Package 'wbacon' reference manual

Package 'wbacon'

Title:	Weighted BACON Algorithms
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>.
Authors:	Tobias Schoch [aut, cre] , R-core [cph] (plot.wbaconlm derives from plot.lm)
Maintainer:	Tobias Schoch <[email protected]>
License:	GPL (>= 2)
Version:	0.6-2
Built:	2024-11-07 06:45:16 UTC
Source:	CRAN

Title:

Weighted BACON Algorithms

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>.

Authors:

Tobias Schoch [aut, cre]

, R-core [cph] (plot.wbaconlm derives from plot.lm)

Maintainer:

Tobias Schoch <[email protected]>

License:

GPL (>= 2)

Version:

0.6-2

Built:

2024-11-07 06:45:16 UTC

Source:

CRAN

Help Index

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

Returns a logical vector that indicates which observations were declared outlier by the method.

Usage

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

Arguments

`object`	object of class `wbaconmv` or `wbaconlm`.
`...`	additional arguments passed to the method.

Value

A logical vector.

Examples

data(swiss)
m <- wBACON(swiss)
is_outlier(m)

data(swiss)
m <- wBACON(swiss)
is_outlier(m)

Weighted Median

Description

median_w computes the weighted population median.

Usage

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

Arguments

`x`	`[numeric vector]` observations.
`w`	`[numeric vector]` weights (same length as vector `x`).
`na.rm`	`[logical]` indicating whether `NA` values should be removed before the computation proceeds (default: `FALSE`).

Details

Weighted sample median; see quantile_w for more information.

Value

Weighted estimate of the population median.

Philips data

Description

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

Usage

data(philips)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)
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)
## 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

`x`	object of class `wbaconlm`.
`which`	if a subset of the plots is required, specify a subset of the numbers `1:4`, `[integer]`.
`hex`	toogle a hexagonally binned plot, `[logical]`, default `hex = FALSE`.
`caption`	captions to appear above the plots; `[character]` vector of valid graphics annotations. It can be set to `""` or `NA` to suppress all captions.
`panel`	panel function. The useful alternative to `points`, `panel.smooth` can be chosen by `add.smooth = TRUE`.
`sub.caption`	common title `[character]`—above the figures if there are more than one; used as `sub` (s.`title`) otherwise. If `NULL`, as by default, a possible abbreviated version of `deparse(x$call)` is used.
`main`	title to each plot `[character]`—in addition to `caption`.
`ask`	`[logical]`; if `TRUE`, the user is asked before each plot, see `par(ask=.)`.
`...`	other parameters to be passed through to plotting functions.
`id.n`	number of points to be labelled in each plot, starting with the most extreme, `[integer]`.
`labels.id`	vector of labels `[character]`, from which the labels for extreme points will be chosen. `NULL` uses observation numbers.
`cex.id`	magnification of point labels, `[numeric]`.
`qqline`	`[logical]` indicating if a `qqline()` should be added to the normal Q-Q plot.
`add.smooth`	`[logical]` indicating if a smoother should be added to most plots; see also `panel` above.
`iter.smooth`	the number of robustness iterations `[integer]`, the argument `iter` in `panel.smooth()`.
`label.pos`	positioning of labels `[numeric]`, for the left half and right half of the graph respectively, for plots 1-3.
`cex.caption`	controls the size of `caption`, `[numeric]`.
`cex.oma.main`	controls the size of the `sub.caption` only if that is above the figures when there is more than one, `[numeric]`.

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

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)
## 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

`x`	object of class `wbaconmv`
`which`	if a subset of the plots is required, specify a subset of the numbers `1:2`, `[integer]`.
`caption`	captions to appear above the plots; `[character]` vector of valid graphics annotations. It can be set to `""` or `NA` to suppress all captions.
`hex`	toogle the hexagonal bin plot on/off `[logical]` (default: `hex = FALSE`)
`col`	color of outliers, `[integer]` (default: `col = 2`)
`pch`	plot character of outliers, `[integer]` (default: `pch = 19`)
`ask`	`[logical]`; if `TRUE`, the user is asked before each plot, see `par(ask=.)`.
`alpha`	`[numeric]` tuning constant, level of significance, $0 < \alpha < 1$ ; (default: `alpha = 0.05`).
`maxiter`	`[integer]` maximal number of iterations (default: `maxiter = 20`).
`tol`	numerical termination criterion, `[numeric]` (default: `tol = 1e-5`)
`object`	object of class `wbaconmv`
`...`	additional arguments passed to the method.

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

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, ...)
## 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

`object`	Object of class inheriting from `"lm"`
`newdata`	An optional data frame in which to look for variables with which to predict. If omitted, the fitted values are used.
`se.fit`	A switch `[logical]` indicating if standard errors are required.
`scale`	Scale parameter for std.err. calculation, `[numeric]`.
`df`	Degrees of freedom for scale, `[integer]`.
`interval`	Type of interval calculation, `[character]`. Can be abbreviated.
`level`	Tolerance/confidence level, `[numeric]`.
`type`	Type of prediction (response or model term), `[character]`. Can be abbreviated.
`terms`	If `type = "terms"`, which terms (default is all terms), a `[character]` vector.
`na.action`	function determining what should be done with missing values in `newdata`. The default is to predict `NA`.
`...`	further arguments passed to `predict.lm`

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:

`fit`	vector or matrix as above
`se.fit`	standard error of predicted means
`residual.scale`	residual standard deviations
`df`	degrees of freedom for residual

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

Arguments

`x`	`[numeric vector]` observations.
`w`	`[numeric vector]` weights (same length as vector `x`).
`probs`	`[numeric vector]` vector of probabilities with values in `[0,1]`.
`na.rm`	`[logical]` indicating whether `NA` values should be removed before the computation proceeds (default: `FALSE`).

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

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, ...)
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

`x`	`[matrix]` or `[data.frame]`.
`weights`	`[numeric]` sampling weight (default `weights = NULL`).
`alpha`	`[numeric]` tuning constant, level of significance, $0 < \alpha < 1$ ; (default: `alpha = 0.05`).
`collect`	determines the size $m$ of the initial subset to be $m = collect \cdot p$ , where $p$ is the number of variables, `[integer]`.
`version`	`[character]` method of initialization; `"V1"`: weighted Mahalanobis distances (not robust but affine equivariant); `"V2"` (`default`): Euclidean norm of the data centered by the coordinate-wise weighted median.
`na.rm`	`[logical]` indicating whether `NA` values should be removed before the computation proceeds (default: `FALSE`).
`maxiter`	`[integer]` maximal number of iterations (default: `maxiter = 50`).
`verbose`	`[logical]` indicating whether additional information is printed to the console (default: `TRUE`).
`n_threads`	`[integer]` number of threads used for OpenMP (`default: 2`).
`digits`	`[integer]` minimal number of significant digits.
`...`	additional arguments passed to the method.
`object`	object of class `wbaconmv`.

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

`x`	see function arguments
`weights`	see function arguments
`center`	estimated center of the data
`dist`	Mahalanobis distances
`n`	number of observations
`p`	number of variables
`alpha`	see function arguments
`subset`	final subset of outlier-free data
`cutoff`	see function arguments
`maxiter`	number of iterations until convergence
`version`	see functions arguments
`collect`	see functions arguments
`cov`	covariance matrix
`converged`	logical that indicates whether the algorithm converged
`call`	the matched call

References

Examples

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

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

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, ...)
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

`formula`	an object of class `formula`: a symbolic description of the model to be fitted.
`weights`	`[numeric]` sampling weight (default `weights = NULL`).
`data`	a `data.frame` object.
`collect`	determines the size $m$ of the initial subset to be $m = collect \cdot p$ , where $p$ is the number of variables, `[integer]`.
`na.rm`	`[logical]` indicating whether `NA` values should be removed before the computation proceeds (default: `FALSE`).
`alpha`	`[numeric]` tuning constant, level of significance, $0 < \alpha < 1$ ; (default: `alpha = 0.05`).
`version`	method to initialize the basic subset, `[character]`: Version `"V1"` of Billor et al. (2000) yields affine equivariant but not robust estimators; Version `"V1"` yields estimators that are robust but not affine equivariant; (default: `V2`).
`maxiter`	`[integer]` maximal number of iterations (default: `maxiter = 50`).
`verbose`	`[logical]` indicating whether additional information is printed to the console (default: `TRUE`).
`original`	`[logical]` if `original = TRUE` the subset of the $m = collect \cdot p$ smallest observations (small w.r.t. to the Mahalanobis distances) is taken from the subset generated by Algorithm 3 as the basic subset for regression [this is the original method of Billor et al. (2000)]; otherwise (i.e., when `original = FALSE`) the subset that results from Algorithm 3 of Billor et al. (2000) is taken to be the basic subset for regression (default `original = FALSE`).
`n_threads`	`[integer]` number of threads used for OpenMP (`default: 2`).
`digits`	`[integer]` minimal number of significant digits.
`object`	object of class `wbaconlm`.
`x`	object of class `wbaconlm`.
`...`	additional arguments passed to the method.

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

`coefficients`	a named vector of coefficients
`residuals`	the residuals (for all observations in the data.frame not only the ones in the final subset
`rank`	the numeric rank of the fitted linear model (i.e.. number of variables in the design matrix
`fitted.values`	fitted values
`df.residual`	the residual degrees of freedom (computed for the observations in the final subset)
`call`	the matched call
`terms`	the `terms` object
`model`	the `model.frame` used
`weights`	weights
`qr`	the `qr` object of the linear model fit for the final subset
`subset`	the subset
`reg`	a list with additional details on `wBACON_reg`
`mv`	a list with details on the results of `wBACON` that have been used to initialize `wBACON_reg`

References

Examples

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

Package 'wbacon'

Help Index

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

Description

Details

Author(s)

References

Flag Outliers

Description

Usage

Arguments

Value

See Also

Examples

Weighted Median

Description

Usage

Arguments

Details

Value

See Also

Philips data

Description

Usage

Format

Details

Source

Examples

Plot Diagnostics for an Object of Class wbaconlm

Description

Usage

Arguments

Details

Value

References

See Also

Plot Diagnostics for an Object of Class wbaconmv

Description

Usage

Arguments

Details

Value

References

See Also

Predicted Values Based on the Weighted BACON Linear Regression

Description

Usage

Arguments

Value

See Also

Examples

Weighted Sample Quantiles

Description

Usage

Arguments

Details

Value

References

See Also

Weighted BACON Algorithm for Multivariate Outlier Detection

Description

Usage

Arguments

Details

Incomplete/missing data

Assumptions

Utility functions and tools

Value

References

See Also

Examples

Robust Fitting Linear Regression Models by the BACON Algorithm

Description

Usage

Arguments

Details

Assumptions

Utility functions and tools

Value

References

Plot Diagnostics for an Object of Class `wbaconlm`

Plot Diagnostics for an Object of Class `wbaconmv`