wle (version 0.9-91)

wle.glm.control: Auxiliary for Controlling GLM Robust Fitting

Description

Auxiliary function as user interface for glm robust fitting. Typically only used when calling wle.glm or wle.glm.fit.

Usage

wle.glm.control(boot = 30, group = NULL, num.sol = 1, 
  raf = c("GKL", "PWD", "HD", "NED", "SCHI2"), tau = 0.1, 
  cutpoint = 0, powerdown = 1, delta = NULL, smooth = NULL,
  asy.smooth=0.031, tol = 10^(-6), equal = 10^(-3),
  max.iter = 500, window.size = NULL, use.asymptotic = NULL, 
  use.smooth=TRUE, mle.dispersion = FALSE, verbose = FALSE)

Arguments

boot

interger. Number of starting points based on boostrap subsamples to use in the search of the roots.

group

integer. Dimension of the bootstap subsamples. The default value is $max(round(size/2),var+1)$ where $size$ is the number of observations and $var$ is the number of predictors.

num.sol

interger. Maximum number of roots to be searched.

raf

type of Residual adjustment function to be used:

raf="GKL": Generalized Kullback-Leibler family RAF (see details),

raf="PWD": Power Divergence family RAF (see details),

raf="HD": Hellinger Distance RAF,

ra

tau

positive real. Used in selecting the member of the RAF family in the case of GKL or PWD.

cutpoint

a value in the interval [0,1].

powerdown

a non negative number.

delta

between (0,1). Used in the construction of the weights for the Binomial family.

smooth

the value of the smoothing parameter; used in the evaluation of weights in the case of continuous models.

asy.smooth

the value of the smoothing parameter; used in the evaluation of asymptotic weights. or in the case of continuous models.

tol

the absolute accuracy to be used to achieve convergence of the algorithm.

equal

the absolute value for which two roots are considered the same. Two roots are compared using the corresponding final weights.

max.iter

maximum number of iterations.

window.size

positive real or NULL. The observations with a distance, in the predictors space, less than this threshold are used to estimate the conditional distribution for a given level of the predictor.

use.asymptotic

interger or NULL. The minimum number of observations for the level of the predictors under which asymptotic weights are used.

use.smooth

if TRUE the smoothed model is used in the computation of the Pearson Residuals. For now, the option is used only for the Gamma family.

mle.dispersion

if TRUE the weighted likelihood estimator for dispersion is used otherwise the weighted chi-sqaured statistics is used.

verbose

if TRUE warnings are printed.

Value

• A list with the arguments as components.

Details

The Generalized Kullback-Leibler family RAF is defined as: $$\ln(tau*x+1)/tau$$ for $tau > 0$.

The Power Divergence family RAF is defined as: $$tau*((x + 1)^(1/tau) - 1)$$ for $0 < tau < Inf$ while $$\ln(x+1)$$ for $tau=Inf$.

References

Agostinelli, C. and Alqallaf, F. (2009) Robust inference in Generalized Linear Models. Manuscript in preparation.

See Also

wle.glm

Examples

### A variation on  example(wle.glm) :

## Annette Dobson's example ...
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
oo <- options(digits = 12) # to see more when tracing :
wle.glm.D93X <- wle.glm(counts ~ outcome + treatment, family=poisson(),
                control=list(glm=glm.control(trace = TRUE), 
                wle=wle.glm.control(raf='GKL', tau=0.15)))
options(oo)
coef(wle.glm.D93X)