Overlap between robust glm and weighted glm in R

Question

I sometimes have to vectorise the Huber weights from a robust regression and use them in a lm. Recently I've had to do something similar for a logistic model but I'm slightly worried because I don't get very similar results

library(robustbase)
data(vaso)
ROB <- glmrob(Y ~Volume+Rate, family=binomial("logit"), data=vaso)
ROB
glm(Y ~Volume+Rate,data=vaso,family=binomial("logit"))
glm(Y ~Volume+Rate,data=vaso,weights=ROB$w.r,family=binomial("logit"))

The coefficients from the weighted glm are more similar to the robust regression than the unweighted glm, but is there a way to make them the same? I can get the same results with a robust (rlm) and weighted lm but this doesn't seem to be the case with glm. I haven't looked at the glm robust regression in detail so what I'm asking may be impossible...

Thanks for your help

Answer 1

That’s no surprise. Because the binomial distribution is skewed (except pi equals 0.5), a consistency correction is need in each iteration step when a robust psi function is applied. Hence, the robust estimated is not equivalent to a weighted maximum likelihood estimator in glm. Although for the Gaussian case, you obtain the same estimated values as the robust method using a weighted least-square method (using the “correct” weights), the results will differ for confidence intervals and hypothesis tests. The robust result will consider that the robust method may downweight some “good” observations.