Paper on DHARMa / statistical justification for DHARMa residuals

[florianhartig]

From a user

With regards to the DHARMa package, I was wondering if your "more exact statistical justification for the approach in an accompanying paper" was available to take a look at. The use of randomized quantile residuals as an omnibus diagnostic tool seems to be gaining steam from being one of the default diagnostics within GAMLSS and recently being recommended as a diagnostic for model-based ordination in statistical ecology.

Other than those resources, and the below working paper, I am unaware of additional written discussion beyond the paper that introduced them and the underlying theorems upon which the approach is based.

https://arxiv.org/abs/1708.08527

[florianhartig]

Mea culpa, I have been wanting to write this paper for so long. Maybe this summer. I had some other people asking about it.

About other references: I think there are quite a bit more references that the unsuspecting eye suggests, although they might be scattered. I believe the integer randomisation procedure as such is sufficiently covered by Dunn and Smyth (1996). To simulate from the fitted model is known as the parametric bootstrap, and the recommendation to use this has popped up in various places over the years (Simon Wood who develops mgcv always recommended it, I seem to remember it was also mentioned in Gelman & Hill 2007). Moreover, Bayesians have used the same or similar procedures (alas, often with the Dunn & Smyth trick) for years, see discussion in https://esajournals.onlinelibrary.wiley.com/doi/10.1002/ecm.1314. The difference is obviously that they sample from the posterior instead of the MLE. There is some work / discussion to do about the exact distributional properties, as residuals won't be exactly uniform for biased estimators (e.g. REs).