[R-sig-ME] inflated standard error for zero counts in Poisson lmer

[Ben Bolker]

Claire Brittain <claire_brittain at ...> writes:

#   Dear R users, I am running a mixed model on some count data (n=90)
#  using lmer with a Poisson error distribution and have two nested
#  random effects based on repeated sampling of locations.  One of my
#  explanatory variables is a three level factor with n=30 observations
#  for each level (in the R output below it's the factor
#  "nathabcat"). When you plot this factor against the counts you can
#  see that for one level the counts are very high, for one level low
#  and for another level extremely low - that is all the counts for
#  that level were zero (in the R output copied below
#  "nathabcatlow"). In the model the difference between the very high
#  and low levels comes out as significant but the difference between
#  the high level and the extremely low level is non-significant. This
#  does not make sense and it appears to come from an incredibly high
#  standard error for the model estimate of the extremely low factor
#  level. Intuitively I think that the standard error should not be
#  high as all the values in that level are zero. It seems as though
#  the model is not treating the zeros as I would expect.  If I
#  transform the count variable to x+1 so all the zeros become 1s it
#  runs fine with no inflated standard error and the model finds a
#  significant difference between the extremely low and high levels of
#  the explanatory factor. Even if I add a single 1 to the zero counts
#  in the extremely low level of the explanatory factor the model runs
#  normally.  Can anyone suggest why having only zeros is causing this
#  problem?  

  Not sure, by try searching for "Hauck-Donner effect".  It is
discussed in Venables and Ripley (Modern Applied Statistics in S)