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

[v_coudrain at voila.fr]

Thank you very much. There is still a "small" problem. If then the estimate of the variable to be set as an offset is not around 1, I should not put it as an offset. 
How do I then can control for its effect? 

Best,
Valérie


> Message du 18/01/13 à 21h29
> De : "Highland Statistics Ltd" 
> A : v_coudrain at voila.fr
> Copie à : r-sig-mixed-models at r-project.org
> Objet : Re: Offset vs fixed factor in a mixed poisson model
> 
> On 18/01/2013 16:09, v_coudrain at voila.fr wrote:
> > 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?
> 
> Valerie,
> Yes...indeed that is what the offset is doing. Double the value of the 
> x....you assume that the expected value of your response also doubles. 
> Just write out the equation for a Poisson and you will see:
> 
> Y_i ~ Poisson(mu_i)
> E(Y_i) = mu_i
> mu_i = exp(alpha + beta * z + 1 * log(x))
> = x* exp(alpha + beta * z)
> 
> Double x....double mu
> 
> 
> Keep in mind that when you analyse a ratio you implicitly do the same; 
> 1/2 = 100/ 200 = 0.5
> 
> >> 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.
> 
> 'would be nice' and collinearity don't go together very well.
> 
> > Ben Bolker suggested that the parameter estimate for using a variable as an offset should be about one. What is your opinion on this?
> 
> Ben is a clever cookie....and he is right.
> 
> Alain
> 
> 
> > Best,
> > Valérie
> >
> > ___________________________________________________________
> > Envie de changer de frigo ou de gazinière ? Les soldes électroménager sont sur Voila.fr http://shopping.voila.fr/vitrine/electromenager
> >
> 
> 
> -- 
> 
> Dr. Alain F. Zuur
> First author of:
> 
> 1. Analysing Ecological Data (2007).
> Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
> URL: www.springer.com/0-387-45967-7
> 
> 
> 2. Mixed effects models and extensions in ecology with R. (2009).
> Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer.
> http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9
> 
> 
> 3. A Beginner's Guide to R (2009).
> Zuur, AF, Ieno, EN, Meesters, EHWG. Springer
> http://www.springer.com/statistics/computational/book/978-0-387-93836-3
> 
> 
> 4. Zero Inflated Models and Generalized Linear Mixed Models with R. (2012) Zuur, Saveliev, Ieno.
> http://www.highstat.com/book4.htm
> 
> Other books: http://www.highstat.com/books.htm
> 
> 
> Statistical consultancy, courses, data analysis and software
> Highland Statistics Ltd.
> 6 Laverock road
> UK - AB41 6FN Newburgh
> Tel: 0044 1358 788177
> Email: highstat at highstat.com
> URL: www.highstat.com
> URL: www.brodgar.com
> 
> 

___________________________________________________________
Envie de changer de frigo ou de gazinière ? Les soldes électroménager sont sur Voila.fr http://shopping.voila.fr/vitrine/electromenager