# What's the practical meaning of alpha in a GLM with gamma family?

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? • I've bee assuming by alpha that you mean the shape parameter of the gamma; can you clarify whether you mean that or something else (such as the intercept in your model for the mean) Mar 20, 2017 at 12:44
• yes, I meant the shape parameter!
– user45065
Mar 20, 2017 at 12:47

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 ... ... 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.

• Yes, I get that, but what can I infer? E.g., is it valid to say that the higher the value the steeper the decline of y values for low x values? Or, that for small alpha values there is a less abrupt turning point between high y/low x and low y/high x?
– user45065
Mar 20, 2017 at 12:10
• See my edit above... Mar 20, 2017 at 12:29