DCML regression estimator

Description

This function computes the DCML regression estimator. This function is used internally by lmrobdetDCML, and not meant to be used directly.

Usage

DCML(x, y, z, z0, control)

Arguments

Value

a list with the following components

Author(s)

Victor Yohai, victoryohai@gmail.com, Matias Salibian-Barrera, matias@stat.ubc.ca

References

http://www.wiley.com/go/maronna/robust

See Also

DCML, MMPY, SMPY

Robust R^2 coefficient of determination

Description

This function computes a robust version of the R^2 coefficient of determination. It is used internally by lmrobdetMM, and not meant to be used directly.

Usage

INVTR2(RR2, family, cc)

Arguments

Details

This function computes a robust version of the R^2 coefficient. It is used internally by lmrobdetMM, and not meant to be used directly.

Value

An unbiased version of the robust R^2 coefficient of determination.

Author(s)

Victor Yohai, victoryohai@gmail.com

References

http://www.wiley.com/go/maronna/robust

MM regression estimator using Pen~a-Yohai candidates

Description

This function computes MM-regression estimator using Pen~a-Yohai candidates for the initial S-estimator. This function is used internally by lmrobdetMM, and not meant to be used directly.

Usage

MMPY(X, y, control, mf)

Arguments

Value

an lmrob object witht the M-estimator obtained starting from the S-estimator computed with the Pen~a-Yohai initial candidates. The properties of the final estimator (efficiency, etc.) are determined by the tuning constants in the argument control.

Author(s)

Victor Yohai, victoryohai@gmail.com, Matias Salibian-Barrera, matias@stat.ubc.ca

References

http://www.wiley.com/go/maronna/robust

See Also

DCML, MMPY, SMPY

SM regression estimator using Pen~a-Yohai candidates

Description

This function computes a robust regression estimator when there are categorical / dummy explanatory variables. It uses Pen~a-Yohai candidates for the S-estimator. This function is used internally by lmrobdetMM, and not meant to be used directly.

Usage

SMPY(mf, y, control, split)

Arguments

Value

an lmrob object witht the M-estimator obtained starting from the MS-estimator computed with the Pen~a-Yohai initial candidates. The properties of the final estimator (efficiency, etc.) are determined by the tuning constants in the argument control.

Author(s)

Victor Yohai, victoryohai@gmail.com, Matias Salibian-Barrera, matias@stat.ubc.ca

References

http://www.wiley.com/go/maronna/robust

See Also

DCML, MMPY, SMPY

Alcohol data

Description

This data set contains physicochemical characteristics of 44 aliphatic alcohols. The aim of the experiment was the prediction of the solubility on the basis of molecular descriptors.

Usage

data(alcohol)

Format

An object of class "data.frame".

Details

Format: 44 cases and 7 continuous variables. The columns are: 1. SAG=solvent accessible surface-bounded molecular volume 2. V=volume 3. log PC (PC=octanol–water partitions coefficient) 4. P=polarizability 5. RM=molar refractivity 6. Mass 7. log(Solubility) (response)

Source

Romanelli, G.P., Martino, C.M. and Castro, E.A. (2001), Modeling the solubility of aliphatic alcohols via molecular descriptors, Journal of the Chemical Society of Pakistan, 23, 195-199.

Examples

data(alcohol)

Algae data

Description

Each row of the data set is a set of 90 measurements at a river in some place in Europe. There are 11 predictors. The response is the logarithm of the abundance of a certain class of algae. Description: The columns are: 1. season, categorical (1,2,3,4 for winter, spring, summer and autumn) 2. river size (categorical) (1,2,3 for small, medium and large) 3. fluid velocity (categorical) (1,2,3 for low, medium and high) 4-11 (numerci): content of nitrogen in the form of nitrates, nitrites and ammonia, and other chemical compounds. Col. 12 ia the response: abundance of a type of algae (type 6 in the complete file). For simplicity we deleted the rows with missing values and took the logarithm of the response.

Usage

data(algae)

Format

An object of class "data.frame".

Details

Format 90 rows, 12 columns (3 categorical, 9 numeric)

Source

Hettich, S. and Bay, S.D. (1999), The UCI KDD Archive http://kdd.ics.uci.edu. Irvine, CA: University of California, Department of Information and Computer Science.

References

References go here.

Examples

data(algae)

Biochem data

Description

Two biochemical measurements on 12 men with similar weights.

Usage

data(biochem)

Format

An object of class "data.frame".

Details

Format: Numeric, 12 rows, two columns

Source

Seber, G.A.F. (1984), Multivariate Observations. New York: John Wiley.

Examples

data(biochem)

Tuning parameter the rho loss functions

Description

This function computes the tuning constant that yields an MM-regression estimator with a desired asymptotic efficiency when computed with a rho function in the corresponding family. The output of this function can be passed to the functions lmrobdet.control, scaleM and rho.

Usage

bisquare(e)

Arguments

Value

A length-1 vector with the corresponding tuning constant.

Author(s)

Kjell Konis

Examples

# Tuning parameters for an 85%-efficient M-estimator at a Gaussian model
bisquare(.85)

Breslow Data

Description

Patients suffering from simple or complex partial seizures were randomized to receive either the antiepileptic drug progabide or a placebo. At each of four successive post randomization clinic visits, the number of seizures occuring over the previous two weeks was reported.

Usage

data(breslow.dat)

Format

An object of class "data.frame".

Details

Description: A data frame with 59 observations on the following 12 variables: ID: an integer value specifying the patient identification number; Y1: an integer value, the number of seizures during the first two week period; Y2: an integer value, the number of seizures during the second two week period; Y3: an integer value, the number of seizures during the third two week period. Y4: an integer value, the number of seizures during the fourth two week period; Base: an integer value giving the eight-week baseline seizure count; Age: an integer value giving the age of the parient in years; Trt: the treatment: a factor with levels placebo and progabide; Ysum: an integer value, the sum of Y1, Y2, Y3 and Y4; sumY: an integer value, the sum of Y1, Y2, Y3 and Y4; Age10: a numeric value, Age divided by 10; Base4: a numeric value, Base divided by 4.

Format: Numeric, 59 rows and 12 columns.

Source

Breslow, N. E., and Clayton, D. G. (1993), "Approximate Inference in Generalized Linear Mixed Models," Journal of the American Statistical Association, Vol. 88, No. 421, pp. 9-25.

Thrall, P. F., and Vail, S. C. (1990), "Some Covariance Models for Longitudinal Count Data With Overdispersion," Biometrics, Vol. 46, pp. 657-671.

Examples

data(breslow.dat)

Bus data

Description

This data set corresponds to a study in automatic vehicle recognition. Each of the 218 rows corresponds to a view of a bus silhouette, and contains 18 attributes of the image. It was decided to exclude variable 9 and divide the remaining variables by their MADN’s.

Usage

data(bus)

Format

An object of class "data.frame".

Details

Description: The following features were extracted from the silhouettes. 1. compactness 2. circularity 3. distance circularity 4. radius ratio 5. principal axis aspect ratio 6. maximum length aspect ratio 7. scatter ratio 8. elongatedness 9. principal axis rectangularity 10. maximum length rectangularity 11. scaled variance along major axis 12. scaled variance along minor axis 13. scaled radius of gyration 14. skewness about major axis 15. skewness about minor axis 16. kurtosis about minor axis 17. kurtosis about major axis 18. hollows ratio

Format: Numeric, 218 rows and 18 columns.

Source

Hettich, S. and Bay, S.D. (1999), The UCI KDD Archive http://kdd.ics.uci.edu. Irvine, CA: University of California, Department of Information and Computer Science.

Examples

data(bus)

Approximate covariance matrix of the DCML regression estimator.

Description

The estimated covariance matrix of the DCML regression estimator. This function is used internally and not meant to be used directly.

Usage

cov.dcml(res.LS, res.R, CC, sig.R, t0, p, n, control)

Arguments

Value

The covariance matrix estimate.

Author(s)

Victor Yohai, victoryohai@gmail.com

Classical Covariance Estimation

Description

Compute an estimate of the covariance/correlation matrix and location vector using classical methods.

Usage

covClassic(
  data,
  corr = FALSE,
  center = TRUE,
  distance = TRUE,
  na.action = na.fail,
  unbiased = TRUE
)

Arguments

Details

Its main intention is to return an object compatible to that produced by covRob, but fit using classical methods.

Value

a list with class “covClassic” containing the following elements:

Note

Originally, and in S-PLUS, this function was called cov; it has been renamed, as that did mask the function in the standard package stats.

Examples

data(wine)
round( covClassic(wine)$cov, 2)

Robust multivariate location and scatter estimators

Description

This function computes robust estimators for multivariate location and scatter.

Usage

covRob(X, type = "auto", maxit = 50, tol = 1e-04, corr = FALSE)

Arguments

Details

This function computes robust estimators for multivariate location and scatter. The default behaviour (type = "auto") computes a "Rocke" estimator (as implemented in covRobRocke) if the number of variables is greater than or equal to 10, and an MM-estimator with a SHR rho function (as implemented in covRobMM) otherwise.

Value

A list with class “covClassic” with the following components:

Author(s)

Ricardo Maronna, rmaronna@retina.ar

References

http://www.wiley.com/go/maronna/robust

See Also

covRobRocke, covRobMM

Examples

data(bus)
X0 <- as.matrix(bus)
X1 <- X0[,-9]
tmp <- covRob(X1)
round(tmp$cov[1:10, 1:10], 3)
tmp$mu

MM robust multivariate location and scatter estimator

Description

This function computes an MM robust estimator for multivariate location and scatter with the "SHR" loss function.

Usage

covRobMM(X, maxit = 50, tolpar = 1e-04, corr = FALSE)

Arguments

Details

This function computes an MM robust estimator for multivariate location and scatter with the "SHR" loss function.

Value

A list with class “covRob” containing the following elements

Author(s)

Ricardo Maronna, rmaronna@retina.ar

References

http://www.wiley.com/go/maronna/robust

Examples

data(bus)
X0 <- as.matrix(bus)
X1 <- X0[,-9]
tmp <- covRobMM(X1)
round(tmp$cov[1:10, 1:10], 3)
tmp$mu

Rocke's robust multivariate location and scatter estimator

Description

This function computes Rocke's robust estimator for multivariate location and scatter.

Usage

covRobRocke(
  X,
  initial = "K",
  maxsteps = 5,
  propmin = 2,
  qs = 2,
  maxit = 50,
  tol = 1e-04,
  corr = FALSE
)

Arguments

Details

This function computes Rocke's robust estimator for multivariate location and scatter.

Value

A list with class “covRob” containing the following elements:

Author(s)

Ricardo Maronna, rmaronna@retina.ar

References

http://www.wiley.com/go/maronna/robust

Examples

data(bus)
X0 <- as.matrix(bus)
X1 <- X0[,-9]
tmp <- covRobRocke(X1)
round(tmp$cov[1:10, 1:10], 3)
tmp$mu

RFPE of submodels of an lmrobdetMM fit

Description

This function computes the RFPE for the MM-estimators obtained with lmrobdetMM by recomputing it, successively removing each of a number of specified terms. It is used internally by step.lmrobdetMM and not meant to be used directly.

Usage

## S3 method for class 'lmrobdetMM'
drop1(object, scope, scale, keep, ...)

Arguments

Value

An anova object consisting of the term labels, the degrees of freedom, and Robust Final Prediction Errors (RFPE) for each subset model. If keep is missing, the anova object is returned. If keep is present, a list with components "anova" and "keep" is returned. In this case, the "keep" component is a matrix of mode "list", with a column for each subset model, and a row for each component kept.

Author(s)

Victor Yohai, victoryohai@gmail.com, Matias Salibian-Barrera, matias@stat.ubc.ca

References

http://www.wiley.com/go/maronna/robust

See Also

lmrobdetMM

Minimum Volume Ellipsoid covariance estimator

Description

This function uses a fast algorithm to compute the Minimum Volume Ellipsoid (MVE) for multivariate location and scatter.

Usage

fastmve(x, nsamp = 500)

Arguments

Details

This function computes the Minimum Volume Ellipsoid (MVE) for multivariate location and scatter, using a fast algorithm related to the fast algorithm for S-regression estimators (see lmrob).

Value

A list with the following components:

Author(s)

Matias Salibian-Barrera, matias@stat.ubc.ca

References

http://www.wiley.com/go/maronna/robust

Examples

data(bus)
X0 <- as.matrix(bus)
X1 <- X0[,-9]
tmp <- fastmve(X1)
round(tmp$cov[1:10, 1:10], 3)
tmp$center

Flour data

Description

Determinations of the copper content in wholemeal flour (in parts per million), sorted in ascending order. Format: numeric vector of size 24.

Usage

data(flour)

Format

An object of class "data.frame".

Source

Analytical Methods Committee (1989), Robust statistics-How not to reject outliers, Analyst, 114, 1693-1702.

References

References go here.

Examples

data(flour)

Glass data

Description

Measurements of the presence of seven chemical constituents in 76 pieces of glass from nonfloat car windows.

Usage

data(glass)

Format

An object of class "data.frame".

Details

Format: 76 cases and 7 continuous variables. Description: The columns are: 1. RI refractive index 2. Na2O sodium oxide (unit measurement: weight percent in corresponding oxide, as are the rest of attributes) 3. MgO magnesium oxide 4. Al2O3 aluminum oxide 5. SiO2 silcon oxide 6. K2O potassium oxide 7. CaO calcium oxide

Source

Hettich, S. and Bay, S.D. (1999), The UCI KDD Archive http://kdd.ics.uci.edu, Irvine, CA: University of California, Department of Information and Computer Science.

Examples

data(glass)

Hearing data

Description

Prevalence rates in percent for men aged 55–64 with hearing levels 16 decibels or more above the audiometric zero.

Usage

data(hearing)

Format

An object of class "data.frame".

Details

Format: Two-way ANOVA. Description: The rows correspond to different frequencies and to normal speech. 1. 500 hertz 2. 1000 hertz 3. 2000 hertz 4. 3000 hertz 5. 4000 hertz 6. 6000 hertz 7. Normal speech The columns classify the data in seven occupational groups: 1. professional–managerial 2. farm 3. clerical sales 4. craftsmen 5. operatives 6. service 7. laborers

Source

Roberts, J. and Cohrssen, J. (1968), Hearing levels of adults, US National Center for Health Statistics Publications, Series 11, No. 31

Examples

data(hearing)

Tuning parameter the rho loss functions

Description

This function computes the tuning constant that yields an MM-regression estimator with a desired asymptotic efficiency when computed with a rho function in the corresponding family. The output of this function can be passed to the functions lmrobdet.control, scaleM and rho.

Usage

huber(e)

Arguments

Value

A length-1 vector with the corresponding tuning constant.

Author(s)

Kjell Konis

Examples

# Tuning parameters for an 85%-efficient M-estimator at a Gaussian model
huber(.95)

Image data

Description

These data are part of a synthetic aperture satellite radar image corresponding to a suburb of Munich, and contain the values corresponding to three frequency bands for each of 1573 pixels of a radar image.

Usage

data(image)

Format

An object of class "data.frame".

Details

Format: 1573 cases and 3 variables.

Source

Source: Frery, A. (2005), Personal communication.

Examples

data(image)

Robust multivariate location and scatter estimators

Description

This function computes robust multivariate location and scatter estimators using both random and deterministic starting points.

Usage

initPP(X, muldirand = 20, muldifix = 10, dirmin = 1000)

Arguments

Details

This function computes robust multivariate location and scatter using both Pen~a-Prieto and random candidates.

Value

A list with the following components:

Author(s)

Ricardo Maronna, rmaronna@retina.ar, based on original code by D. Pen~a and J. Prieto

References

http://www.wiley.com/go/maronna/robust

Examples

data(bus)
X0 <- as.matrix(bus)
X1 <- X0[,-9]
tmp <- initPP(X1)
round(tmp$cov[1:10, 1:10], 3)
tmp$center

Leukemia Data

Description

Records for 33 leukemia patients.

Usage

data(leuk.dat)

Format

An object of class "data.frame".

Details

Description: The following features are present: wbc: white blood cell count; ag: presence or absence of a certain morphological characteristic in the white cells; and y: binary response variable, equals 1 if the patient survives more than 52 weeks, 0 otherwise.

Format: Numeric, 33 rows and 3 columns.

Source

Cook, R.D. and Weisberg, S. (1982). Residuals and Influence in Regression, Chapman and Hall; Johnson, W. (1985), Influence measures for logistic regression: another point of view, Biometrika, 72, 59-65.

Examples

data(leuk.dat)

Robust estimators for linear regression with fixed designs

Description

This function computes a robust regression estimator for a linear models with fixed designs.

Usage

lmrobM(
  formula,
  data,
  subset,
  weights,
  na.action,
  model = TRUE,
  x = FALSE,
  y = FALSE,
  singular.ok = TRUE,
  contrasts = NULL,
  offset = NULL,
  control = lmrobM.control()
)

Arguments

Details

This function computes robust regression estimators for linear models with fixed designs. It computes an L1 estimator, and uses it as a starting point to find a minimum of a re-descending M estimator. The scale is set to a quantile of the absolute residuals from the L1 estimator. This function makes use of the functions lmrob.fit, lmrob..M..fit, .vcov.avar1, lmrob.S and lmrob.lar, from robustbase, along with utility functions used by these functions, modified so as to include use of the analytic form of the optimal psi and rho functions (for the optimal psi function , see Section 5.8.1 of Maronna, Martin, Yohai and Salibian Barrera, 2019)

Value

A list with the following components:

Author(s)

Victor Yohai, vyohai@gmail.com, based on lmrob

References

http://www.wiley.com/go/maronna/robust

Examples

data(shock)
cont <- lmrobM.control(bb = 0.5, efficiency = 0.85, family = "bisquare")
shockrob <- lmrobM(time ~ n.shocks, data = shock, control=cont)
shockrob
summary(shockrob)

Tuning parameters for lmrobM

Description

This function sets tuning parameters for the M estimators of regression implemented in lmrobM.

Usage

lmrobM.control(
  bb = 0.5,
  efficiency = 0.99,
  family = "opt",
  tuning.chi,
  tuning.psi,
  max.it = 100,
  rel.tol = 1e-07,
  mscale_tol = 1e-06,
  mscale_maxit = 50,
  trace.lev = 0
)

Arguments

Value

A list with the necessary tuning parameters.

Author(s)

Matias Salibian-Barrera, matias@stat.ubc.ca

Examples

data(coleman, package='robustbase')
m2 <- lmrobM(Y ~ ., data=coleman, control=lmrobM.control())
m2
summary(m2)

Tuning parameters for lmrobdetMM and lmrobdetDCML

Description

This function sets tuning parameters for the MM estimator implemented in lmrobdetMM and the Distance Constrained Maximum Likelihood regression estimators computed by lmrobdetDCML.

Usage

lmrobdet.control(
  bb = 0.5,
  efficiency = 0.95,
  family = "mopt",
  tuning.psi,
  tuning.chi,
  compute.rd = FALSE,
  corr.b = TRUE,
  split.type = "f",
  initial = "S",
  max.it = 100,
  refine.tol = 1e-07,
  rel.tol = 1e-07,
  refine.S.py = 1e-07,
  refine.PY = 10,
  solve.tol = 1e-07,
  trace.lev = 0,
  psc_keep = 0.5,
  resid_keep_method = "threshold",
  resid_keep_thresh = 2,
  resid_keep_prop = 0.2,
  py_maxit = 20,
  py_eps = 1e-05,
  mscale_maxit = 50,
  mscale_tol = 1e-06,
  mscale_rho_fun = "bisquare"
)

Arguments

Details

The argument family specifies the name of the family of loss function to be used. Current valid options are "bisquare", "opt", "mopt", "optV0" and "moptV0". "mopt" is a modified version of the optimal psi function to make it strictly increasing close to 0, and to make the corresponding weight function non-increasing.

Value

A list with the necessary tuning parameters.

Choice of Rho Loss Function

As of RobStatTM Versopm 1.0.7, the opt and mopt rhos functions are calculated using polynomials, rather than using the standard normal error function (erf) as in versions of RobStatTM prior to 1.0.7. The numerical results one now gets with the opt or mopt choices will differ by small amounts from those in earlier RobStatTM versions. Users who wish to replicate results from releases prior to 1.0.7 may do so using the family arguments family = "optV0" or family = "moptV0". Note that the derivative of the rho loss function, known as the "psi" function, is not the derivative of the rho polynomial,instead it is still the analytic optimal psi function whose formula is given in the second of the Vignettes referenced just below.

Related Vignettes

For further details, see the Vignettes "Polynomial Opt and mOpt Rho Functions", and "Optimal Bias Robust Regression Psi and Rho".

Author(s)

Matias Salibian-Barrera, matias@stat.ubc.ca

See Also

scaleM.

Examples

data(coleman, package='robustbase')
m2 <- lmrobdetMM(Y ~ ., data=coleman, control=lmrobdet.control(refine.PY=50))
m2
summary(m2)

Robust Distance Constrained Maximum Likelihood estimators for linear regression

Description

This function computes robust Distance Constrained Maximum Likelihood estimators for linear models.

Usage

lmrobdetDCML(
  formula,
  data,
  subset,
  weights,
  na.action,
  model = TRUE,
  x = !control$compute.rd,
  y = FALSE,
  singular.ok = TRUE,
  contrasts = NULL,
  offset = NULL,
  control = lmrobdet.control()
)

Arguments

Details

This function computes Distance Constrained Maximum Likelihood regression estimators computed using an MM-regression estimator based on Pen~a-Yohai candidates (instead of subsampling ones). This function makes use of the functions lmrob.fit, lmrob..M..fit, .vcov.avar1, lmrob.S and lmrob.lar, from robustbase, along with utility functions used by these functions, modified so as to include use of the analytic form of the optimal psi and rho functions (for the optimal psi function , see Section 5.8.1 of Maronna, Martin, Yohai and Salibian Barrera, 2019)

Value

A list with the following components:

Author(s)

Matias Salibian-Barrera, matias@stat.ubc.ca, based on lmrob

References

http://www.wiley.com/go/maronna/robust

See Also

DCML, MMPY, SMPY

Examples

data(coleman, package='robustbase')
m1 <- lmrobdetDCML(Y ~ ., data=coleman)
m1
summary(m1)

Robust likelihood ratio test for linear hypotheses

Description

This function computes a robust likelihood ratio test for linear hypotheses.

Usage

lmrobdetLinTest(object1, object2)

Arguments

Value

A list with the following components: c("test","chisq.pvalue","f.pvalue","df")

Author(s)

Victor Yohai, vyohai@gmail.com

References

http://www.wiley.com/go/maronna/robust

Examples

data(oats)
cont <- lmrobdet.control(bb = 0.5, efficiency = 0.85, family = "bisquare")
oats1M <- lmrobM(response1 ~ variety+block, control=cont, data=oats)
oats1M_var <- lmrobM(response1 ~ block, control=cont, data=oats)
( anov1M_var <- rob.linear.test(oats1M, oats1M_var) )

Robust Linear Regression Estimators

Description

This function computes an MM-regression estimators for linear models using deterministic starting points.

Usage

lmrobdetMM(
  formula,
  data,
  subset,
  weights,
  na.action,
  model = TRUE,
  x = !control$compute.rd,
  y = FALSE,
  singular.ok = TRUE,
  contrasts = NULL,
  offset = NULL,
  control = lmrobdet.control()
)

Arguments

Details

This function computes MM-regression estimators computed using Pen~a-Yohai candidates (instead of subsampling ones). This function makes use of the functions lmrob.fit, lmrob..M..fit, .vcov.avar1, lmrob.S and lmrob.lar, from robustbase, along with utility functions used by these functions, modified so as to include use of the analytic form of the optimal psi and rho functions (for the optimal psi function , see Section 5.8.1 of Maronna, Martin, Yohai and Salibian Barrera, 2019).

Value

A list with the following components:

Choice of Rho Loss Function

This is done by the user choice of family = "opt" or family = "mopt" in the function lmrobdet.control. As of RobStatTM Versopm 1.0.7, the opt and mopt rhos functions are calculated using polynomials, rather than using the standard normal error function (erf) as in versions of RobStatTM prior to 1.0.7. The numerical results one now gets with the opt or mopt choices will differ by small amounts from those in earlier RobStatTM versions. Users who wish to replicate results from releases prior to 1.0.7 may do so using the family arguments family = "optV0" or family = "moptV0". Note that the derivative of the rho loss function, known as the "psi" function, is not the derivative of the rho polynomial, instead it is still the optimal psi function referred to above.

Related Vignettes

For further details, see the Vignettes "Polynomial Opt and mOpt Rho Functions", and "Optimal Bias Robust Regression Psi and Rho".

Author(s)

Matias Salibian-Barrera, matias@stat.ubc.ca, based on lmrob from package robustbase

References

http://www.wiley.com/go/maronna/robust

See Also

DCML, MMPY, SMPY

Examples

data(coleman, package='robustbase')
m2 <- lmrobdetMM(Y ~ ., data=coleman)
m2
summary(m2)

Robust Final Prediction Error

Description

This function computes the robust Final Prediction Errors (RFPE) for a robust regression fit using M-estimates.

Usage

lmrobdetMM.RFPE(object, scale = NULL, bothVals = FALSE)

Arguments

Value

If the argument bothVals is FALSE, the robust final prediction error (numeric). Otherwise, the two terms of the RFPE expression in equation (5.39), Section 5.6.2 of Maronna et al. (2019), http://www.wiley.com/go/maronna/robust, are returned separately in a list with components named minRhoMM.C and penaltyRFPE

Author(s)

Victor Yohai, victoryohai@gmail.com, Matias Salibian-Barrera, matias@stat.ubc.ca

References

http://www.wiley.com/go/maronna/robust

See Also

lmrobdetMM

Examples

data(coleman, package='robustbase')
m2 <- lmrobdetMM(Y ~ ., data=coleman)
lmrobdetMM.RFPE(m2)

Robust univariate location and scale M-estimators

Description

This function computes M-estimators for location and scale.

Usage

locScaleM(x, psi = "mopt", eff = 0.95, maxit = 50, tol = 1e-04, na.rm = FALSE)

Arguments

Details

This function computes M-estimators for location and scale.

Value

A list with the following components:

Author(s)

Ricardo Maronna, rmaronna@retina.ar

References

http://www.wiley.com/go/maronna/robust

Examples

set.seed(123)
r <- rnorm(150, sd=1.5)
locScaleM(r)
# 10% of outliers, sd of good points is 1.5
set.seed(123)
r2 <- c(rnorm(135, sd=1.5), rnorm(15, mean=-10, sd=.5))
locScaleM(r2)

Bianco and Yohai estimator for logistic regression

Description

This function computes the M-estimator proposed by Bianco and Yohai for logistic regression. By default, an intercept term is included and p parameters are estimated. Modified by Yohai (2018) to take as initial estimator a weighted ML estimator with weights derived from the MCD estimator. For more details we refer to Croux, C., and Haesbroeck, G. (2002), "Implementing the Bianco and Yohai estimator for Logistic Regression"

Usage

logregBY(x0, y, intercept = 1, const = 0.5, kmax = 1000, maxhalf = 10)

Arguments

Value

A list with the following components:

Author(s)

Christophe Croux, Gentiane Haesbroeck, Victor Yohai

References

http://www.wiley.com/go/maronna/robust

Examples

data(skin)
Xskin <- as.matrix( skin[, 1:2] )
yskin <- skin$vasoconst
skinBY <- logregBY(Xskin, yskin, intercept=1)
skinBY$coeff
skinBY$standard.deviation

Bianco and Yohai estimator for logistic regression

Description

This function computes the weighted M-estimator of Bianco and Yohai in logistic regression. By default, an intercept term is included and p parameters are estimated. Modified by Yohai (2018) to take as initial estimator a weighted ML estimator computed with weights derived from the MCD estimator of the continuous explanatory variables. The same weights are used to compute the final weighted M-estimator. For more details we refer to Croux, C., and Haesbroeck, G. (2002), "Implementing the Bianco and Yohai estimator for Logistic Regression"

Usage

logregWBY(x0, y, intercept = 1, const = 0.5, kmax = 1000, maxhalf = 10)

Arguments

Value

A list with the following components:

Author(s)

Christophe Croux, Gentiane Haesbroeck, Victor Yohai

References

http://www.wiley.com/go/maronna/robust

Examples

data(skin)
Xskin <- as.matrix( skin[, 1:2] )
yskin <- skin$vasoconst
skinWBY <- logregWBY(Xskin, yskin, intercept=1)
skinWBY$coeff
skinWBY$standard.deviation

Weighted likelihood estimator for the logistic model

Description

This function computes a weighted likelihood estimator for the logistic model, where the weights penalize high leverage observations. In this version the weights are zero or one.

Usage

logregWML(x0, y, intercept = 1)

Arguments

Value

A list with the following components:

Author(s)

Victor Yohai

References

http://www.wiley.com/go/maronna/robust

Examples

data(skin)
Xskin <- as.matrix( skin[, 1:2] )
yskin <- skin$vasoconst
skinWML <- logregWML(Xskin, yskin, intercept=1)
skinWML$coeff
skinWML$standard.deviation

Mineral data

Description

Contents (in parts per million) of 22 chemical elements in 53 samples of rocks in Western Australia. Two columns (8 and 9) were selected for use in this book.

Usage

data(mineral)

Format

An object of class "data.frame".

Details

Format: Numeric with 53 rows and 2 columns:

Source

Smith, R.E., Campbell, N.A. and Lichfield, A. (1984), Multivariate statistical techniques applied to pisolitic laterite geochemistry at Golden Grove, Western Australia, Journal of Geochemical Exploration, 22, 193-216.

Examples

data(mineral)

Tuning parameter for a rho function in the modified (asymptotic bias-) optimal family

Description

This function computes the tuning constant that yields an MM-regression estimator with a desired asymptotic efficiency when computed with a rho function in the corresponding family. The output of this function can be passed to the functions lmrobdet.control, scaleM and rho.

Usage

mopt(e)

Arguments

Value

A vector with named elements containing the corresponding tuning parameters.

Author(s)

Kjell Konis

Examples

# Tuning parameters for an 85%-efficient M-estimator at a Gaussian model
mopt(.85)

Tuning parameter for a rho function in the modified (asymptotic bias-) optimal family

Description

This function computes the tuning constant that yields an MM-regression estimator with a desired asymptotic efficiency when computed with a rho function in the corresponding family. The output of this function can be passed to the functions lmrobdet.control, scaleM and rho.

Usage

moptv0(e)

Arguments

Value

A vector with named elements containing the corresponding tuning parameters.

Author(s)

Kjell Konis

Examples

# Tuning parameters for an 85%-efficient M-estimator at a Gaussian model
moptv0(.85)

Neuralgia data

Description

Neuralgia data. More details here.

Usage

data(neuralgia)

Format

An object of class "data.frame".

Source

Source goes here.

References

References go here.

Examples

data(neuralgia)

Oats data

Description

Yield of grain for eight varieties of oats in five replications of a randomized-block experiment

Usage

data(oats)

Format

An object of class "data.frame".

Details

Format: Two-way ANOVA table with 8 rows and 5 columns.

Source

Scheffe, H. (1959), Analysis of Variance. New York: John Wiley.

References

References go here.

Examples

data(oats)

Tuning parameter for a rho function in the (asymptotic bias-) optimal family

Description

This function computes the tuning constant that yields an MM-regression estimator with a desired asymptotic efficiency when computed with a rho function in the corresponding family. The output of this function can be passed to the functions lmrobdet.control, scaleM and rho.

Usage

opt(e)

Arguments

Value

A vector with named elements containing the corresponding tuning parameters.

Author(s)

Kjell Konis

Examples

# Tuning parameters for an 85%-efficient M-estimator at a Gaussian model
opt(.85)

Tuning parameter for a rho function in the (asymptotic bias-) optimal family

Description

This function computes the tuning constant that yields an MM-regression estimator with a desired asymptotic efficiency when computed with a rho function in the corresponding family. The output of this function can be passed to the functions lmrobdet.control, scaleM and rho.

Usage

optv0(e)

Arguments

Value

A vector with named elements containing the corresponding tuning parameters.

Author(s)

Kjell Konis

Examples

# Tuning parameters for an 85%-efficient M-estimator at a Gaussian model
optv0(.85)

Robust principal components

Description

This function computes robust principal components based on the minimization of the "residual" M-scale.

Usage

pcaRobS(X, ncomp, desprop = 0.9, deltasca = 0.5, maxit = 100)

Arguments

Value

A list with the following components:

Author(s)

Ricardo Maronna, rmaronna@retina.ar, based on original code by D. Pen~a and J. Prieto

References

http://www.wiley.com/go/maronna/robust

Examples

data(bus)
X0 <- as.matrix(bus)
X1 <- X0[,-9]
ss <- apply(X1, 2, mad)
mu <- apply(X1, 2, median)
X <- scale(X1, center=mu, scale=ss)
q <- 3  #compute three components
rr <- pcaRobS(X, q, 0.99)
round(rr$eigvec, 3)

Robust Principal Components Cont'd

Description

This function uses the pcaRobS function to compute all principal components while behaving similarly to the prcomp function

Usage

prcompRob(x, rank. = NULL, delta.scale = 0.5, max.iter = 100L)

Arguments

Value

Author(s)

Gregory Brownson, gregory.brownson@gmail.com

Examples

data(wine)

p.wine <- prcompRob(wine)
summary(p.wine)

## Choose only 5
p5.wine <- prcompRob(wine, rank. = 5)
summary(p5.wine)

IRWLS iterations for S- or M-estimators

Description

This function performs iterative improvements for S- or M-estimators.

Usage

refine.sm(
  x,
  y,
  initial.beta,
  initial.scale,
  k = 50,
  conv = 1,
  b,
  cc,
  family,
  step = "M",
  tol
)

Arguments

Details

This function performs iterative improvements for S- or M-estimators. Both iterations are formally the same, the only difference is that for M-iterations the residual scale estimate remains fixed, while for S-iterations it is updated at each step. In this case, we follow the Fast-S algorithm of Salibian-Barrera and Yohai an use one step updates for the M-scale, as opposed to a full computation. This as internal function.

Value

A list with the following components:

Author(s)

Matias Salibian-Barrera, matias@stat.ubc.ca.

Resex data

Description

A monthly series of inward movement of residential telephone extensions in a fixed geographic area from January 1966 to May 1973.

Usage

data(resex)

Format

An object of class "data.frame".

Details

Format: numeric vector of size 89.

Source

Source Engineering, 2nd. Edition, New York, John Wiley.

References

Brubacher. S.R. (1974), Time series outlier detection and modeling with interpolation, Bell Laboratories Technical Memo.

Examples

data(resex)

Rho functions

Description

This function returns the value of the "rho" loss function used to compute either an M-scale estimator or a robust regression estimator. It currently can be used to compute the bisquare, optimal and modified optimal loss functions.

Usage

rho(u, family = " bisquare", cc, standardize = TRUE)

Arguments

Value

The value(s) of rho at u

Author(s)

Matias Salibian-Barrera, matias@stat.ubc.ca

Examples

# Evaluate rho tuned for 85% efficiency
rho(u=1.1, family='bisquare', cc=bisquare(.85))
# Evaluate rho tuned for 50% breakdown
rho(u=1.1, family='opt', cc=lmrobdet.control(bb=.5, family='opt')$tuning.chi)

The first derivative of the rho function

Description

The first derivative of the rho function

Usage

rhoprime(u, family, cc, standardize = FALSE)

Arguments

Value

The value of the first derivative rho evaluated at u

Author(s)

Matias Salibian-Barrera, matias@stat.ubc.ca

Examples

# Evaluate the derivative of a rho function tuned for 85% efficiency
rhoprime(u=1.1, family='bisquare', cc=bisquare(.85))
# Evaluate the derivative of a rho function tuned for 50% breakdown
rhoprime(u=1.1, family='opt', cc=lmrobdet.control(bb=.5, family='opt')$tuning.chi)

The second derivative of the rho function

Description

The second derivative of the rho function

Usage

rhoprime2(u, family, cc, standardize = FALSE)

Arguments

Value

The value of the second derivative of rho evaluated at u

Author(s)

Matias Salibian-Barrera, matias@stat.ubc.ca

Examples

# Evaluate the 2nd derivative of a rho function tuned for 85% efficiency
rhoprime2(u=1.1, family='bisquare', cc=bisquare(.85))
# Evaluate the 2nd derivative of a rho function tuned for 50% breakdown
rhoprime2(u=1.1, family='opt', cc=lmrobdet.control(bb=.5, family='opt')$tuning.chi)

M-scale estimator

Description

This function computes an M-scale, which is a robust scale (spread) estimator. M-estimators of scale are a robust alternative to the sample standard deviation. Given a vector of residuals r, the M-scale estimator s solves the non-linear equation mean(rho(r/s, cc))=delta, where delta determines the breakdown point of the estimator, and cc is a tuning parameter calculated to obtain consistency under a Gaussian model. The breakdown point of the estimator is min(delta, 1-delta), so the optimal choice for delta is 0.5. To obtain a consistent estimator the constant cc is chosen such that E(rho(Z, cc)) = delta, where Z is a standard normal random variable.

Usage

scaleM(
  u,
  delta = 0.5,
  family = "bisquare",
  max.it = 100,
  tol = 1e-06,
  tolerancezero = .Machine$double.eps,
  tuning.chi = lmrobdet.control(family = family, bb = delta)$tuning.chi
)

Arguments

Details

The iterative algorithm starts from the scaled median of the absolute values of the input vector, and then cycles through the equation s^2 = s^2 * mean(rho(r/s, cc)) / delta.

Value

The scale estimate value at the last iteration or at convergence.

Author(s)

Matias Salibian-Barrera, matias@stat.ubc.ca

Examples

set.seed(123)
r <- rnorm(150, sd=1.5)
scaleM(r)
sd(r)
# 10% of outliers, sd of good points is 1.5
set.seed(123)
r2 <- c(rnorm(135, sd=1.5), rnorm(15, mean=-5, sd=.5))
scaleM(r2, family='opt')
sd(r2)

Shock data

Description

Times recorded for a rat to go through a shuttlebox in successive attempts. If the time exceeded 5 seconds, the rat received an electric shock for the duration of the next attempt. The data are the number of shocks received and the average time for all attempts between shocks.

Usage

data(shock)

Format

An object of class "data.frame".

Details

Format: Numeric matrix with 16 rows and 2 columns

Source

Bond, N.W. (1979), Impairment of shuttlebox avoidance-learning following repeated alcohol withdrawal episodes in rats, Pharmacology, Biochemistry and Behavior, 11, 589-591.

References

References go here.

Examples

data(shock)

Skin data

Description

These data correspond to a study of the relationship between air inspiration and blood circulation in the skin.

Usage

data(skin)

Format

An object of class "data.frame".

Details

Description: The covariates are the logarithms of the volume of air inspired (log VOL) and of the inspiration rate (log RATE). The response (column 3) is the presence or absence of vasoconstriction of the skin of the digits after air inspiration. Format Numeric, 23 rows and 3 columns.

Source

Finney, D.J. (1947), The estimation from individual records of the relationship between dose and quantal response, Biometrika, 34, 320-334.

Examples

data(skin)

Stackloss data

Description

Observations from 21 days operation of a plant for the oxidation of ammonia as a stage in the production of nitric acid.

Usage

data(stackloss)

Format

An object of class "data.frame".

Details

Format: 21 cases and 4 continuous variables. Description: The columns are: 1. air flow 2. cooling water inlet temperature (C) 3. acid concentration ( 4. Stack loss, defined as the percentage of ingoing ammonia that escapes unabsorbed (response)

Source

Brownlee, K.A. (1965), Statistical Theory and Methodology in Science and Engineering, 2nd Edition, New York: John Wiley & Sons, Inc.

Examples

data(stackloss)

Robust stepwise using RFPE

Description

This function performs stepwise model selection on a robustly fitted linear model using the RFPE criterion and the robust regression estimators computed with lmrobdetMM. Only backwards stepwise is currently implemented.

Usage

step.lmrobdetMM(
  object,
  scope,
  direction = c("both", "backward", "forward"),
  trace = TRUE,
  keep = NULL,
  steps = 1000,
  whole.path = FALSE
)

Arguments

Details

Presently only backward stepwise selection is supported. During each step the Robust Final Prediction Error (as computed by the function lmrobdetMM.RFPE) is calculated for the current model and for each sub-model achievable by deleting a single term. If the argument whole.path is FALSE, the function steps to the sub-model with the lowest Robust Final Prediction Error or, if the current model has the lowest Robust Final Prediction Error, terminates. If the argument whole.path is TRUE, the function steps through all smaller submodels removing, at each step, the variable that most reduces the Robust Final Prediction Error. The scale estimate from object is used to compute the Robust Final Prediction Error throughout the procedure.

Value

If whole.path == FALSE the function returns the robust fit as obtained by lmrobdetMM using the final model. If whole.path == TRUE a list is returned containing the RFPE of each model on the sequence of submodels. The names of the components of this list are the formulas that correspods to each model.

Author(s)

Victor Yohai, victoryohai@gmail.com, Matias Salibian-Barrera, matias@stat.ubc.ca

References

http://www.wiley.com/go/maronna/robust

See Also

DCML, MMPY, SMPY

Examples

cont <- lmrobdet.control(bb = 0.5, efficiency = 0.85, family = "bisquare")
set.seed(300)
X <- matrix(rnorm(50*6), 50, 6)
beta <- c(1,1,1,0,0,0)
y <- as.vector(X %*% beta) + 1 + rnorm(50)
y[1:6] <- seq(30, 55, 5)
for (i in 1:6) X[i,] <- c(X[i,1:3],i/2,i/2,i/2)
Z <- cbind(y,X)
Z <- as.data.frame(Z)
obj <- lmrobdetMM(y ~ ., data=Z, control=cont)
out <- step.lmrobdetMM(obj)

Vehicle data

Description

The original data set contains an ensemble of shape feature extractors to the 2D silhouettes of different vehicles. The purpose is to classify a given silhouette as one of four types of vehicle, using a set of 18 features extracted from the silhouette. Here we deal with the "van" type, which has 217 cases. Description; The following features were extracted from the silhouettes. 1. compactness 2. circularity 3. distance circularity 4. radius ratio 5. principal axis aspect ratio 6. maximum length aspect ratio 7. scatter ratio 8. elongatedness 9. principal axis rectangularity 10. maximum length rectangularity 11. scaled variance along major axis 12. scaled variance along minor axis 13. scaled radius of gyration 14. skewness about major axis 15. skewness about minor axis 16. kurtosis about minor axis 17. kurtosis about major axis 18. hollows ratio

Usage

data(vehicle)

Format

An object of class "data.frame".

Details

Format: Numeric, 217 rows and 18 columns.

Source

Turing Institute, Glasgow, and are available at https://archive.ics.uci.edu/ml/datasets/Statlog+(Vehicle+Silhouettes).

Examples

data(vehicle)

Waste data

Description

Waste data. The original data are the result of a study on production waste and land use by Golueke and McGauhey (1970), and contain nine variables, of which we consider six.

Usage

data(waste)

Format

An object of class "data.frame".

Details

Format: 40 cases and 6 continuous variables. Description: The columns are 1. industrial land (acres) 2. fabricated metals (acres) 3. trucking and wholesale trade (acres) 4. retail trade (acres) 5. restaurants and hotels (acres) 6. solid waste (millions of tons), response

Source

Golueke, C.G. and McGauhey, P.H. (1970), Comprehensive Studies of Solid Waste Management, US Department of Health, Education and Welfare, Public Health Services Publication No. 2039.

References

Golueke, C.G. and McGauhey, P.H. (1970), Comprehensive Studies of Solid Waste Management, US Department of Health, Education and Welfare, Public Health Services Publication No. 2039.

Examples

data(waste)

Wine data

Description

It contains, for each of 59 wines grown in the same region in Italy, the quantities of 13 constituents. The original purpose of the analysis was to classify wines from different cultivars by means of these measurements. In this example we treat cultivar one.

Usage

data(wine)

Format

An object of class "data.frame".

Details

Format: Numeric, 59 rows and 13 columns. Description: The attributes are: 1. Alcohol 2. Malic acid 3. Ash 4. Alcalinity of ash 5. Magnesium 6. Total phenols 7. Flavanoids 8. Nonflavanoid phenols 9. Proanthocyanins 10. Color intensity 11. Hue 12. OD280/OD315 of diluted wines 13. Proline

Source

Hettich, S. and Bay, S.D. (1999), The UCI KDD Archive http://kdd.ics.uci.edu. Irvine, CA: University of California, Department of Information and Computer Science.

Examples

data(wine)