[R] Time Series Count Models

[Brett Gordon]

Paul,

Thank you so much for your thoughtful reply. I agree - there are many
possible descriptions for my data, and I realize that I don't want to
get bogged down with figuring out the 'best' model if something simple
will work well. For me, I think the difficulty is going to be handling
the cumulative aspect of the lagged variable.

To be clear, suppose that y_1, ..., y_T are the counts. At time t=3, I
want to include the quantity (y_1 + y_2) as an independent variable,
and so on. I wonder if this is as simple as solving a conditional ML
problem......I'll have to look more deeply into it.

Again, thanks for the references.

-Brett 

On 7/18/05, Paul Johnson <pauljohn at ku.edu> wrote:
> Dear Brett:
> 
> There are books for this topic that are more narrowly tailored to your
> question. Lindsey's Models for Repeated Measurements and Diggle, et al's
> Analysis of Longitudinal Data.  Lindsey offers an R package on his web
> site. If you dig around, you will find many modeling papers on this,
> although in my mind none coalesced into a completely clear path such as
> "throw in these variables and you will get the right estimates".
> 
> The problem, as you will see, is that there are many possible
> mathematical descriptions of the idea that there is time dependence in a
> count model.
> 
> My political science colleagues John Williams and Pat Brandt published 2
> articles on time series with counts.  My favorite is the second one
> here.  There is R code for the Pests model.
> http://www.utdallas.edu/~pbrandt/pests/pests.htm
> 
> Brandt, Patrick T., John T. Williams, Benjamin O. Fordham and Brian
> Pollins. 2000. "Dynamic Modelling For Persistent Event Count Time
> Series." American Journal of Political Science 44(4): 823-843.
> 
> Brandt, Patrick T. and John T. Williams. 2001. "A Linear Poisson
> Autoregressive Model: the Poisson AR(p) Model." Political Analysis 9(2):
> 164-184.
> 
> I worked really hard on TS counts a while ago because a student was
> trying that.  If you look at J Lindsay's book Models for Repeated
> Measures you will make some progress on understanding his method
> kalcount. That's in the repeated library you get from his web site.
> 
> Here are the notes I made a couple of years ago
> 
> http://lark.cc.ku.edu/~pauljohn/stats/TimeSeries/
> 
> Look for files called TSCountData*.pdf.
> 
> 
> It all boils down to the fact that you can't just act like it is an OLS
> model and throw Y_t-1 or something like that on the right had side.
> Instead, you have to think in a more delicate way about the process you
> are modeling and hit it from that other direction.
> 
> Here are some of the articles for which I kept copies.
> 
> U. Bokenholt, "Mixed INAR(1) Poisson regression models" Journal of
> Econometrics, 89 (1999): 317-338
> 
> A.C. Harvey and C. Fernandes, "Time Series Models for Count or
> Qualitative Observations, " Journal of Business & Economic Statistics, 4
> (1989): 407-
> 
> 
> I recall liking this one a lot
> 
> J E Kelsall and Scott Zeger and J M Samet "Frequency Domain Log-linear
> Models; air pollution and mortality" Appl. Statis 48 1999 331-344.
> 
> Good luck, let me know what you find out.
> 
> pj
> 
> Brett Gordon wrote:
> > Hello,
> >
> > I'm trying to model the entry of certain firms into a larger number of
> > distinct markets over time. I have a short time series, but a large
> > cross section (small T, big N).
> >
> > I have both time varying and non-time varying variables. Additionally,
> > since I'm modeling entry of firms, it seems like the number of
> > existing firms in the market at time t should depend on the number of
> > firms at (t-1), so I would like to include the lagged cumulative count.
> >
> > My basic question is whether it is appropriate (in a statistical
> > sense) to include both the time varying variables and the lagged
> > cumulative count variable. The lagged count aside, I know there are
> > standard extensions to count models to handle time series. However,
> > I'm not sure if anything changes when lagged values of the cumulative
> > dependent variable are added (i.e. are the regular standard errors
> > correct, are estimates consistent, etc....).
> >
> > Can I still use one of the time series count models while including
> > this lagged cumulative value?
> >
> > I would greatly appreciate it if anyone can direct me to relevant
> > material on this. As a note, I have already looked at Cameron and
> > Trivedi's book.
> >
> > Many thanks,
> >
> > Brett
> >
> > ______________________________________________
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> 
> 
> --
> Paul E. Johnson                       email: pauljohn at ku.edu
> Dept. of Political Science            http://lark.cc.ku.edu/~pauljohn
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>