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From |
"Kieran McCaul" <kamccaul@meddent.uwa.edu.au> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: autocorrelation in Poisson regression, follow-up |

Date |
Wed, 6 Aug 2008 10:49:52 +0800 |

Stas has suggested a couple of models that might indicate autocorrelation but, as he has commented, it's difficult to see how they would occur. Let's imagine that someone is modelling disease counts in a population over time and they have arrived at a Poisson model that incorporates a lagged variable - the count or the rate in the previous year. This would indicate two things to me: 1. Obviously, the cohort is carrying with it some information that is dependent on the rate in the previous year and is predictive of the rate in the subsequent year. 2. The Poisson model is not appropriate. Suppose in this population, only a small proportion are at risk of getting the disease and the remainder are not at risk but these cannot be identified. If a high disease count in one year removed a significant proportion of those susceptible from the cohort then, in the next year, a lower count and hence a lower rate would be observed. This would look like autocorrelation, but it's not. It is caused by extreme heterogeneity in risk within the population being followed. The Poisson model is wrong. The Poisson model assumes that everyone is at risk and that all the person-time accumulated by the cohort as it moves through time is all at-risk person-time. In the absence of unexplained heterogeneity of risk, if you are following a cohort over time and you split the total person-time at risk into the person-time observed in the first year, in the second year, etc, then these are all independent samples of the person-time at risk. If disease counts are being generated by a Poisson process, then the counts in each year will depend only on the characteristics of the person-time accrued in each year. They are all independent, there is no autocorrelation. So if the process you are modelling is truly Poisson, you shouldn't have to worry about autocorrelation. One thing that does worry me, however, is that in your follow-up email you said you were modelling a count that was "the number of groups founded". What exactly does that mean? -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Stas Kolenikov Sent: Wednesday, 6 August 2008 8:19 AM To: statalist@hsphsun2.harvard.edu Subject: Re: st: autocorrelation in Poisson regression, follow-up 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 L.dev- 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 <asilva100@live.com> 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 http://stas.kolenikov.name Small print: I use this email account for mailing lists only. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: autocorrelation in Poisson regression, follow-up***From:*Antonio Silva <asilva100@live.com>

**Re: st: autocorrelation in Poisson regression, follow-up***From:*"Stas Kolenikov" <skolenik@gmail.com>

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