wle.glm.weights: Weights based on Weighted Likelihood for the GLM model
In wle: Weighted Likelihood Estimation

Description Usage Arguments Value Author(s) References See Also Examples

Evaluate the weights for a given GLM model

wle.glm.weights(y, x, fitted.values, family = gaussian(),
  dispersion = 1, raf = "GKL", tau = 0.1, smooth = NULL,
  asy.smooth=0.031, window.size = NULL, use.asymptotic = NULL,
  use.smooth=TRUE, tol=10^(-6), dist.method = "euclidean",
  cutpoint = 0, powerdown = 1)

`y`	`y` is a vector of observations of length `n`.
`x`	`x` is a design matrix of dimension `n * p`.
`fitted.values`	the fitted mean values, obtained by transforming the linear predictors by the inverse of the link function. Often obtain as a result of `wle.glm.fit call`.
`family`	a description of the error distribution and link function to be used in the model. This can be a character string naming a family function, a family function or the result of a call to a family function. (See `family` for details of family functions.)
`dispersion`	value of the dispersion parameter. Used only in the Gamma family for now.
`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, `raf="NED"`: Negative Exponential Disparity RAF, `raf="SCHI2"`: Symmetric Chi-Squared Disparity RAF.
`tau`	positive real. Used in selecting the member of the RAF family in the case of `GKL` or `PWD`.
`smooth`	the value of the smoothing parameter; used in the case of continuous models.
`asy.smooth`	the value of the smoothing parameter; used in the evaluation of asymptotic weights.
`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.
`tol`	the tolerance used in the numerical calculations. For now, the option is used only for the Gamma family.
`dist.method`	distance method passed to `dist` to measure the distance between predictor rows.
`cutpoint`	a value in the interval [0,1].
`powerdown`	a non negative number.

A list with two components

`weights`	the weights associated to the observations.
`asy`	logical. If `TRUE` the corresponding weights is evaluated using asymptotic considerations based on Anscombe residuals.

Claudio Agostinelli and Fatemah Al-quallaf

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

wle.glm

# tau=0.1
wgr.D93 <- extractRoot(wle.glm.D93)
# tau=0.2
w1wgr.D93 <- wle.glm.weights(y = wgr.D93$y, x = wgr.D93$x,
  fitted.values = wgr.D93$fitted.values, family = wgr.D93$family,
  raf = "GKL", tau = 0.2, smooth = 0.031, window.size = NULL,
  use.asymptotic = NULL, dist.method = "euclidean")
# tau=0.3
w2wgr.D93 <- wle.glm.weights(y = wgr.D93$y, x = wgr.D93$x,
  fitted.values = wgr.D93$fitted.values, family = wgr.D93$family,
  raf = "GKL", tau = 0.3, smooth = 0.031, window.size = NULL,
  use.asymptotic = NULL, dist.method = "euclidean")

plot(wgr.D93$wle.weights, ylim=c(0,1), ylab='Weights')
points(w1wgr.D93$weights, col=2)
points(w2wgr.D93$weights, col=3)
legend('bottomright', legend=expression(tau==0.1, tau==0.2, tau==0.3),
  pch=rep(1,3), col=1:3, inset=0.05)