Hi Lin,

It is really a matter of trail and error.
Try the simplest models first (GLM, family=poisson or NB) and have a look at your residuals.
If they look funny then you are either using the wrong distribution to model your response variable or your predictors (Xs) are not very good at explaining the way the response occurs. You do not need to worry about the distribution of the predictor variables. Another reason for unusual residuals is if you have some kind of autocorrelation (e.g. a location/spatial effect). This would require the use of mixed models GLMMs and depends on your survey design.

Unless you have A LOT of zeroes, you may be able to get away with not using ZIP or ZIB by using the more flexible 'quasi poisson' family. You can check and see which model works best by comparing their AIC values.

How many explanatory (X) variables are you looking at?  If you have a very big dataset and a lot of explanatory variables it may be worthwhile looking into boosted regression trees.
Otherwise, stick to the simple GLMs.

Lin, these are quite general questions which are well addressed in a lot of text books like those written by Zuur, and Quinn and Keough. I suggest you have a good read of these to get your head around these concepts and also get help from your colleagues.

All the best,
Liz


On 02/08/2012, at 8:50 AM, lgj200306 <lgj200306@163.com> wrote:

> Thanks Liz, Brian and Mollie. Your replies are helpful for me. 
> I have realized the complexity of analysing the count data. Different methods should be selected according to the structure of my data. But if the explanatory data table is composed by several  variables and I want to make clear the relative contribution of each explanatory variable to the variation of response variable, can I achieve it based on the Poisson, negative bionmial, zero-inflated Poisson, zero-inflated negative binomial or other models (except the simple linear regression model)?
> Thanks for your attention and best wishes for you!
>  
> Lin
> Aug 1st, 2012
> 
> At 2012-08-02 06:17:03,"Liz Pryde" <elizabethpryde@gmail.com> wrote:
> >Hello Lin,
> >
> >It's a bit difficult to give you an exact answer without knowing what the data set is.
> >That said, in general, count data does usually follow a poisson or neg binomial distribution. When you log transform such data, you are trying to normalise its distribution so that you can apply OLS regression (which assumes a normal distribution for the Y data to give you 'correct' significance values). One of the problems with this is that when you have data that can't be negative (e.g. counts) OLS regression on count data can give you estimations of your predicted values that may be negative (and hence, nonsensical). Also, when mean values are very low (near zero or zero), transforming the data becomes ineffective. GLMs overcome this problem because they explicitly model the X-Y relationship through the link function and ALSO model the mean-variance relationship (which is what is happening when you choose 'family= '). So they 'normalise' and 'linearise' the data as well as 'model' the error. Poisson data will generally have a variance that increases with increasing mean. On occasion this variance may be higher than expected (overdispersed) and so the negative binomial becomes appropriate.
> >
> >I hope this helps.
> >The O'Hara paper that was mentioned below gives an excellent explanation of this.
> >
> >Liz
> >
> >
> >On 02/08/2012, at 3:42 AM, lgj200306 <lgj200306@163.com> 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 
> >> 	[[alternative HTML version deleted]]
> >> 
> >> _______________________________________________
> >> R-sig-ecology mailing list
> >> R-sig-ecology@r-project.org
> >> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
> >
> >Liz Pryde
> >PhD Candidate (off-campus @ The University of Melbourne)
> >School of Earth and Environmental Sciences
> >James Cook University, QLD
> >
> >elizabethpryde@gmail.com
> >epryde@unimelb.edu.au
> >
> >
> 
> 

Liz Pryde
PhD Candidate (off-campus @ The University of Melbourne)
School of Earth and Environmental Sciences
James Cook University, QLD

elizabethpryde@gmail.com
epryde@unimelb.edu.au



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