Extract diagnostic metrics (Effective Sample Size (`ESS`

), `Rhat`

and Monte
Carlo Standard Error `MCSE`

).

## Usage

```
diagnostic_posterior(posterior, ...)
# S3 method for default
diagnostic_posterior(posterior, diagnostic = c("ESS", "Rhat"), ...)
# S3 method for stanreg
diagnostic_posterior(
posterior,
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(
posterior,
diagnostic = "all",
effects = c("fixed", "random", "all"),
component = c("conditional", "zi", "zero_inflated", "all"),
parameters = NULL,
...
)
```

## Arguments

- posterior
A

`stanreg`

,`stanfit`

,`brmsfit`

, or`blavaan`

object.- ...
Currently not used.

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

`"ESS"`

,`"Rhat"`

,`"MCSE"`

or`"all"`

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

- component
Should all predictor variables, predictor variables for the conditional model, the zero-inflated part of the model, the dispersion term or the instrumental variables be returned? Applies to models with zero-inflated and/or dispersion formula, or to models with instrumental variable (so called fixed-effects regressions). May be abbreviated. Note that the

*conditional*component is also called*count*or*mean*component, depending on the model.- 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

```
# \donttest{
# rstanarm models
# -----------------------------------------------
model <- suppressWarnings(
rstanarm::stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200, refresh = 0)
)
diagnostic_posterior(model)
#> 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
# -----------------------------------------------
model <- brms::brm(mpg ~ wt + cyl, data = mtcars)
#> Compiling Stan program...
#> Start sampling
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 7e-06 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.07 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: 0.023 seconds (Warm-up)
#> Chain 1: 0.018 seconds (Sampling)
#> Chain 1: 0.041 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 3e-06 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.03 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: 0.024 seconds (Warm-up)
#> Chain 2: 0.021 seconds (Sampling)
#> Chain 2: 0.045 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 3e-06 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.03 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: 0.024 seconds (Warm-up)
#> Chain 3: 0.02 seconds (Sampling)
#> Chain 3: 0.044 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 3e-06 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.03 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: 0.021 seconds (Warm-up)
#> Chain 4: 0.022 seconds (Sampling)
#> Chain 4: 0.043 seconds (Total)
#> Chain 4:
diagnostic_posterior(model)
#> Parameter Rhat ESS MCSE
#> 1 b_Intercept 1.000297 4618.359 0.02593799
#> 2 b_cyl 1.003470 1868.916 0.01002953
#> 3 b_wt 1.003250 1697.213 0.01926801
# }
```