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Which is the dispersion parameter in your GLM?
In R GLM assumes shape to be a constant (as linear regression assumes constant variance). To satisfy this assumption dispersion ( ϕ) is introduced: For the simple case glm (x ~ 1, family = Gamma (link = ‘identity)), summary.glm gives you estimate, that is equal to μ (note that default link is ‘inverse’ and estimate = 1 / μ) and dispersion is ϕ.
Which is the default link for a gamma GLM?
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
What are the parameters of the gamma family?
Gamma distribution defined by two parameters – shape ( α) and rate ( β ). There is alternative parameterization through mean ( μ) and shape, which is used in GLM. We take μ = α / β and put it into place of rate (as β = α / μ ), resulting in function G a m m a ( μ, α).
Are there different ways to parameterize the gamma distribution?
There are multiple ways to parameterize the Gamma distribution, so it’s important to pay attention when moving between languages and functions. As with many optimization exercises, we can force a term (here shape) to be positive by fitting in log-space.
Which is the dispersion parameter for gamma family?
To satisfy this assumption dispersion ( ϕ) is introduced: For the simple case glm (x ~ 1, family = Gamma (link = ‘identity)), summary.glm gives you estimate, that is equal to μ (note that default link is ‘inverse’ and estimate = 1 / μ) and dispersion is ϕ. Thanks for contributing an answer to Cross Validated!
How is the shape parameter used in GLM?
There is alternative parameterization through mean ( μ) and shape, which is used in GLM. We take μ = α / β and put it into place of rate (as β = α / μ ), resulting in function G a m m a ( μ, α). In R GLM assumes shape to be a constant (as linear regression assumes constant variance).
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