Posteriors Sampling Diagnostic — diagnostic

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

Usage

diagnostic_posterior(posterior, ...)

# Default S3 method
diagnostic_posterior(posterior, diagnostic = c("ESS", "Rhat"), ...)

# S3 method for class 'stanreg'
diagnostic_posterior(
  posterior,
  diagnostic = "all",
  effects = "fixed",
  component = "location",
  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 variables for fixed effects ("fixed"), random effects ("random") or both ("all") 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). See details in section Model Components .May be abbreviated. Note that the conditional component also refers to the count or mean component - names may differ, depending on the modeling package. There are three convenient shortcuts (not applicable to all model classes):

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".

Model components

Possible values for the component argument depend on the model class. Following are valid options:

"all": returns all model components, applies to all models, but will only have an effect for models with more than just the conditional model component.
"conditional": only returns the conditional component, i.e. "fixed effects" terms from the model. Will only have an effect for models with more than just the conditional model component.
"smooth_terms": returns smooth terms, only applies to GAMs (or similar models that may contain smooth terms).
"zero_inflated" (or "zi"): returns the zero-inflation component.
"location": returns location parameters such as conditional, zero_inflated, or smooth_terms (everything that are fixed or random effects - depending on the effects argument - but no auxiliary parameters).
"distributional" (or "auxiliary"): components like sigma, dispersion, beta or precision (and other auxiliary parameters) are returned.

For models of class brmsfit (package brms), even more options are possible for the component argument, which are not all documented in detail here. See also ?insight::find_parameters.

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 0.35422559
#> 2        gear 0.9917174 206.3058 0.06266168
#> 3          wt 0.9978902 186.7773 0.04708337

# 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 9e-06 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
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#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.019 seconds (Warm-up)
#> Chain 1:                0.016 seconds (Sampling)
#> Chain 1:                0.035 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!
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#> 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.
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#> 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!
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#> Chain 4:  Elapsed Time: 0.019 seconds (Warm-up)
#> Chain 4:                0.02 seconds (Sampling)
#> Chain 4:                0.039 seconds (Total)
#> Chain 4: 
diagnostic_posterior(model)
#>     Parameter     Rhat      ESS        MCSE
#> 1 b_Intercept 1.000297 4618.359 0.025634483
#> 2       b_cyl 1.003470 1868.916 0.009916104
#> 3        b_wt 1.003250 1697.213 0.019012061
# }