R Under development (unstable) (2023-06-09 r84528 ucrt) -- "Unsuffered Consequences"
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> ## recreating exact fit problem for categorical data
> require(robustbase)
Loading required package: robustbase
> 
> ## some simple balanced dataset with one grouping variable
> ngrp <- 10
> nrep <- 10
> set.seed(2)
> data <- data.frame(y = rnorm(ngrp*nrep), grp=rep(letters[1:ngrp], each=nrep))
> ## this works fine
> m1 <- lmrob(y ~ grp, data)
> 
> ## now contaminate the dataset
> data2 <- data
> data2$y[1:48] <- 1e10
> try(m2 <- lmrob(y ~ grp, data2, trace.lev = 3))
lmrob_S(n = 100, nRes = 500): fast_s() [non-large n]:
 Subsampling 500 times to find candidate betas:
   refine_fast_s(s0=-1, convChk=FALSE):    too many zeroes -> scale=0 & quit refinement
  Sample[  0]:   after refine_(*, conv=F):
   beta_ref : 1e+10 0 0 0 0 -1e+10 -1e+10 -1e+10 -1e+10 -1e+10 
   with ||beta_ref - beta_cand|| = 0, --> sc = 0
 |s|=0: Have 62 (too many) exact zeroes -> leaving refinement!
lmrob.S(): scale = 0; coeff.=
 [1]  1e+10  0e+00  0e+00  0e+00  0e+00 -1e+10 -1e+10 -1e+10 -1e+10 -1e+10
init *NOT* converged; init$scale = 0, init$coef:
  (Intercept)        grpb        grpc        grpd        grpe        grpf 
      1e+10       0e+00       0e+00       0e+00       0e+00      -1e+10 
       grpg        grph        grpi        grpj 
     -1e+10      -1e+10      -1e+10      -1e+10 
Warning messages:
1: In lmrob.S(x, y, control = control) :
  S-estimated scale == 0:  Probably exact fit; check your data
2: In lmrob.fit(x, y, control, init = init) :
  initial estim. 'init' not converged -- will be return()ed basically unchanged
> ## All observations of group "e" get rob. weight of 0:
> weights <- c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1) ## from trace output
> weights %*% m1$x
     (Intercept) grpb grpc grpd grpe grpf grpg grph grpi grpj
[1,]          90   10   10   10    0   10   10   10   10   10
> 
> proc.time()
   user  system elapsed 
   0.18    0.04    0.23