You may want to take a look at a paper by Julia Kelsall and Scott Zeger in
JRSS(C) - 1999, pp. 331-344. This paper describes a frequency domain
approach to log-linear regression modeling of poisson-distributed count
data, accounting for correlation and over-dispersion. There are also some S
functions available to implement the methodology.
Ravi.
-----Original Message-----
From: pauljohn at ukans.edu <pauljohn at ukans.edu>
Cc: r-help at stat.math.ethz.ch <r-help at stat.math.ethz.ch>
Date: Tuesday, November 20, 2001 11:04 AM
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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