Hi,

I got two problematic k values when using the LOO package. See the output as below:

```
> r_eff_ML <- relative_eff(exp(GMM_ML_fit_4c$draws("log_lik")), cores = 16)
> loo_waic_ML<-waic(GMM_ML_fit_4c$draws("log_lik"))
Warning message:
12 (3.0%) p_waic estimates greater than 0.4. We recommend trying loo instead.
> loo_ML <- loo(GMM_ML_fit_4c$draws("log_lik"), r_eff = r_eff_ML, cores = 16)
Warning message:
Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.
> print(loo_waic_ML)
Computed from 6000 by 405 log-likelihood matrix
Estimate SE
elpd_waic -1545.6 40.6
p_waic 32.5 5.4
waic 3091.3 81.1
12 (3.0%) p_waic estimates greater than 0.4. We recommend trying loo instead.
> print(loo_ML)
Computed from 6000 by 405 log-likelihood matrix
Estimate SE
elpd_loo -1545.6 40.5
p_loo 32.5 5.3
looic 3091.2 80.9
------
Monte Carlo SE of elpd_loo is NA.
Pareto k diagnostic values:
Count Pct. Min. n_eff
(-Inf, 0.5] (good) 403 99.5% 3
(0.5, 0.7] (ok) 0 0.0% <NA>
(0.7, 1] (bad) 2 0.5% 61
(1, Inf) (very bad) 0 0.0% <NA>
See help('pareto-k-diagnostic') for details.
```

See the PSIS diagnostic plot below:

Because the number is small, I tried to “refit the model once for each of these problematic observations”, which is recommended from this vignette (Using the loo package (version >= 2.0.0)). My code is as follows:

```
> if (any(pareto_k_values(loo_ML) > 0.7)) {
+ loo_ML <- loo(GMM_ML_fit_4c$draws("log_lik"), save_psis = TRUE, k_threshold = 0.7)
+ }
Warning messages:
1: Relative effective sample sizes ('r_eff' argument) not specified.
For models fit with MCMC, the reported PSIS effective sample sizes and
MCSE estimates will be over-optimistic.
2: Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.
> print(loo_ML)
Computed from 6000 by 405 log-likelihood matrix
Estimate SE
elpd_loo -1545.6 40.5
p_loo 32.4 5.3
looic 3091.1 80.9
------
Monte Carlo SE of elpd_loo is NA.
Pareto k diagnostic values:
Count Pct. Min. n_eff
(-Inf, 0.5] (good) 403 99.5% 821
(0.5, 0.7] (ok) 1 0.2% 211
(0.7, 1] (bad) 1 0.2% 531
(1, Inf) (very bad) 0 0.0% <NA>
See help('pareto-k-diagnostic') for details.
```

The question is why I still got two problematic k values. Did I do something wrong? Does anyone have suggestions?

Thank you so much for helping me!

Best,

Doria