Solved – Interpret deviance residual plot in poisson regression

Question

Below is a deviance residual plot obtained from a poisson regression.

Since deviance residuals is a form of standardized residuals, we do expect it to have a constant variance. However, when there are lines of points how can we interpret the plot.

Answer 1

The apparent curved lines stem from the fact that actual observations are discrete numbers, while the modeled expectations are continuous. At each $\eta$, the vertical distance between the curves should be an integer multiple of $1/\sqrt{\mu}$ ($\mu$ being the fitted value).

What interests you is whether the spread is the same for each $\eta$. In the above case, I'd say "no": For $\eta < -2$ the data and the fit match almost perfectly, while for $\eta > 0$ they noticeably differ.