# Interpreting QQ plot of poisson regression

This is the QQ plot resulting after fitting a poisson regression.

I found in a book saying that central line corresponds to zero cases in the response. I can imagine that for zero response cases standardized deviance residuals is negative. But how one can specifically say that the central line of the plot corresponds to zeros? What is the logic behind the argument

• When you say central line what exactly are you referring to? I do not see a line anywhere on the plot. Commented Aug 16, 2017 at 14:03
• See stats.stackexchange.com/questions/295340/… for an example, with R code, for making qqplots for a generalized linear model, based on simulation. Commented Dec 2, 2017 at 17:48

The line does not correspond to zeros. The Poisson distribution is for counts, which cannot go below $0$. You can see that there are points below the line. Instead, it is drawn through the middle of the distribution to give you a visual point (er, line) of reference. There are various algorithms for drawing the line, a common one is to draw a line connecting the first and third quartiles. I can't tell if that's what was done in your case.

At any rate, the qq-plot is constructed to help you assess if the residuals are normally distributed. But for a Poisson regression that doesn't make a lot of sense. So, I would probably ignore that plot.

Plotting to understand your model, and to check your assumptions is a very good thing to do, though. You can find some good ideas here: Diagnostic plots for count regression.

• Thanks @gung. If you have not mistaken I am referring to the central line of points in the graph (I have replaced the previous image to give more clarity). Not to the dashed reference line. Commented Aug 16, 2017 at 15:18
• Those wouldn't have been zeros. I'll scratch out the part about how the dotted line is drawn, but the bulk of the answer remains appropriate. Commented Aug 16, 2017 at 15:20
• Youcan construxt a qqplot using theoretical quantiles from a poisson distribution, say, the poisson distribution with the same mean as the data Commented Aug 23, 2017 at 19:45
• @Kjetil However, it would be bizarre if the standardized residuals ever looked remotely like any Poisson distribution! They won't be positive and they won't be integral. The plot in the question is a good illustration.
– whuber
Commented May 22, 2018 at 15:29
• @whuber: Of course you are right. I should have pointed to stats.stackexchange.com/questions/267461/… for simulated residuals Commented Jun 8, 2018 at 23:41