onto the corresponding subset of response variables. The subset is iteratively enlarged to include as many “good” observations as possible.

The original approach of Billor et al. (2000) obtains by specifying the argument original = TRUE.

Models for wBACON_reg are specified symbolically. A typical model has the form response ~ terms, where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response.

A formula has an implied intercept term. To remove this use either y ~ x - 1 or y ~ 0 + x. See formula or lm for for more details.

The weights argument can be used to specify sampling weights or case weights.

It is not possible to fit multiple response variables (on the r.h.s. of the formula, i.e. multivariate models) in one call.

The method cannot deal with missing values. If the argument na.rm is set to TRUE the method behaves like na.omit.

Assumptions

The algorithm assumes that the non-outlying data follow a linear (homoscedastic) regression model and that the independent variables have (roughly) an elliptically contoured distribution. “Although the algorithms will often do something reasonable even when these assumptions are violated, it is hard to say what the results mean.” (Billor et al., 2000, p. 289)

In line with Billor et al. (2000, p. 290), we use the term outlier “nomination” rather than “detection” to highlight that algorithms should not go beyond nominating observations as potential outliers. It is left to the analyst to finally label outlying observations as such.

Utility functions and tools

The generic functions coef, fitted, residuals, and vcov extract the estimate coefficients, fitted values, residuals, and the covariance matrix of the estimated coefficients.

The function summary summarizes the estimated model.

Value

An object of class wbaconlm with slots

References

Billor N., Hadi A.S. and Vellemann P.F. (2000). BACON: Blocked Adaptive Computationally efficient Outlier Nominators. Computational Statistics and Data Analysis, 34, pp. 279–298. doi:10.1016/S0167-9473(99)00101-2

Schoch, T. (2021). wbacon: Weighted BACON algorithms for multivariate outlier nomination (detection) and robust linear regression, Journal of Open Source Software, 6 (62), 3238 doi:10.21105/joss.03238

See Also

plot gives diagnostic plots for an wbaconlm object.

predict is used for prediction (incl. confidence and prediction intervals).

Examples

data(iris)
m <- wBACON_reg(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width,
    data = iris)
m

# model summary
summary(m)

# names of potential outliers
is_outlier(m, names = TRUE)