Solved – What’s the practical meaning of alpha in a GLM with gamma family

gamma distributiongeneralized linear model

I am fitting several models of the form..

glm(DV ~ I(1/IV), family = Gamma(link = "log")

.. and am looking for ways to compare the models obtained for different variables. I am wondering if the alpha value is of any practical use?

For the three plots below the alpha values are 17.85, 9.03 and 6.27. Do these values contain any information that helps me to interpret my data, or to compare the different variables?

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Best Answer

The values of the alpha-parameter of the gamma describe the shape of the distribution at any given value of IV (essentially giving an idea how skewed the conditional distribution is -- the smaller $\alpha$ is, the more skew)

In a GLM, it doesn't change the mean ...

plot of gamma densities for varying values of the shape parameter

... so it has no impact on the fitted curves in your plots; it only describes the shape of the distribution about the mean.

The steepness of the descent of the curves in your plots is determined by the coefficient of your IV. You might find it instructive to look at your plots (of the data and the fitted model) on the log scale.

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