Accessing the contents of a stanfit object

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)

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.

list_of_draws <- extract(fit)
print(names(list_of_draws))

[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:

head(list_of_draws$mu)

[1] 20.836497 12.060795 10.175120  9.520696  6.096034  7.859518

head(list_of_draws$tau)

[1] 14.905177  7.899398 26.940079  2.048036 19.108677  4.378995

head(list_of_draws$theta)

          
iterations      [,1]      [,2]       [,3]      [,4]       [,5]      [,6]
      [1,] 28.726974  9.439800   3.888388 15.339154  7.7346833 17.664277
      [2,]  4.700456 16.206078   7.751389 10.825984 -0.9480708  5.075414
      [3,] 24.922388 11.790502   6.009507 11.390416  6.3207077  7.306853
      [4,] 10.815966  9.828443   9.355722  9.044572  9.7469111  7.148323
      [5,] 17.501890  2.933129 -16.807166 -2.578389 -2.4783181  1.142213
      [6,]  5.616234  2.031239   7.773633  8.855767  8.5948272  8.086332
          
iterations      [,7]      [,8]
      [1,] 24.957668 14.090334
      [2,] 13.347809 15.401941
      [3,] 15.622450 31.626042
      [4,] 11.053766  9.552939
      [5,]  8.771172 15.201472
      [6,] 13.032274  0.103350

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:

matrix_of_draws <- as.matrix(fit)
print(colnames(matrix_of_draws))

 [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__"

df_of_draws <- as.data.frame(fit)
print(colnames(df_of_draws))

 [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__"

array_of_draws <- as.array(fit)
print(dimnames(array_of_draws))

$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:

print(dim(matrix_of_draws))
print(dim(df_of_draws))
print(dim(array_of_draws))

[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:

mu_and_theta1 <- as.matrix(fit, pars = c("mu", "theta[1]"))
head(mu_and_theta1)

          parameters
iterations        mu  theta[1]
      [1,]  8.725579 10.215258
      [2,]  9.226547 11.440963
      [3,] 15.899183 33.442211
      [4,]  3.241677  3.780407
      [5,]  7.509794  3.163952
      [6,]  6.485575  5.913785

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         8.03134880 0.12101259 5.1677701  -2.0380719   4.6592144
tau        6.59041549 0.14568776 5.6008007   0.2773337   2.4968590
eta[1]     0.38208289 0.01499024 0.9451615  -1.4660826  -0.2432909
eta[2]    -0.01569986 0.01415572 0.8978636  -1.8122466  -0.6076035
eta[3]    -0.19538335 0.01485024 0.9273103  -2.0419114  -0.8001488
eta[4]    -0.05392870 0.01381316 0.8822209  -1.7583078  -0.6355066
eta[5]    -0.33887850 0.01409636 0.8530216  -1.9339251  -0.9058867
eta[6]    -0.20933652 0.01316414 0.8898184  -1.9389494  -0.8007213
eta[7]     0.33777380 0.01514154 0.8590626  -1.4159776  -0.2037721
eta[8]     0.07570978 0.01498566 0.9437228  -1.7859882  -0.5473077
theta[1]  11.48411741 0.15569415 8.4652775  -2.1680738   6.0199819
theta[2]   7.82245427 0.08511068 6.3415271  -5.0159470   3.8104565
theta[3]   6.36484448 0.12193545 7.6663689 -10.4674407   2.1200451
theta[4]   7.56946935 0.09640997 6.4548621  -5.5564139   3.6792036
theta[5]   5.30928037 0.10785842 6.3324894  -8.5331457   1.5769709
theta[6]   6.22346676 0.09747826 6.5826572  -8.2492415   2.4799313
theta[7]  10.71783910 0.11940361 6.6978000  -1.2805184   6.4235510
theta[8]   8.65574392 0.13520688 8.0679915  -7.2725471   4.0054656
lp__     -39.50903872 0.07598791 2.6496622 -45.5537291 -41.1068886
                   50%         75%      97.5%    n_eff      Rhat
mu        8.054478e+00  11.2207326  18.678096 1823.666 1.0000454
tau       5.225528e+00   9.1012987  20.652894 1477.931 1.0037510
eta[1]    3.865713e-01   1.0122973   2.219547 3975.527 0.9998628
eta[2]   -6.638748e-04   0.5795009   1.807664 4023.060 0.9992227
eta[3]   -1.913628e-01   0.4101593   1.656482 3899.269 1.0004837
eta[4]   -7.720218e-02   0.5137489   1.764653 4079.137 0.9997942
eta[5]   -3.480289e-01   0.1983097   1.437134 3661.898 0.9995048
eta[6]   -2.074909e-01   0.3651111   1.550091 4568.962 0.9993792
eta[7]    3.365219e-01   0.8920357   2.037641 3218.913 1.0015100
eta[8]    7.685418e-02   0.7046980   1.941707 3965.860 0.9999269
theta[1]  1.023291e+01  15.5175399  32.364864 2956.227 0.9997673
theta[2]  7.907364e+00  11.6695588  20.575500 5551.619 0.9996755
theta[3]  6.779341e+00  10.9805161  21.030802 3952.933 0.9994922
theta[4]  7.703315e+00  11.5038791  20.591890 4482.601 0.9999101
theta[5]  5.837589e+00   9.5163070  16.501357 3446.996 1.0012477
theta[6]  6.649826e+00  10.4868048  18.648563 4560.232 0.9999849
theta[7]  1.023562e+01  14.4673170  25.607596 3146.512 1.0030312
theta[8]  8.427871e+00  12.9113150  26.403308 3560.683 0.9999748
lp__     -3.925657e+01 -37.6681354 -35.083758 1215.884 1.0023318

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  8.031349 0.1210126 5.167770 1.705679 14.28522 1823.666 1.000045
tau 6.590415 0.1456878 5.600801 1.021370 13.81310 1477.931 1.003751

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  1.705679 14.28522
tau 1.021370 13.81310

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] 0.8894886 0.9646873 0.8557073 0.8995515

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] -1.931844

$tau
[1] 0.3738421

$eta
[1]  0.992145893 -0.571812941  1.505868780  0.752517743  0.009724263
[6]  1.950971272 -1.890238232  0.897926154

$theta
[1] -1.560938 -2.145612 -1.368887 -1.650521 -1.928209 -1.202489 -2.638495
[8] -1.596161

(P)RNG seed

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

print(get_seed(fit))

[1] 1665972213

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  0.027  0.024
chain:2  0.025  0.030
chain:3  0.025  0.025
chain:4  0.026  0.027