I would just point out that if your data are counts but are bounded to a 
small range of values (e.g., 0 - 4), then neither the Poisson, negative 
binomial or their zero-inflated counterparts are likely to be useful 
approaches.   So just because you have count data does not imply that a 
Poisson or negative binomial pdf is a good modeling choice.  Other 
alternatives like quantile count regression, ordinal logistic regression, 
and even least squares regression may be more useful with counts bounded 
to a small range of values.

Brian

Brian S. Cade, PhD

U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO  80526-8818

email:  brian_cade@usgs.gov
tel:  970 226-9326



From:
"Brooks,Mollie E" <mbrooks@ufl.edu>
To:
<r-sig-ecology@r-project.org>
Date:
08/01/2012 12:18 PM
Subject:
Re: [R-sig-eco] Log transformed simple linear regression and Poisson 
regression
Sent by:
r-sig-ecology-bounces@r-project.org



Hi Lin,
If y is count data, then you should probably model it with either the 
Poisson or negative binomial distributions because these are for counts. 
You can sometimes get away with the normal distribution if the counts 
are very large.

There is an article by O'Hara and Kotz in Methods in Ecology and 
Evolution titled "Do not log-transform count data". So your first 
approach is probably unacceptable.

The similarity is that Poisson regressions typically use a log link 
function (the function glm does this by default). A log link means that 
the model follows the same exponential form that you've specified in 
your first approach (except for the +1). If y does not appear to have an 
accelerating relationship with the predictors, you can try an identity 
link, but it is more fragile.

cheers,
Mollie

On Thu, 2 Aug 2012 01:42:16 +0800 (CST), lgj200306 wrote:
> Hi, everyone,
> I used two methods to analysis the relationship between y (count 
> data) and x.
> 1) log transformed simple linear regression:
>>lm(log(y+1)~x1+x2+x3,data)
> 2) Poisson regression:
>>glm(y~x1+x2+x3,family=poisson())
>
> Some one told that these two ways are very similar, but other one
> told that the Poisson regression does not fit the y but the lambda
> (parameter of the poisson distribution). I am not sure which one is
> right. Can anybody help me?
> Thanks for your attention and best wishes for you!
>
> Lin
> Aug 1st, 2012
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>
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> R-sig-ecology@r-project.org
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