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.
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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.
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$\begingroup$ This is not good advice - it looks like that line corresponds to the observed $0$ values. It is also generally a bad looking plot for fitted values less than $2$ (which is roughly $\hat {\eta}<0.69$ -most of the data) $\endgroup$ – probabilityislogic Aug 1 '18 at 10:30
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