poissonMT: Robust Fitting of Poisson Generalized Linear Models using MT...
In poissonMT: Robust M-Estimators Based on Transformations for Poisson Model

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

View source: R/poissonMT.R

poissonMT is used to fit generalized linear models by robust MT method. The model is specified by the x and y components.

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  poissonMT(x, y, start, weights = NULL, tol = 1e-08, maxit = 100,
  m.approx = NULL, mprime.approx = NULL, psi = "bisquare",
  cc = 2.3, na.to.zero = TRUE)

`x`	design matrix of dimension n p*.
`y`	vector of observations of length `n`.
`start`	starting values for the parameters in the linear predictor.
`weights`	an optional vector of weights to be used in the fitting process (in addition to the robustness weights computed in the fitting process).
`tol`	convergence tolerance for the parameter vector.
`maxit`	integer specifying the maximum number of IRWLS iterations.
`m.approx`	a function that return the value, for each linear predictor, that makes the estimating equation Fisher consistent. If `NULL` the default internal function is used.
`mprime.approx`	a function that return the value, for each linear predictor, corresponding to the first derivative of `m.approx`. If `NULL` the default internal function is used.
`psi`	the name of the `psi` function. At the moment only the `bisquare` is available.
`cc`	tuning constant c for Tukey's bisquare psi-function.
`na.to.zero`	logical, should the eventual `NA` in the coefficients be replaced by `0`?

A list with the following components

`coefficients`	a vector of coefficients.
`fitted.values`	the fitted mean values, obtained by transforming the linear predictors by the inverse of the link function.
`linear.predictors`	the linear fit on link scale.
`residuals`	residuals on the transformed scale.
`weights`	the working weights, that is the weights in the final iteration of the IWLS fit.
`w.r`	robustness weights for each observations.
`prior.weights`	the weights initially supplied, a vector of `1`s if none were.
`converged`	logical. Was the IWLS algorithm judged to have converged?
`iter`	the number of iterations used by the influence algorithm.
`obj`	value of the MT objective function at `coefficients`.

Claudio Agostinelli, Marina Valdora and Victor J. Yohai

C. Agostinelli, M. Valdora and V.J Yohai (2018) Initial Robust Estimation in Generalized Linear Models with a Large Number of Covariates. Submitted.

M. Valdora and V.J. Yohai (2014) Robust estimators for Generalized Linear Models. Journal of Statistical Planning and Inference, 146, 31-48.

glmrobMT, glmrob and cubinf

  data(epilepsy)
  x <- model.matrix( ~ Age10 + Base4*Trt, data=epilepsy)
  poissonMTsetwd(tempdir())  
  start <- poissonMTinitial(x=x, y=epilepsy$Ysum)$coefficients
  Efit3 <- poissonMT(x=x, y=epilepsy$Ysum, start=start)