robcbi-package: Robust Fit for Discrete Generalized Linear Model

In robcbi: Conditionally Unbiased Bounded Influence Estimates

Robust Fit for Discrete Generalized Linear Model

Description

Conditionally unbiased bounded influence estimates as described in Kuensch et al. (1989) in three special cases of the Generalized Linear Model: Bernoulli, Binomial, and Poisson distributed responses.

Details

Package:	cubinf
#Version:	1.0
#Date:	2013-07-04
License:	GPL (>= 2)

Author(s)

A. Marazzi <[e-mail]>

Maintainer: A. Randriamiharisoa <[e-mail]>

References

Kuensch, H.R., Stefanski L.A., Carroll R.J. (1989). Conditionally unbiased bounded-influence estimation in general regression models, with application to generalized linear models. Journal of the American Statistical Association, 84, 460-466.

Marazzi, A. (1993). Algorithms, Routines, and S-functions for robust Statistics. Chapman and Hall, New York.

Examples

 library(robcbi)
# First example
 data(Finney)
 Vol <- Finney$Vol; Rate <- Finney$Rate; Resp <- Finney$Resp
## Not run: 
 plot(Vol,Rate,type="n")
 points(Vol[Resp==0],Rate[Resp==0],pch=5, cex=1.2)
 points(Vol[Resp==1],Rate[Resp==1],pch=16,cex=1.2)

## End(Not run)
 lVol <-log(Vol); lRate <- log(Rate)
 z.glm <- glm(Resp~lVol+lRate,family=binomial)
 summary(z.glm)
 z.cub <- glm(Resp~lVol+lRate,family=binomial,method="cubinf", ufact=3.2)
 summary(z.cub)
 weights(z.cub)
## Not run: 
 plot(z.cub, smooth=TRUE, ask=TRUE)

## End(Not run)
 comp <- fits.compare(z.glm,z.cub)
 comp
## Not run: 
 plot(comp)

## End(Not run)
# Second example
 data(Breslow)
## Not run:  
 help(Breslow)

## End(Not run)
 y  = Breslow$sumY
 x1 = Breslow$Age10
 x2 = Breslow$Base4
 x3 = rep(0,length(y))
 x3[Breslow$Trt=="progabide"] = 1
 x4 = x2*x3
 CBA = glm(y~x1+x2+x3+x4,family=poisson,method=cubinf,ufact=3.2)
## Not run: 
 plot(CBA,num=5)

## End(Not run)
 weights(CBA)
#
# compute the $R_n^2$ statistic (Section 2.5) to compare CBA 
# with a reduced model with three variables:
#
 CBA.red = update(CBA, .~.-x3-x4)
 np = 5       # number of parameters of the full model
 nq = 3       # number of parameters of the reduced model
 CVR = covar(CBA)
 CFF = coef(CBA)
 K22 = CVR[(nq+1):np,(nq+1):np]
 cff = as.matrix(CFF[(nq+1):np])
 Rn2 = t(cff)%*%solve(K22)%*%cff
 Rn2

robcbi documentation built on Aug. 22, 2023, 1:06 a.m.