[R-sig-ME] Offset vs fixed factor in a mixed poisson model

[v_coudrain at voila.fr]

Dear Alain,

Thank you for your reply. I tried to understand what you said, but have some difficulties:

> If you use a covariate as an offset then you essentially saying: double 
> the value of the variable used for the offset, double the numbers 
> (strictly speaking: the expected value). 

What do you mean wirh "double the value"? Does it mean that if the value of the offset double, then the expected value of my response variable should double? 
And if I have offset(logx), then doubling the log of my variable will double the estimate of the response variable?

> Quite often sampling effort is used as an offset as it is not really interesting to model a 
> cause-effect relationship between sampling effort and your response.

Indeed I don't directly have different sampling effort, but I am testing species richness in 3 years in a growing population, such that the abundance of individuals 
strongly increased between the year. The situation is quite similar as if we had increased the sampling effort over the years.

> If you have a model with:
> glm(y ~ x, family = poisson)
> glm(y ~ x + offset(z), family = poisson)

> and x is significant in the first model...but not in the second, then 
> either the offset explains most variation, or x and the offset are 
> highly correlated? Plot x versus z...and plot x versus log(z)...

x and z are indeed quite correlated, but it would be "nice" to see if x still explains some variation in my data independently of z. 

Ben Bolker suggested that the parameter estimate for using a variable as an offset should be about one. What is your opinion on this?

Best,
Valérie

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