I’m trying to account for some quite extensive overdispersion in my data by modelling the residual variance via a varying intercept for each observation:

```
m0 <- brm(new_songs ~ 1 + (1|obs), data=df, family=poisson(),
chains=4, cores = 4, iter = 4000, warmup = 1000)
```

Converge and mixing is good, but the Pareto k diagnostics are really bad:

```
Computed from 12000 by 85 log-likelihood matrix
Estimate SE
elpd_loo -245.7 12.0
p_loo 65.7 1.8
looic 491.5 23.9
------
Monte Carlo SE of elpd_loo is NA.
Pareto k diagnostic values:
Count Pct. Min. n_eff
(-Inf, 0.5] (good) 0 0.0% <NA>
(0.5, 0.7] (ok) 9 10.6% 182
(0.7, 1] (bad) 70 82.4% 23
(1, Inf) (very bad) 6 7.1% 9
```

When modelling using a negative binomial, however, all is good, though looic is a bit higher:

```
Estimate SE
elpd_loo -351.6 20.7
p_loo 3.1 1.2
looic 703.2 41.3
```

Yet, when looking at the different pp_checks, the poisson model seems to be doing quite OK (see the attached images).

So my question is: should I be worried about the pareto diagnostics (I probably should), or does anyone have a suggestion about how to improve them?

- Operating System: MacOS 10.14.6
- brms Version: brms_2.10.1