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 http://www.econ.kuleuven.be/public/NDBAE06/programs/roblog/; instead, the recommended interface is glmrob(*, method = "BY") or ... method = "WBY" .., see glmrob.

Usage

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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.

See Also

The more typical way to compute BY-estimates (via formula and methods): glmrob(*, method = "WBY") and .. method = "BY".

Examples

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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) )

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