# Robust Fit for Discrete Generalized Linear Model 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. package ## Details ||| |:--|:--| |Package:|cubinf| |#Version:|1.0| |#Date:|2013-07-04| |License:|GPL (>= 2)| ## Author(s) A. Marazzi Maintainer: A. Randriamiharisoa ## 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 ```r 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-package