Accessing the contents of a stanfit object

Stan Development Team

2025-03-10

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 2 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]  1.488474 12.571451 13.223202 13.182046  9.952339  6.912193
[1]  7.348914  2.445517 11.517335  6.213301  2.031371  6.779524
          
iterations      [,1]      [,2]      [,3]      [,4]       [,5]       [,6]
      [1,]  1.421816  8.687649 -4.603498  3.790294  -7.045458  0.2615451
      [2,] 18.550676  7.680755  8.966955  9.016272  11.423769 11.2204210
      [3,] 19.469451 15.344126 -7.727168 12.178930 -10.599775 -0.3549827
      [4,] 17.924275 18.694583  5.284061  6.666718  15.316291  7.8929871
      [5,]  6.701938  9.075823  7.907170  9.715682   8.907089  8.4608342
      [6,] 18.766974  4.349427 17.361541 15.550801  10.938264  8.9511055
          
iterations      [,7]      [,8]
      [1,]  5.431451  3.543596
      [2,] 10.538840 11.336251
      [3,] 22.247510 15.918756
      [4,] 12.085506  6.242551
      [5,] 11.771131 10.389010
      [6,]  1.082676 16.802566


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,]  9.113228 16.140227
      [2,]  7.255361 13.368290
      [3,]  8.528363  6.428964
      [4,] 11.081210 10.227082
      [5,]  6.307817 17.404911
      [6,]  9.964439 10.520016


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%
mu         8.007536523 0.11552570 4.9513594  -1.9222026   4.8085181
tau        6.603336325 0.20329568 5.9753551   0.1728432   2.3550279
eta[1]     0.405848953 0.01740855 0.9445708  -1.5378558  -0.2115446
eta[2]    -0.005753395 0.01536444 0.8715120  -1.7185355  -0.5699245
eta[3]    -0.193857013 0.01468770 0.9281523  -1.9635021  -0.7952254
eta[4]    -0.029155838 0.01411412 0.8804588  -1.7737136  -0.6176649
eta[5]    -0.375402748 0.01516514 0.8448021  -2.0341022  -0.9238896
eta[6]    -0.241978864 0.01642085 0.8841485  -1.9634660  -0.8197734
eta[7]     0.359738764 0.01419410 0.8817446  -1.4207733  -0.2133717
eta[8]     0.042265806 0.01497848 0.9345390  -1.8312333  -0.5703946
theta[1]  11.617935090 0.15769026 8.0765444  -1.7867502   6.2750730
theta[2]   7.861712373 0.09983657 6.1704677  -4.3241709   3.9818037
theta[3]   6.206286455 0.14492356 7.7547427 -11.6068964   2.2516888
theta[4]   7.716195812 0.10641752 6.4435087  -5.8913169   3.8734140
theta[5]   5.135076545 0.10994314 6.3509612  -8.5487429   1.3567338
theta[6]   6.066552756 0.11290372 6.5880615  -8.2913121   2.2740856
theta[7]  10.848994521 0.11477964 6.6068494  -0.6215770   6.3721026
theta[8]   8.423405371 0.16037401 7.7122152  -6.9216603   3.9199716
lp__     -39.511483098 0.08383706 2.7126153 -45.6854960 -41.0851014
                  50%         75%      97.5%     n_eff      Rhat
mu         7.99938904  11.2302155  17.788888 1836.9262 1.0008051
tau        5.32920107   9.1688847  20.906005  863.9153 1.0092509
eta[1]     0.42352102   1.0301003   2.286020 2944.0421 1.0015993
eta[2]    -0.01734074   0.5535907   1.747688 3217.4620 0.9995929
eta[3]    -0.22615731   0.4379316   1.668864 3993.2935 0.9998402
eta[4]    -0.02884515   0.5350051   1.766398 3891.4407 1.0001105
eta[5]    -0.38248559   0.1727490   1.348492 3103.2517 1.0001840
eta[6]    -0.25233752   0.3164041   1.546743 2899.0733 1.0004464
eta[7]     0.37455001   0.9322649   2.112452 3858.9593 0.9992021
eta[8]     0.03593027   0.6630956   1.892417 3892.7749 0.9999310
theta[1]  10.58113818  15.7662776  30.691080 2623.2604 1.0027785
theta[2]   7.86537082  11.7120898  20.491776 3819.9426 1.0007652
theta[3]   6.73261820  10.9262648  20.222523 2863.2339 1.0005658
theta[4]   7.78588984  11.7445980  20.171425 3666.2201 1.0008216
theta[5]   5.67497248   9.4494177  16.407779 3336.8956 1.0012809
theta[6]   6.44470369  10.3757100  18.241870 3404.8561 1.0017153
theta[7]  10.25285845  14.6639662  25.201119 3313.2870 1.0007526
theta[8]   8.20517778  12.7200294  25.290306 2312.5454 0.9996591
lp__     -39.23347400 -37.6547307 -34.883334 1046.8978 1.0039047

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  8.007537 0.1155257 4.951359 1.7419720 14.30474 1836.9262 1.000805
tau 6.603336 0.2032957 5.975355 0.7929309 13.71782  863.9153 1.009251

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  1.7419720 14.30474
tau 0.7929309 13.71782


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] 0.8294264 0.8707689 0.8714515 0.8549241
max_treedepth_by_chain <- sapply(sampler_params, function(x) max(x[, "treedepth__"]))
print(max_treedepth_by_chain)
[1] 4 4 4 5


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] -1.816114

$tau
[1] 0.2009296

$eta
[1]  0.62080058  1.59983405  1.94531031 -0.31126034  1.52920856  0.08217944
[7] -1.04723954  1.18908654

$theta
[1] -1.691376 -1.494659 -1.425243 -1.878655 -1.508850 -1.799601 -2.026535
[8] -1.577191


(P)RNG seed

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

print(get_seed(fit))
[1] 750571131


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  0.034  0.029
chain:2  0.035  0.034
chain:3  0.033  0.029
chain:4  0.033  0.032