Extract diagnostic metrics (Effective Sample Size (`ESS`

), `Rhat`

and Monte
Carlo Standard Error `MCSE`

).

## Usage

```
diagnostic_posterior(posteriors, diagnostic = c("ESS", "Rhat"), ...)
# S3 method for stanreg
diagnostic_posterior(
posteriors,
diagnostic = "all",
effects = c("fixed", "random", "all"),
component = c("location", "all", "conditional", "smooth_terms", "sigma",
"distributional", "auxiliary"),
parameters = NULL,
...
)
# S3 method for brmsfit
diagnostic_posterior(
posteriors,
diagnostic = "all",
effects = c("fixed", "random", "all"),
component = c("conditional", "zi", "zero_inflated", "all"),
parameters = NULL,
...
)
```

## Arguments

- posteriors
A

`stanreg`

,`stanfit`

,`brmsfit`

, or`blavaan`

object.- diagnostic
Diagnostic metrics to compute. Character (vector) or list with one or more of these options:

`"ESS"`

,`"Rhat"`

,`"MCSE"`

or`"all"`

.- ...
Currently not used.

- effects
Should parameters for fixed effects, random effects or both be returned? Only applies to mixed models. May be abbreviated.

- component
Which type of parameters to return, such as parameters for the conditional model, the zero-inflated part of the model, the dispersion term, the instrumental variables or marginal effects be returned? Applies to models with zero-inflated and/or dispersion formula, or to models with instrumental variables (so called fixed-effects regressions), or models with marginal effects from mfx. May be abbreviated. Note that the

*conditional*component is also called*count*or*mean*component, depending on the model. There are three convenient shortcuts:`component = "all"`

returns all possible parameters. If`component = "location"`

, location parameters such as`conditional`

,`zero_inflated`

,`smooth_terms`

, or`instruments`

are returned (everything that are fixed or random effects - depending on the`effects`

argument - but no auxiliary parameters). For`component = "distributional"`

(or`"auxiliary"`

), components like`sigma`

,`dispersion`

,`beta`

or`precision`

(and other auxiliary parameters) are returned.- parameters
Regular expression pattern that describes the parameters that should be returned.

## Details

**Effective Sample (ESS)** should be as large as possible, although for
most applications, an effective sample size greater than 1000 is sufficient
for stable estimates (Bürkner, 2017). The ESS corresponds to the number of
independent samples with the same estimation power as the N autocorrelated
samples. It is is a measure of “how much independent information
there is in autocorrelated chains” (Kruschke 2015, p182-3).
**Rhat** should be the closest to 1. It should not be larger than 1.1
(Gelman and Rubin, 1992) or 1.01 (Vehtari et al., 2019). The
split Rhat statistic quantifies the consistency of an ensemble of Markov
chains.
**Monte Carlo Standard Error (MCSE)** is another measure of accuracy of the
chains. It is defined as standard deviation of the chains divided by their
effective sample size (the formula for `mcse()`

is from Kruschke 2015, p.
187). The MCSE “provides a quantitative suggestion of how big the
estimation noise is”.

## References

Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.

Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., and Bürkner, P. C. (2019). Rank-normalization, folding, and localization: An improved Rhat for assessing convergence of MCMC. arXiv preprint arXiv:1903.08008.

Kruschke, J. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press.

## Examples

```
# \dontrun{
# rstanarm models
# -----------------------------------------------
if (require("rstanarm", quietly = TRUE)) {
model <- stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200, refresh = 0)
diagnostic_posterior(model)
}
#> Warning: The largest R-hat is 1.13, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
#> Warning: Markov chains did not converge! Do not analyze results!
#> Parameter Rhat ESS MCSE
#> 1 (Intercept) 0.9980336 182.6025 0.36283152
#> 2 gear 0.9917174 206.3058 0.06519599
#> 3 wt 0.9978902 186.7773 0.04770867
# brms models
# -----------------------------------------------
if (require("brms", quietly = TRUE)) {
model <- brms::brm(mpg ~ wt + cyl, data = mtcars)
diagnostic_posterior(model)
}
#> Compiling Stan program...
#> Start sampling
#>
#> SAMPLING FOR MODEL '2d19b3a372313df641edf05db5e9f303' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 1e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.1 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 2000 [ 0%] (Warmup)
#> Chain 1: Iteration: 200 / 2000 [ 10%] (Warmup)
#> Chain 1: Iteration: 400 / 2000 [ 20%] (Warmup)
#> Chain 1: Iteration: 600 / 2000 [ 30%] (Warmup)
#> Chain 1: Iteration: 800 / 2000 [ 40%] (Warmup)
#> Chain 1: Iteration: 1000 / 2000 [ 50%] (Warmup)
#> Chain 1: Iteration: 1001 / 2000 [ 50%] (Sampling)
#> Chain 1: Iteration: 1200 / 2000 [ 60%] (Sampling)
#> Chain 1: Iteration: 1400 / 2000 [ 70%] (Sampling)
#> Chain 1: Iteration: 1600 / 2000 [ 80%] (Sampling)
#> Chain 1: Iteration: 1800 / 2000 [ 90%] (Sampling)
#> Chain 1: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 0.027323 seconds (Warm-up)
#> Chain 1: 0.024058 seconds (Sampling)
#> Chain 1: 0.051381 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL '2d19b3a372313df641edf05db5e9f303' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 7e-06 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.07 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
#> Chain 2:
#> Chain 2: Iteration: 1 / 2000 [ 0%] (Warmup)
#> Chain 2: Iteration: 200 / 2000 [ 10%] (Warmup)
#> Chain 2: Iteration: 400 / 2000 [ 20%] (Warmup)
#> Chain 2: Iteration: 600 / 2000 [ 30%] (Warmup)
#> Chain 2: Iteration: 800 / 2000 [ 40%] (Warmup)
#> Chain 2: Iteration: 1000 / 2000 [ 50%] (Warmup)
#> Chain 2: Iteration: 1001 / 2000 [ 50%] (Sampling)
#> Chain 2: Iteration: 1200 / 2000 [ 60%] (Sampling)
#> Chain 2: Iteration: 1400 / 2000 [ 70%] (Sampling)
#> Chain 2: Iteration: 1600 / 2000 [ 80%] (Sampling)
#> Chain 2: Iteration: 1800 / 2000 [ 90%] (Sampling)
#> Chain 2: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 2:
#> Chain 2: Elapsed Time: 0.029673 seconds (Warm-up)
#> Chain 2: 0.027675 seconds (Sampling)
#> Chain 2: 0.057348 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL '2d19b3a372313df641edf05db5e9f303' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 6e-06 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3:
#> Chain 3:
#> Chain 3: Iteration: 1 / 2000 [ 0%] (Warmup)
#> Chain 3: Iteration: 200 / 2000 [ 10%] (Warmup)
#> Chain 3: Iteration: 400 / 2000 [ 20%] (Warmup)
#> Chain 3: Iteration: 600 / 2000 [ 30%] (Warmup)
#> Chain 3: Iteration: 800 / 2000 [ 40%] (Warmup)
#> Chain 3: Iteration: 1000 / 2000 [ 50%] (Warmup)
#> Chain 3: Iteration: 1001 / 2000 [ 50%] (Sampling)
#> Chain 3: Iteration: 1200 / 2000 [ 60%] (Sampling)
#> Chain 3: Iteration: 1400 / 2000 [ 70%] (Sampling)
#> Chain 3: Iteration: 1600 / 2000 [ 80%] (Sampling)
#> Chain 3: Iteration: 1800 / 2000 [ 90%] (Sampling)
#> Chain 3: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 3:
#> Chain 3: Elapsed Time: 0.028834 seconds (Warm-up)
#> Chain 3: 0.029708 seconds (Sampling)
#> Chain 3: 0.058542 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL '2d19b3a372313df641edf05db5e9f303' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 6e-06 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4:
#> Chain 4:
#> Chain 4: Iteration: 1 / 2000 [ 0%] (Warmup)
#> Chain 4: Iteration: 200 / 2000 [ 10%] (Warmup)
#> Chain 4: Iteration: 400 / 2000 [ 20%] (Warmup)
#> Chain 4: Iteration: 600 / 2000 [ 30%] (Warmup)
#> Chain 4: Iteration: 800 / 2000 [ 40%] (Warmup)
#> Chain 4: Iteration: 1000 / 2000 [ 50%] (Warmup)
#> Chain 4: Iteration: 1001 / 2000 [ 50%] (Sampling)
#> Chain 4: Iteration: 1200 / 2000 [ 60%] (Sampling)
#> Chain 4: Iteration: 1400 / 2000 [ 70%] (Sampling)
#> Chain 4: Iteration: 1600 / 2000 [ 80%] (Sampling)
#> Chain 4: Iteration: 1800 / 2000 [ 90%] (Sampling)
#> Chain 4: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 4:
#> Chain 4: Elapsed Time: 0.027826 seconds (Warm-up)
#> Chain 4: 0.028333 seconds (Sampling)
#> Chain 4: 0.056159 seconds (Total)
#> Chain 4:
#> Parameter Rhat ESS MCSE
#> 1 b_Intercept 0.9997601 4553.140 0.025783250
#> 2 b_cyl 1.0007901 2017.036 0.009788731
#> 3 b_wt 1.0005248 1974.860 0.018154517
# }
```