BYlogreg | R Documentation |

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`

.

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

`x0` |
a numeric |

`y` |
numeric |

`initwml` |
logical for selecting one of the two possible methods for computing the initial value of the optimization process. If If |

`addIntercept` |
logical indicating that a column of |

`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 |

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 |

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

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

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"`

.

```
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, well used to be closer than now,
## with the (2023-05, VT) change of covMcd() scale-correction
stopifnot( all.equal(vWBY, v.BY, tolerance = 0.008) ) # was ~ 1e-4 till 2023-05
```

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