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I apologize if this has been asked and answered elsewhere -- I've tried to find the answer and could not.

In R, if you use the normal plot() command on a glm object, one of the graphs displayed is a QQ plot. It explicitly states at the top that it is Normal QQ plot.

However, GLMs (unlike simple LMs) allow one to assume that the response variable is not normally distributed. For instance, you may specify in your glm equation that you are assuming a gamma distribution.

Why does R show a normal QQ plot in such a case? Why isn't the QQ against a gamma distribution? Is there even any value in looking at the normal QQ plot unless your "family" parameter in your glm setup is "gaussian"?

Many, many thanks for any help.

bilibraker
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SirBeaverton
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    Because its the _residuals_ that are assumed to be normally distributed, and that's what R is helping you to assess. – Edward Jun 14 '20 at 06:09
  • Thanks very much Edward. So should the residuals of any glm with a continuous distribution be approximately normal? (I assume that for a binomial, for instance, they will not be.) The residuals on the model I created (with a gamma distribution) are concave up in plot.lm. But they look normal in glm.diag.plot, which I don't understand. – SirBeaverton Jun 14 '20 at 16:55
  • Edward, you might find this link interesting, which I just came across: https://stats.stackexchange.com/questions/295340/what-to-do-with-glm-gamma-when-residuals-are-not-normally-distributed/302413#302413 – SirBeaverton Jun 14 '20 at 17:07

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R does show a normal QQ plot in such a case because R does not have a plot.glm function and calls plot.lm even for glm objects, which in most cases isn't very useful.

See e.g., here for diagnostic plots for glms with gamma distributions.

Dominik S. Meier
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  • Dominik, thank you very much for that helpful link. Maybe you can answer a further question. I ran the glm.diag.plot function on a glm, and got a very different QQ plot than I get when I run the normal plot.lm. However, what I see in the documentation indicates that both use standardized residuals for this plot (though glm.diag.plot uses jackknifed residuals for the residuals vs fitted graph, and plot.lm does not). That seems very puzzling. Any idea what would cause that? – SirBeaverton Jun 14 '20 at 16:51
  • Sorry I have to pass on this one, I am not familiar with these models, but I knew that glm doesn't assume normality of residuals. But just ask another question on Cross Validated – Dominik S. Meier Jun 14 '20 at 20:09