poissonMT (version 0.3-5)

poissonMT: Robust Fitting of Poisson Generalized Linear Models using MT robust method

Description

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

Usage

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 \(n \times p\).

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 1s 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.

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

glmrobMT, glmrob and cubinf

Examples

# NOT RUN {
  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)
# }