[R] Time Series Event Count: Great Responses So Far!

[Paul E Johnson]

In case more of you come across my request from this morning, I've
already gotten several great tips, which I summarize here since one or
two of these did not come across R-help as well.

A team of fellow political scientists is on this problem like
"white-on-rice"!

Brandt, Patrick, John T. Williams Benjamin O. Fordham, and Brian
Pollins. 
2000. "Dynamic Modeling for Persistent Event Count Time Series" American 
Journal of Political Science. 44(4): 823-843.

Brandt, Patrick and John T. Williams. 2001. "A Linear Poisson
Autoregressive 
Model: The Poisson AR(p)" Political Analysis. 9(2): 164-184.

There is software for implementing these models in GAUSS on Patrick
Brandt's webpage, 
http://www.psci.unt.edu/~brandt/pests/pests.htm. He said he is working
out R versions as well!


Jake Bowers pointed me to Jim Lindsey's packages for Nonlinear
Regression and Repeated
Measurements which has some functions which appear very promising:
http://alpha.luc.ac.be/~lucp0753/rcode.html

Thomas Lumley pointed out that instead of NB, one can get a
Poisson-Normal mixture out of this by changing the assumption on the
error term.  He pointed me at some articles that are exactly on point

- Zeger (Biometrika 1988, pp621-629) gives an estimation procedure for a
time series count model that is based on a Poisson-Normal mixture.

- Something more or less similar is discussed by Davis et al (Biometrika
2000, p491-505)

And he to consider "sandwich estimators" (or similar) for longitudinal
data. He wrote "Some of these (eg the Newey-West estimator) have been
used in econometrics for a long time. Although they
are most often used for continuous response variables they work
perfectly well for counts.  Stata 7.0 does the Newey-West estimator for
generalised linear models, which may be what you had heard about.  These
and related sandwich-type estimators are reviewed by Lumley & Heagerty
(JRSSB
1999,pp459-477).  I have R code, but again only for generalised linear
models, not for zero-inflation models."

Thomas added:
- The Poisson-Normal model leads to a loglinear marginal model that can
be fitted by glm(), and I would expect something similar  to be true of
the zero-inflation model. This means that you may be able to just
estimate a marginal model (unless you are actually interested in
inference about
the correlation structure).  In principle this could be inefficient, but
for very discrete data there isn't much information in the
autocorrelation.

- The full likelihood is intractable anyway -- it doesn't factorise the
way a Gaussian AR-1 does.  That's one reason Bayesians like these
models:
MCMC is the easy way out computationally (though still not trivial).
There's a fairly popular approximate maximum likelihood method called
PQL
that works reasonably well except in binary and small count data.

I've also learned that I should look up these articles:

McKenzie, E. 1988. Some ARMA models for dependent sequences of Poisson
counts. Advanced Applied Probability. 20: 822-835

Bockenholt, U. 1999. Mixed INAR(1) Poisson regression models. J. of
Econometrics, 89: 317-338.


-- 
Paul E. Johnson                       email: pauljohn at ukans.edu
Dept. of Political Science            http://lark.cc.ukans.edu/~pauljohn
University of Kansas                  Office: (785) 864-9086
Lawrence, Kansas 66045                FAX: (785) 864-5700
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