Offset vs fixed factor in a mixed poisson model
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, Val?rie
Message du 18/01/13 ? 21h29 De : "Highland Statistics Ltd" A : v_coudrain at voila.fr Copie ? : 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, Val?rie
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-- 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 gazini?re ? Les soldes ?lectrom?nager 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