Accessing the contents of a stanfit object

Stan Development Team

2024-01-10

This vignette demonstrates how to access most of data stored in a stanfit object. A stanfit object (an object of class "stanfit") contains the output derived from fitting a Stan model using Markov chain Monte Carlo or one of Stan’s variational approximations (meanfield or full-rank). Throughout the document we’ll use the stanfit object obtained from fitting the Eight Schools example model:

library(rstan)
fit <- stan_demo("eight_schools", refresh = 0)
Warning: There were 1 divergent transitions after warmup. See
https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
to find out why this is a problem and how to eliminate them.
Warning: Examine the pairs() plot to diagnose sampling problems
class(fit)
[1] "stanfit"
attr(,"package")
[1] "rstan"

Posterior draws

There are several functions that can be used to access the draws from the posterior distribution stored in a stanfit object. These are extract, as.matrix, as.data.frame, and as.array, each of which returns the draws in a different format.


extract()

The extract function (with its default arguments) returns a list with named components corresponding to the model parameters.

[1] "mu"    "tau"   "eta"   "theta" "lp__" 

In this model the parameters mu and tau are scalars and theta is a vector with eight elements. This means that the draws for mu and tau will be vectors (with length equal to the number of post-warmup iterations times the number of chains) and the draws for theta will be a matrix, with each column corresponding to one of the eight components:

[1]  5.383476  4.259927  3.773597  5.466592  6.588603 13.404230
[1]  3.4376655  3.8935749 21.2406208  1.0448334  0.0428121  0.1155494
          
iterations      [,1]      [,2]      [,3]      [,4]       [,5]       [,6]
      [1,]  4.073177  4.784386  5.980737  5.431588  6.7625026 -1.7959618
      [2,] -5.478766 -2.610753  5.670680  2.879631  5.1155202 -0.1764268
      [3,] 30.829292  7.974888  7.947629  4.284104 -0.3401116 16.7858948
      [4,]  5.696482  7.297221  4.605994  6.486964  6.1890079  5.1381530
      [5,]  6.504383  6.618376  6.610435  6.579370  6.5386955  6.6227491
      [6,] 13.421515 13.463637 13.422910 13.271886 13.4840941 13.4339324
          
iterations      [,7]      [,8]
      [1,]  3.064505  1.695676
      [2,]  7.233268 -0.929307
      [3,] 12.418555 12.867065
      [4,]  5.527287  8.000315
      [5,]  6.686698  6.625466
      [6,] 13.321305 13.466787


as.matrix(), as.data.frame(), as.array()

The as.matrix, as.data.frame, and as.array functions can also be used to retrieve the posterior draws from a stanfit object:

 [1] "mu"       "tau"      "eta[1]"   "eta[2]"   "eta[3]"   "eta[4]"  
 [7] "eta[5]"   "eta[6]"   "eta[7]"   "eta[8]"   "theta[1]" "theta[2]"
[13] "theta[3]" "theta[4]" "theta[5]" "theta[6]" "theta[7]" "theta[8]"
[19] "lp__"    
 [1] "mu"       "tau"      "eta[1]"   "eta[2]"   "eta[3]"   "eta[4]"  
 [7] "eta[5]"   "eta[6]"   "eta[7]"   "eta[8]"   "theta[1]" "theta[2]"
[13] "theta[3]" "theta[4]" "theta[5]" "theta[6]" "theta[7]" "theta[8]"
[19] "lp__"    
$iterations
NULL

$chains
[1] "chain:1" "chain:2" "chain:3" "chain:4"

$parameters
 [1] "mu"       "tau"      "eta[1]"   "eta[2]"   "eta[3]"   "eta[4]"  
 [7] "eta[5]"   "eta[6]"   "eta[7]"   "eta[8]"   "theta[1]" "theta[2]"
[13] "theta[3]" "theta[4]" "theta[5]" "theta[6]" "theta[7]" "theta[8]"
[19] "lp__"    

The as.matrix and as.data.frame methods essentially return the same thing except in matrix and data frame form, respectively. The as.array method returns the draws from each chain separately and so has an additional dimension:

[1] 4000   19
[1] 4000   19
[1] 1000    4   19

By default all of the functions for retrieving the posterior draws return the draws for all parameters (and generated quantities). The optional argument pars (a character vector) can be used if only a subset of the parameters is desired, for example:

          parameters
iterations        mu   theta[1]
      [1,] 12.294436 10.2946760
      [2,]  8.083146  7.2673147
      [3,]  7.050771 24.2162877
      [4,]  9.663047 11.2475908
      [5,]  7.068416  5.9276186
      [6,] -2.398115  0.9736401


Posterior summary statistics and convergence diagnostics

Summary statistics are obtained using the summary function. The object returned is a list with two components:

fit_summary <- summary(fit)
print(names(fit_summary))
[1] "summary"   "c_summary"

In fit_summary$summary all chains are merged whereas fit_summary$c_summary contains summaries for each chain individually. Typically we want the summary for all chains merged, which is what we’ll focus on here.

The summary is a matrix with rows corresponding to parameters and columns to the various summary quantities. These include the posterior mean, the posterior standard deviation, and various quantiles computed from the draws. The probs argument can be used to specify which quantiles to compute and pars can be used to specify a subset of parameters to include in the summary.

For models fit using MCMC, also included in the summary are the Monte Carlo standard error (se_mean), the effective sample size (n_eff), and the R-hat statistic (Rhat).

print(fit_summary$summary)
                 mean    se_mean        sd        2.5%         25%          50%
mu         8.12522362 0.10543295 4.9418227  -1.6916254   4.8892048   8.07321948
tau        6.58614056 0.13328284 5.3510302   0.3028005   2.5433639   5.33964019
eta[1]     0.39724794 0.01513050 0.9543864  -1.5419715  -0.2031095   0.41086420
eta[2]    -0.01075482 0.01530338 0.8483966  -1.7073219  -0.5758459  -0.02502340
eta[3]    -0.22081500 0.01677053 0.9275588  -2.0440687  -0.8354153  -0.22846245
eta[4]    -0.03561663 0.01484608 0.8959867  -1.8110925  -0.6209377  -0.02911226
eta[5]    -0.38864870 0.01489854 0.8891847  -2.1672920  -0.9612040  -0.40092400
eta[6]    -0.19644806 0.01520503 0.8923989  -1.9271772  -0.7897538  -0.21008728
eta[7]     0.36064597 0.01511057 0.8727346  -1.4024953  -0.1905596   0.36105649
eta[8]     0.05628648 0.01545371 0.9486657  -1.7995728  -0.5671822   0.05449893
theta[1]  11.78534121 0.16684539 8.5954849  -1.5310472   6.1435927  10.40794080
theta[2]   7.96961129 0.09413415 6.2626214  -4.8075733   4.2037808   7.96903459
theta[3]   6.09287412 0.13829410 7.7266011 -11.8098608   2.0036229   6.61427388
theta[4]   7.62404665 0.10095742 6.6220885  -5.8614275   3.5185197   7.66786315
theta[5]   5.08963645 0.10133845 6.4625099  -9.0375331   1.2950346   5.67086449
theta[6]   6.30804934 0.10871398 6.8057938  -8.6100492   2.2471665   6.63691149
theta[7]  10.80131200 0.11700021 6.7325358  -1.0770481   6.2887084  10.25576210
theta[8]   8.62092983 0.14475281 8.1621693  -6.8275700   3.9479337   8.26511019
lp__     -39.54481281 0.07849596 2.6604631 -45.6436033 -41.1301979 -39.29168235
                 75%      97.5%    n_eff      Rhat
mu        11.4339051  17.962924 2196.957 1.0006081
tau        9.2721739  20.020787 1611.856 1.0005018
eta[1]     1.0157440   2.234923 3978.708 0.9999563
eta[2]     0.5353172   1.721535 3073.427 0.9993953
eta[3]     0.3833220   1.663098 3059.068 1.0000438
eta[4]     0.5619414   1.736866 3642.333 0.9996340
eta[5]     0.1840037   1.415889 3562.020 1.0017262
eta[6]     0.3957598   1.635603 3444.635 0.9999902
eta[7]     0.9309946   2.103064 3335.819 1.0008580
eta[8]     0.6739109   1.931676 3768.433 0.9993490
theta[1]  16.0149389  33.139961 2654.070 1.0005255
theta[2]  11.8857421  20.546013 4426.066 0.9995913
theta[3]  10.7650010  20.444246 3121.546 1.0005744
theta[4]  11.8440778  20.968700 4302.426 0.9997326
theta[5]   9.5195398  16.565089 4066.811 0.9996950
theta[6]  10.7773185  18.676699 3919.104 1.0002833
theta[7]  14.7056071  25.422768 3311.190 1.0004802
theta[8]  12.8273735  26.781811 3179.488 0.9994721
lp__     -37.6681294 -35.074027 1148.735 1.0016283

If, for example, we wanted the only quantiles included to be 10% and 90%, and for only the parameters included to be mu and tau, we would specify that like this:

mu_tau_summary <- summary(fit, pars = c("mu", "tau"), probs = c(0.1, 0.9))$summary
print(mu_tau_summary)
        mean   se_mean       sd      10%      90%    n_eff     Rhat
mu  8.125224 0.1054329 4.941823 1.927823 14.34993 2196.957 1.000608
tau 6.586141 0.1332828 5.351030 1.018044 13.78748 1611.856 1.000502

Since mu_tau_summary is a matrix we can pull out columns using their names:

mu_tau_80pct <- mu_tau_summary[, c("10%", "90%")]
print(mu_tau_80pct)
         10%      90%
mu  1.927823 14.34993
tau 1.018044 13.78748


Sampler diagnostics

For models fit using MCMC the stanfit object will also contain the values of parameters used for the sampler. The get_sampler_params function can be used to access this information.

The object returned by get_sampler_params is a list with one component (a matrix) per chain. Each of the matrices has number of columns corresponding to the number of sampler parameters and the column names provide the parameter names. The optional argument inc_warmup (defaulting to TRUE) indicates whether to include the warmup period.

sampler_params <- get_sampler_params(fit, inc_warmup = FALSE)
sampler_params_chain1 <- sampler_params[[1]]
colnames(sampler_params_chain1)
[1] "accept_stat__" "stepsize__"    "treedepth__"   "n_leapfrog__" 
[5] "divergent__"   "energy__"     

To do things like calculate the average value of accept_stat__ for each chain (or the maximum value of treedepth__ for each chain if using the NUTS algorithm, etc.) the sapply function is useful as it will apply the same function to each component of sampler_params:

mean_accept_stat_by_chain <- sapply(sampler_params, function(x) mean(x[, "accept_stat__"]))
print(mean_accept_stat_by_chain)
[1] 0.8946750 0.8043410 0.8784134 0.7977858
max_treedepth_by_chain <- sapply(sampler_params, function(x) max(x[, "treedepth__"]))
print(max_treedepth_by_chain)
[1] 5 4 4 4


Model code

The Stan program itself is also stored in the stanfit object and can be accessed using get_stancode:

code <- get_stancode(fit)

The object code is a single string and is not very intelligible when printed:

print(code)
[1] "data {\n  int<lower=0> J;          // number of schools\n  real y[J];               // estimated treatment effects\n  real<lower=0> sigma[J];  // s.e. of effect estimates\n}\nparameters {\n  real mu;\n  real<lower=0> tau;\n  vector[J] eta;\n}\ntransformed parameters {\n  vector[J] theta;\n  theta = mu + tau * eta;\n}\nmodel {\n  target += normal_lpdf(eta | 0, 1);\n  target += normal_lpdf(y | theta, sigma);\n}"
attr(,"model_name2")
[1] "schools"

A readable version can be printed using cat:

cat(code)
data {
  int<lower=0> J;          // number of schools
  real y[J];               // estimated treatment effects
  real<lower=0> sigma[J];  // s.e. of effect estimates
}
parameters {
  real mu;
  real<lower=0> tau;
  vector[J] eta;
}
transformed parameters {
  vector[J] theta;
  theta = mu + tau * eta;
}
model {
  target += normal_lpdf(eta | 0, 1);
  target += normal_lpdf(y | theta, sigma);
}


Initial values

The get_inits function returns initial values as a list with one component per chain. Each component is itself a (named) list containing the initial values for each parameter for the corresponding chain:

inits <- get_inits(fit)
inits_chain1 <- inits[[1]]
print(inits_chain1)
$mu
[1] 0.9807931

$tau
[1] 3.772335

$eta
[1] -1.5529622 -0.8238692 -1.2685297 -1.0187685 -0.3050989  1.7212214  1.6778877
[8]  0.2406339

$theta
[1] -4.8775012 -2.1271178 -3.8045261 -2.8623432 -0.1701422  7.4738173  7.3103483
[8]  1.8885450


(P)RNG seed

The get_seed function returns the (P)RNG seed as an integer:

print(get_seed(fit))
[1] 1349966339


Warmup and sampling times

The get_elapsed_time function returns a matrix with the warmup and sampling times for each chain:

print(get_elapsed_time(fit))
        warmup sample
chain:1  0.085  0.064
chain:2  0.043  0.037
chain:3  0.041  0.034
chain:4  0.065  0.057