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

[Highland Statistics Ltd]

On 18/01/2013 16:34, v_coudrain at voila.fr wrote:
> 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?
What about:

Y_i ~Poisson(mu_i)
log(mu_i) = alpha + beta_1 * x_i + beta_2 * z_i

That's a model where beta_1 shows the partial effect of x_i.....which 
means...the effect of x_i while taking into account z_i..and vice versa.

But now your collinearity is going to cause some trouble. I am not sure 
whether the partial linear regression equivalent for a Poisson GLMM 
exists.....

Alain


> 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
>


-- 

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