[R] Time series count model?

[David Barron]

One way to do this in R is using the package gee (Generalized Estimation
Equations).  The people to read are Liang and Zeger, who also describe a
quasi-likelihood approach to your problem (I don't have the references to
hand, but they are probably in the help pages for gee).  You might also want
to look at an old paper of mine:  David N. Barron 1992. "The Analysis of
Count Data: Over-dispersion and Autocorrelation." In Peter V. Marsden (ed.)
Sociological Methodology 22:179-220. New York: Blackwell.  I think I'm right
in saying that Stata also has a way of estimating gee models, though I've
never used Stata so I might be wrong.

David

----- Original Message -----
From: <pauljohn at ukans.edu>
Cc: <r-help at stat.math.ethz.ch>
Sent: Tuesday, November 20, 2001 2:36 PM
Subject: [R] Time series count model?


> I fear I need someone to throw a brick at my head to shake loose
> the cobwebs. And it might as well be the r friends as anybody!
>
> I am trying to counsel a student who has count data (with many
> 0's and small nuumbers) that is a time series.  He was fitting
> linear models to this data, but the count nature of the data
> causes me a lot of concern, and I am looking around for a time
> series approach to a model which allows all the bells and
> whistles of count models. By chance, I notice that Congdon's
> WinBUGS examples have an example that has a count model with
> time series issues, but I fear it might be too great of a leap
> for us to justify a paradigm switch to Bayesian statistics in
> order to fit this one model.
>
> If you were using R, how would you get a foot hold on this
> problem?
>
> I want a NegativeBinomial count model (terminology maybe
> ambiguous: that means a Poisson with input (mean) value derived
> from a Gamma(Xb,1) process) and the possiblity of zero-inflated
> data, which means the likelihood of an observation is multiplied
> by 1 or 0 according to a draw from a logistic distribution. (I
> realize this is starting to sound junked up, but Scott Long's
> book on Regression with Qualitative Depenedent Variables writes
> out all the details.)
>
> Because the theory that inspires this model is a dynamic
> process, it has a lagged dependent variable on the right hand
> side. So when I say X here, I mean a matrix in which lagged y's
> are included as columns. So the individual observation's
> likelihood is (I believe this is the Negative Binomial model
> with zero inflagion factor)
>
> input = draw from Gamma(exp(Xb),1))
> zif = draw from logistic(Xb)
>
> if (zif == 1) then:
> p(y |X,b) = Pois( input )
>
> if (zif == 0) then:
> y=0
>
> I suppose it is not necessarily true the zero inflation logit
> part depends on the exact same coefficients as the Gamma part,
> but lets worry about that later....
>
> We have a copy of Stata sitting around here and the students
> have found in there a canned procedure to estimate that model,
> it does various specificiation tests, such as a test for whether
> the zero inflation part is necessary.  But that does not attend
> to the time-series part. I don't do Stata myself, I am learning
> R, and would like to see if I can do this in R.
>
> We need to incorporate the possibility of an "error term" that
> is influenced by its own lagged values in the usual ARIMA
> sense.  Looking back to the justification for the Negative
> Binomial in the first place, I remember one justification for
> the NB model was a Poisson with heterogeneity.
>
> p(y | X,b) = Pois (exp(Xb + e))
>
> I don't think I ever understood very well why this leads to a NB
> model. Maybe that's where I need to study.
>
> Nevertheless, where can I go if I start with that theory, but
> the e are not independent, say they are MA(1)
>
> e_t = g*e_{t-1} + u_t
>
> and u_t is Normal(0,sigma^2).
>
> Should I just write out a big log likelihood function and use
> R's optim to fit it?
>
> It seems like I'm missing out on something by going that route,
> though.
>
> --
> 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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