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Re: st: autocorrelation in Poisson regression, follow-up

From   "Stas Kolenikov" <[email protected]>
To   [email protected]
Subject   Re: st: autocorrelation in Poisson regression, follow-up
Date   Tue, 5 Aug 2008 19:18:50 -0500

Ah, that was a teaser. The three ways I was thinking of were:

1. correlation of the Poission counts themselves: poisson y x L.y -- I
cannot think much of any actual process that could generate that sort
of dependence

2. correlation of the Poisson rates: y|x is Poisson with rate lambda =
function of x and L.lambda. That is sort of weird, too, as it assumes
the Poisson rate jumps around exactly at midnight. Or on the 1st of
the month, or on the 1st of the year. Again, it should be a pretty
strange underlying process to have that sort of dependence.

3. Some sort of dependence in deviance residuals -- but those are
derived quantities rather than fundamentals, unlike the standard
Gaussian ARMA processes. You can sorta proceed in a two step way -- to
run the base regression -glm y x, family(poisson) link(log)- get the
residuals out -predict dev, dev-, and run -poisson y x to see
if the coefficient of the latter is zero or not. But again that's a
stupid model.

In general, I hate when referees throw something like that without any
indication of how they want you to proceed. My referee reports are
always a month late, but they have a page of references for two pages
of comments. Can you get along by saying something like "There is no
established method for checking autocorrelations in Poisson
regression, since Poisson processes are intrinsically continuous, and
any discretization is arbitrary -- hence testing for autocorrelations
would require making arbitrary decisions about the time scales at
which the correlations will be present. I will however very much
appreciate it if the reviewer could provide a reference if there is
anything easily available."

On Tue, Aug 5, 2008 at 10:14 AM, Antonio Silva <[email protected]> wrote:
> Stas (and others):
> Thanks for responding to my question. To be honest, I am not sure how to define autocorrelation in this context. I sent out an article for review. The dependent variable is a yearly count variable--number of groups founded. The range is 0-5. I used a simply Poisson regression model with several independent variables. One of the reviewers said the analysis was flawed because I "did not test for autocorrelation on the dependent variable." Unfortunately, the reviewer did not give me any clue as to how to proceed. So I am kind of at a loss here. Essentially, I think the reviewer wanted to make sure the yearly counts were not related to each other in any meaningful way.
> Any further thoughts are appreciated, and I wish I could tell you more about what I need.

You need a better reviewer :))

Stas Kolenikov, also found at
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