# BYlogreg: Bianco-Yohai Estimator for Robust Logistic Regression In robustbase: Basic Robust Statistics

## 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 http://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

 ```1 2 3``` ```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.

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```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) ) ```

### Example output

```Convergence Achieved
Warning messages:
1: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

2: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

k= 1, s1=   1.9992299: => new s1=    2.0696016
k= 2, s1=   2.0696016: => new s1=    2.1155094
Convergence Achieved
Warning messages:
1: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

2: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

(Intercept) log(Volume)  log(Rate) vY
1           1   1.3083328 -0.1923719  1
2           1   1.2527630  0.0861777  1
3           1   0.2231436  0.9162907  1
4           1  -0.2876821  0.4054651  1
5           1  -0.2231436  1.1631508  1
6           1  -0.3566749  1.2527630  1
Convergence Achieved
Warning messages:
1: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

2: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

3: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

4: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

5: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

6: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

7: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

8: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

Convergence Achieved
Warning messages:
1: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

2: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

3: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

4: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

5: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.

6: In (grad.BY %*% xistart) * xistart :
Recycling array of length 1 in array-vector arithmetic is deprecated.