robustbase: BYlogreg – R documentation

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BYlogreg

Bianco-Yohai Estimator for Robust Logistic Regression

Description

Computation of the estimator of Bianco and Yohai (1996) in logistic regression. Now provides both the weighted and regular (unweighted) BY-estimator.

By default, an intercept term is included and p parameters are estimated. For more details, see the reference.

Note: This function is for “back-compatibility” with the BYlogreg() code web-published at KU Leuven, Belgium, and also available as file ‘FunctionsRob/BYlogreg.ssc’ from https://www.wiley.com/legacy/wileychi/robust_statistics/robust.html.

However instead of using this function, the recommended interface is glmrob(*, method = "BY") or ... method = "WBY" .., see glmrob.

Usage

BYlogreg(x0, y, initwml = TRUE, addIntercept = TRUE,
         const = 0.5, kmax = 1000, maxhalf = 10, sigma.min = 1e-4,
         trace.lev = 0)

Arguments

`x0`	a numeric n (p-1)* matrix containing the explanatory variables.
`y`	numeric n-vector of binomial (0 - 1) responses.
`initwml`	logical for selecting one of the two possible methods for computing the initial value of the optimization process. If `initwml` is true (default), a weighted ML estimator is computed with weights derived from the MCD estimator computed on the explanatory variables. If `initwml` is false, a classical ML fit is perfomed. When the explanatory variables contain binary observations, it is recommended to set initwml to FALSE or to modify the code of the algorithm to compute the weights only on the continuous variables.
`addIntercept`	logical indicating that a column of `1` must be added the x matrix.
`const`	tuning constant used in the computation of the estimator (default=0.5).
`kmax`	maximum number of iterations before convergence (default=1000).
`maxhalf`	max number of step-halving (default=10).
`sigma.min`	smallest value of the scale parameter before implosion (and hence non-convergence) is assumed.
`trace.lev`	logical (or integer) indicating if intermediate results should be printed; defaults to `0` (the same as `FALSE`).

Value

a list with components

`convergence`	logical indicating if convergence was achieved
`objective`	the value of the objective function at the minimum
`coefficients`	vector of parameter estimates
`vcov`	variance-covariance matrix of the coefficients (if convergence is TRUE).
`sterror`	standard errors, i.e., simply `sqrt(diag(.$vcov))`, if convergence.

Author(s)

Originally, Christophe Croux and Gentiane Haesbroeck, with thanks to Kristel Joossens and Valentin Todorov for improvements.

Speedup, tweaks, more “control” arguments: Martin Maechler.

References

Croux, C., and Haesbroeck, G. (2003) Implementing the Bianco and Yohai estimator for Logistic Regression, Computational Statistics and Data Analysis 44, 273–295.

Ana M. Bianco and Víctor J. Yohai (1996) Robust estimation in the logistic regression model. In Helmut Rieder, Robust Statistics, Data Analysis, and Computer Intensive Methods, Lecture Notes in Statistics 109, pages 17–34.

Examples

set.seed(17)
x0 <- matrix(rnorm(100,1))
y  <- rbinom(100, size=1, prob= 0.5) # ~= as.numeric(runif(100) > 0.5)
BY <- BYlogreg(x0,y)
BY <- BYlogreg(x0,y, trace.lev=TRUE)

## The "Vaso Constriction"  aka "skin" data:
data(vaso)
vX <- model.matrix( ~ log(Volume) + log(Rate), data=vaso)
vY <- vaso[,"Y"]
head(cbind(vX, vY))# 'X' does include the intercept

vWBY <- BYlogreg(x0 = vX, y = vY, addIntercept=FALSE) # as 'vX' has it already
v.BY <- BYlogreg(x0 = vX, y = vY, addIntercept=FALSE, initwml=FALSE)
## they are relatively close:
stopifnot( all.equal(vWBY, v.BY, tolerance = 2e-4) )

robustbase

Basic Robust Statistics

v0.93-7

GPL (>= 2)

Authors

Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Peter Rousseeuw [ctb] (Qn and Sn), Christophe Croux [ctb] (Qn and Sn), Valentin Todorov [aut] (most robust Cov), Andreas Ruckstuhl [aut] (nlrob, anova, glmrob), Matias Salibian-Barrera [aut] (lmrob orig.), Tobias Verbeke [ctb, fnd] (mc, adjbox), Manuel Koller [aut] (mc, lmrob, psi-func.), Eduardo L. T. Conceicao [aut] (MM-, tau-, CM-, and MTL- nlrob), Maria Anna di Palma [ctb] (initial version of Comedian)

Initial release

2021-01-04