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

## Description

`glmrobMT` is used to fit generalized linear models by robust MT method. The model is specified by the `x` and `y` components and a description of the error distribution. Currently, only implemented for `family=poisson`.

## Usage

 ```1 2 3 4``` ```glmrobMT(x, y, weights=NULL, start=NULL, offset=NULL, family=poisson(), weights.on.x="none", control=glmrobMT.control(), intercept=TRUE, trace.lev=1, include.cubinf=TRUE, m.approx=NULL, mprime.approx=NULL, ...) ```

## Arguments

 `x` design matrix of dimension n * p. `y` vector of observations of length `n`. `weights` an optional vector of weights to be used in the fitting process (in addition to the robustness weights computed in the fitting process). `start` starting values for the parameters in the linear predictor. Note that specifying `start` skips the computation of the initial estimates, but needs to be robust itself. `offset` this can be used to specify an a priori known component to be included in the linear predictor during fitting. At the moment it is not used. `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. At the moment only `poisson` is available. `weights.on.x` a character string (can be abbreviated), a `function` or `list` (see below), or a numeric vector of length `n`, specifying how points (potential outliers) in x-space are downweighted. If `"hat"`, weights on the design of the form √{1-h_{ii}} are used, where h_{ii} are the diagonal elements of the hat matrix. If `"robCov"`, weights based on the robust Mahalanobis distance of the design matrix (intercept excluded) are used where the covariance matrix and the centre is estimated by `cov.rob` from the package MASS. Similarly, if `"covMcd"`, robust weights are computed using `covMcd`. The default is `"none"`. If `weights.on.x` is a `function`, it is called with arguments `(X, intercept)` and must return an n-vector of non-negative weights. If it is a `list`, it must be of length one, and as element contain a function much like `covMcd()` or `cov.rob()` (package MASS), which computes multivariate location and “scatter” of a data matrix `X`. `control` a list of parameters for controlling the fitting process. See the documentation for `glmrobMT.control` for details. `intercept` logical indicating if an intercept at the first column of `x` is present. This information is only used when `weights.on.x` is not set to `none`. `trace.lev` logical (or integer) indicating if intermediate results should be printed; defaults to `0` (the same as `FALSE`). `include.cubinf` logical, if `TRUE` the `cubinf` is also used as possibile starting value. `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. `...` At the moment it is not used.

## Value

A list with the following components:

 `coefficients` a named vector of coefficients. `initial` Initial vector of coefficients. `family` the `family` object used. `residuals` weighted Pearson residuals. `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. `cov` the estimated asymptotic covariance matrix of the estimated coefficients. `converged` logical. Was the IWLS algorithm judged to have converged? `iter` the number of iterations used by the influence algorithm. `cw` the tuning constant c in Tukey's bisquare psi-function. `weights.on.x` how the weights on the design matrix `x` were evaluated. `w.x` weights used to down-weight observations based on the position of the observation in the design space. `w.r` robustness weights for each observations.

## 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.

## See Also

`poissonMT`, `glmrob` and `cubinf`

## Examples

 ```1 2 3 4 5 6``` ``` data(epilepsy) Efit1 <- glm(Ysum ~ Age10 + Base4*Trt, family=poisson, data=epilepsy) x <- model.matrix( ~ Age10 + Base4*Trt, data=epilepsy) poissonMTsetwd(tempdir()) Efit2 <- glmrobMT(x=x, y=epilepsy\$Ysum) ```

poissonMT documentation built on May 2, 2019, 11:01 a.m.