[R] Poisson Regression

[Peter Dalgaard]

On 10/14/2010 06:42 PM, Viechtbauer Wolfgang (STAT) wrote:
> Since the number of parameters then rises linearly with the number of
> subjects, this may be a case where maximum likelihood theory breaks
> down, that is, a Neyman-Scott problem.

My thought too. The basic structure is close to the Rasch (IRT) model,
for which it is known that you need conditional inference to get
consistent estimates of item parameters. My gut feeling is that it could
depend on the size of the lambda, i.e. whether we are looking at many
sparse subject-specific tables. The whole thing is also quite similar to
classical Epi techniques like Mantel-Haenszel, conditional logit, etc.,
without being spot-on since those methods deal with the interaction term
of stratified 2x2 tables.

Then again, isn't the structure here that conditionally on the sum of
the Y_ijk over j and k, we have just a bunch of multinomially
distributed tables, with independence and the SAME row and col
parameters? So just sum them all and estimate.... I.e., the conditional
analysis is trivial, and if it doesn't coincide with full ML, the latter
is most likely wrong anyway!

(With reservation for this being Saturday morning, etc.)


-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com