How to interpret meaning of residual vs. predicted quantile plots in DHARMa? I understand that the lines in the residual vs. predicted quantile plots should be flat at each quantile, but I'm struggling to understand what each line is actually showing. Similarly, what does it mean if only one of the lines is off? I've included an example of this - thanks for any input.


I'm the developer of DHARMa. First of all, I would like to highlight the package help of plotResiduals(), which basically explains what is calculated:

The function plots residuals against a predictor (by default against
the fitted value, extracted from the DHARMa object, or any other
predictor).
Outliers are highlighted in red (for information on definition and
interpretation of outliers, see testOutliers).
To provide a visual aid in detecting deviations from uniformity in
y-direction, the plot function calculates an (optional) quantile
regression of the residuals, by default for the 0.25, 0.5 and 0.75
quantiles. As the residuals should be uniformly distributed for a
correctly specified model, the theoretical expectations for these
regressions are straight lines at 0.25, 0.5 and 0.75, which are
displayed as dashed black lines on the plot. Some deviations from
these expectations are to be expected by chance, however, even for a
perfect model, especially if the sample size is small. The function
therefore tests if deviation of the fitted quantile regression from
the expectation is significant, using testQuantiles. If so, the
significant quantile regression will be highlighted as red, and a
warning will be displayed in the plot.

Based on this, I would conclude that you have slight evidence for a humped-shape res~fitted pattern, which you should interpret as for normal lm residuals, i.e. there seems to be a nonlinearity in the data that is not captured by your model. You could, for example, try to add a quadratic effect for your main predictor(s).
That being said, given the low number of data points, this might as well be a statistical fluke.
