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

## Description

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

## Usage

 ```1 2 3``` ``` 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) ```

## Arguments

 `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`?

## Value

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`.

## Author(s)

Claudio Agostinelli, Marina Valdora and Victor J. Yohai

## References

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`
 ```1 2 3 4 5``` ``` 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) ```