Contents
What is a Gamma Link?
A Gamma error distribution with a log link is a common family to fit GLMs with in ecology. It works well for positive-only data with positively-skewed errors. The Gamma distribution is flexible and can mimic, among other shapes, a log-normal shape. There are multiple ways to parameterize the Gamma distribution in R .
What is a gamma distribution used for?
Gamma Distribution is a Continuous Probability Distribution that is widely used in different fields of science to model continuous variables that are always positive and have skewed distributions. It occurs naturally in the processes where the waiting times between events are relevant.
How are the coefficients of a gamma GLM related?
Generally speaking, the higher the concentration of blood plasma, the faster the clotting. The coefficients of a glm always relate to the mean μ, by way of the assumed link function. The default link for a gamma glm is the inverse link, so the model that has been fitted is
When to use gamma GLMs instead of lognormal?
Also, gamma regression (or other models for nonnegative data) can cope with a broader array of data than the lognormal due to the fact that it can have a mode at 0, such as you have with the exponential distribution, which is in the gamma family, which is impossible for the lognormal.
Is the Gamma Density decomposition available in other GLM models?
This decomposition is not available in most other glm models (see also Logistic Regression – Error Term and its Distribution ). For the gamma glm, we have, specifically, that the gamma density of the observations can be written (here I follow McCullagh & Nelder: “Generalized Linear Models” second edition, chapter 8)
Is the log-linked gamma GLM specification identical to exponential regression?
The log-linked gamma GLM specification is identical to exponential regression: ( α). That’s not a very meaningful value (unless you centered your variables to be be mean zero beforehand). There are at least three way to interpret your model. One is to take derivative of the expected value of y given x with respect to x: