Low ESS and High RHat for Random Intercept & Slope Simulation (rstan and rstanarm)

[joeHoover]

UPDATE

I just ran the same stan_lmer model on the same simulation, with the exception that \sigma_e = \sigma_{u0j} = \sigma_{u1j} = 1 in the DGP. Under those conditions, I observed the same issues with EFF and Rhat as well as comparable correlations between fixed effects and their corresponding random effects in the pairs() plot. I also reran the simulation and model, but with 100 groups instead of 50 (i.e. J = 50). This did not resolve the problem.

So, to summarize, I’m finding that ESS decreases and Rhat increases as \sigma_{u0j} and \sigma_{u1j} approach \sigma_e. I assume I must be doing something wrong here, but I am not sure what.

UPDATE # 2

I just found an old thread where @stijn wrote:

@stijn

If the correct model can perfectly predict the outcomes in the simulated data, the posterior has probability 0 for any non correct model and 1 for the correct model. Stan doesn’t handle does types of discontinuities well.

I guess this could be an issue as I am using the correct model? However, I added an unmodeled variable z with \beta_z = .3 to the simulation and this did not mitigate the issue.

Also, consistent with the low ESS, there is high autocorrelation among the samples for the intercept when the random effect SDs and \sigma_e are equal or close.

However, this completely disappears when the random effect SDs = .2 and \sigma_e = 1.

UPDATE

I just increased the effect of the unmodeled variable z_{tj} to 1 and all of the issues disappeared. So, maybe the issue is that I have been modeling the DGP to closely? FWIW, I only started initially observing these issues when I introduced a random slope to the model.