Q:

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

A:

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.  

