Extract diagnostic metrics (Effective Sample Size (ESS), Rhat and Monte Carlo Standard Error MCSE).

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 stanmvreg
diagnostic_posterior(
posteriors,
diagnostic = "all",
effects = c("fixed", "random", "all"),
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 or brms model. Diagnostic metrics to compute. Character (vector) or list with one or more of these options: "ESS", "Rhat", "MCSE" or "all". Currently not used. Should parameters for fixed effects, random effects or both be returned? Only applies to mixed models. May be abbreviated. 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. 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., \& 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

if (FALSE) {
# rstanarm models
# -----------------------------------------------
if (require("rstanarm", quietly = TRUE)) {
model <- stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200, refresh = 0)
diagnostic_posterior(model)
}

# brms models
# -----------------------------------------------
if (require("brms", quietly = TRUE)) {
model <- brms::brm(mpg ~ wt + cyl, data = mtcars)
diagnostic_posterior(model)
}
}