There are a number of important considerations when simulating from a more complex (hierarchical) model. Re-simulating random effects / hierarchical structure: the first is that in a hierarchical model, several layers of stochasticity are aligned on top of each other. Specifically, in a GLMM, we have a lower level stochastic process (random effect), whose result enters into a higher level (e.g. Poisson distribution). For other hierarchical models such as state-space models, similar considerations apply. When simulating, we have to decide if we want to re-simulate all stochastic levels, or only a subset of those. For example, in a GLMM, it is common to only simulate the last stochastic level (e.g. Poisson) conditional on the fitted random effects.
For controlling how many levels should be re-simulated, the simulateResidual function allows to pass on parameters to the simulate function of the fitted model object. Please refer to the help of the different simulate functions (e.g. ?simulate.merMod) for details. For merMod (lme4) model objects, the relevant parameters are parameters are use.u, and re.form
If the model is correctly specified, the simulated residuals should be flat regardles how many hierarchical levels we re-simulate. The most thorough procedure would therefore be to test all possible options. If testing only one option, I would recommend to re-simulate all levels, because this esentially tests the model structure as a whole. This is the default setting in the DHARMa package. A potential drawback is that re-simulating the lower-level random effects creates more variability, which may reduce power for detecing problems in the upper-level stochatic processes.
Integer responses: a second complication is the treatment of inter responses. Imaging we have observed a 0, and we predict 30% zeros - what is the quantile that we should display for the residual? To deal with this problem and maintain a unifor response, the option integerResponse adds a uniform noise from -0.5 to 0.5 on the simulated and observed response. Note that this works because the expected distribution of this is flat - you can see this via hist(ecdf(runif(10000))(runif(10000)))
Refitting or not: a third issue is how residuals are calculated. simulateResiduals has two options that are controlled by the refit parameter:
1. if refit = F (default), new data is simulated from the fitted model, and residuals are calculated by comparing the observed data to the new data
2. if refit = T, a parametric bootstrap is performed, meaning that the model is refit on the new data, and residuals are created by comparing observed residuals against refitted residuals
The second option is much slower, and only important for running tests that rely on comparing observed to simulated residuals, e.g. the testOverdispersion function
#' How many simulations: about the choice of n: my simulations didn't show major problems with a small n (if you get down to the order of a few 10, you will start seeing discretization artifacts from the empirical cummulative density estimates though). The default of 250 seems safe to me. If you want to be on the safe side, choose a high value (e.g. 1000) for producing your definite results.