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Posteriors Sampling Diagnostic

Source: R/diagnostic_posterior.R
diagnostic_posterior.Rd

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 = "all", ...)

# 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; a list of data frames or matrices representing MCMC chains (rows as samples, columns as parameters); or a 3D array (dimensions: samples, chains, parameters)

...

Currently only used for models of class brmsfit, where a variable argument can be used, which is directly passed to the as.data.frame() method (i.e., as.data.frame(x, variable = variable)).

diagnostic

Diagnostic metrics to compute. Character (vector) or list with one or more of these options: "ESS", "ESS_bulk", "Rhat", "MCSE" or "all". "ESS" returns the tail-ESS (the minimum of the effective sample sizes for the 5% and 95% quantiles), which is the most relevant diagnostic for assessing the reliability of credible intervals and other tail-based quantities. "ESS_bulk" additionally returns the bulk-ESS (the effective sample size for the bulk of the posterior, useful for assessing the reliability of central tendency estimates such as the mean or median). "all" includes both tail and bulk "ESS", "Rhat", and "MCSE".

effects

Should variables for fixed effects ("fixed"), random effects ("random") or both ("all") be returned? Only applies to mixed models. May be abbreviated.

For models of from packages brms or rstanarm there are additional options:

  • "fixed" returns fixed effects.

  • "random_variance" return random effects parameters (variance and correlation components, e.g. those parameters that start with sd_ or cor_).

  • "grouplevel" returns random effects group level estimates, i.e. those parameters that start with r_.

  • "random" returns both "random_variance" and "grouplevel".

  • "all" returns fixed effects and random effects variances.

  • "full" returns all parameters.

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 returned by diagnostic_posterior() is the tail-ESS: it corresponds to the minimum of the effective sample sizes for the 5% and 95% quantiles, and is a diagnostic for the sampling efficiency in the tails of the posterior distribution. It is more relevant than the bulk-ESS for assessing the reliability of credible intervals, probabilities of direction, and other tail-based quantities. Note that the tail-ESS may differ from the ESS reported by brms (Bulk_ESS) or other tools; use "ESS_bulk" to also retrieve the bulk-ESS.

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       MCSE ESS_tail ESS_bulk
#> 1 (Intercept) 0.9980336 0.36239857      156      192
#> 2        gear 0.9917174 0.06502841      155      223
#> 3          wt 0.9978902 0.04771990      150      192

# 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 6e-06 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)
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#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.021 seconds (Warm-up)
#> Chain 1:                0.017 seconds (Sampling)
#> Chain 1:                0.038 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' 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: 
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#> Chain 2:  Elapsed Time: 0.021 seconds (Warm-up)
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#> Chain 2:                0.04 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: 
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#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.035 seconds (Warm-up)
#> Chain 3:                0.019 seconds (Sampling)
#> Chain 3:                0.054 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: 
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#> Chain 4: 
#> Chain 4:  Elapsed Time: 0.019 seconds (Warm-up)
#> Chain 4:                0.021 seconds (Sampling)
#> Chain 4:                0.04 seconds (Total)
#> Chain 4: 
diagnostic_posterior(model)
#>     Parameter     Rhat ESS_tail ESS_bulk       MCSE
#> 1 b_Intercept 1.002513     3129     4728 0.02600493
#> 2       b_cyl 1.003602     1961     1912 0.01004421
#> 3        b_wt 1.003249     1940     1743 0.01934729
# }
set.seed(101)
mkdata <- function(nrow = 1000, ncol = 2, parnm = LETTERS[1:ncol]) {
  x <- as.data.frame(replicate(ncol, rnorm(nrow)))
  names(x) <- parnm
  x
}
dd <- replicate(5, mkdata(), simplify = FALSE)
diagnostic_posterior(dd)
#>   Parameter      Rhat  ESS       MCSE
#> 1         A 1.0012187 2460 0.02455354
#> 2         B 0.9997185 2279 0.01998160