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]  2.717288  6.126390  9.269763  5.466024 12.371736 12.728201

head(list_of_draws$tau)

[1]  8.127311  6.099894  8.431778 20.337739 16.045552  0.629017

head(list_of_draws$theta)

          
iterations     [,1]       [,2]      [,3]       [,4]       [,5]      [,6]
      [1,] 17.37919   6.324138  5.510211  0.7914177   2.904062  6.276932
      [2,] 11.34469  -5.869765  5.637176  8.5654652   4.030264 16.738744
      [3,] 18.70269  11.845173  2.530775  7.8741726   1.411100 -5.637879
      [4,] 30.95059 -10.294568  1.955394  7.5121802 -10.532689 -5.168254
      [5,] 21.34431   3.995896  8.344221  2.2093363  -9.902931 -2.376102
      [6,] 12.73459  12.518335 13.578908 13.0927392  13.360413 13.179632
          
iterations      [,7]      [,8]
      [1,]  5.839641  2.403244
      [2,]  6.168454  4.611533
      [3,]  9.336305  9.989825
      [4,] 18.488237 21.460631
      [5,] 15.664796 10.110411
      [6,] 12.256780 12.888348

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,]  9.227737  8.299509
      [2,]  8.082361  5.790565
      [3,]  8.722221  9.479570
      [4,]  8.315916 15.959164
      [5,]  3.037107 -1.764284
      [6,] 10.983375 22.235240

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         7.791069797 0.11047203 5.0284092  -1.823628   4.5833891
tau        6.621189538 0.15192887 5.7078160   0.213518   2.3989686
eta[1]     0.375167501 0.01413084 0.9043180  -1.440227  -0.2153100
eta[2]     0.006079915 0.01432982 0.8725014  -1.753491  -0.5402504
eta[3]    -0.206966717 0.01363669 0.9154714  -1.952194  -0.8283019
eta[4]    -0.036063071 0.01393823 0.8892260  -1.788453  -0.6291556
eta[5]    -0.332470034 0.01392901 0.8866139  -2.005504  -0.9088546
eta[6]    -0.201343116 0.01341847 0.8775020  -1.907306  -0.7899503
eta[7]     0.344761555 0.01401385 0.9037140  -1.473784  -0.2554285
eta[8]     0.053791608 0.01466782 0.9319365  -1.781152  -0.5517679
theta[1]  11.128155093 0.14970977 8.0661605  -1.681819   5.8217849
theta[2]   7.687423157 0.09307702 6.2900071  -4.955894   3.7368645
theta[3]   6.023535979 0.12609781 7.5978651 -11.143391   1.8603687
theta[4]   7.339617186 0.09576759 6.5351425  -6.595344   3.3172772
theta[5]   5.166822458 0.10259851 6.3686654  -9.257621   1.3233358
theta[6]   6.198681519 0.10924196 6.6624817  -8.143649   2.3000815
theta[7]  10.570322104 0.11143987 6.8693376  -1.487116   5.9502232
theta[8]   8.351327207 0.13041952 7.8078084  -6.844088   3.7857475
lp__     -39.530966428 0.07606357 2.6295864 -45.376958 -41.0873111
                   50%         75%      97.5%    n_eff      Rhat
mu         7.713022157  11.0793992  17.715051 2071.842 0.9999567
tau        5.270943971   9.2272232  21.452016 1411.430 1.0003046
eta[1]     0.379224322   1.0015137   2.168445 4095.497 0.9991383
eta[2]     0.002921243   0.5609610   1.756944 3707.242 0.9993053
eta[3]    -0.215252842   0.3908249   1.642870 4506.834 0.9996002
eta[4]    -0.059869812   0.5115277   1.770089 4070.135 0.9997199
eta[5]    -0.375113690   0.2036155   1.498410 4051.617 0.9993853
eta[6]    -0.219602807   0.3599869   1.570985 4276.520 0.9999683
eta[7]     0.360984365   0.9562135   2.123045 4158.599 0.9993518
eta[8]     0.048763639   0.6783403   1.880174 4036.841 0.9994810
theta[1]  10.132380305  15.3222404  30.952250 2902.909 0.9998498
theta[2]   7.747102020  11.5978132  20.200951 4566.856 0.9994868
theta[3]   6.512108981  10.6715201  20.028821 3630.513 0.9992852
theta[4]   7.438175396  11.5210522  20.094142 4656.644 0.9997170
theta[5]   5.584636110   9.4153610  16.423056 3853.140 0.9992456
theta[6]   6.503581442  10.4355377  18.885154 3719.573 0.9998555
theta[7]   9.974653355  14.5531686  25.620589 3799.693 0.9995101
theta[8]   8.016680253  12.4698016  25.353115 3584.042 0.9996276
lp__     -39.342765161 -37.7184744 -34.893597 1195.147 1.0000859

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  7.79107 0.1104720 5.028409 1.4410093 13.96417 2071.842 0.9999567
tau 6.62119 0.1519289 5.707816 0.9939053 13.94651 1411.430 1.0003046

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  1.4410093 13.96417
tau 0.9939053 13.94651

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] 0.9224838 0.8551551 0.8899882 0.8782613

max_treedepth_by_chain <- sapply(sampler_params, function(x) max(x[, "treedepth__"]))
print(max_treedepth_by_chain)

[1] 4 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] 0.8020384

$tau
[1] 2.83205

$eta
[1] -0.7138932  1.5828580 -1.7463003  0.5080906  0.9833842 -1.2372880  0.8546742
[8] -0.5458396

$theta
[1] -1.2197427  5.2847710 -4.1435708  2.2409763  3.5870313 -2.7020228  3.2225183
[8] -0.7438065

(P)RNG seed

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

print(get_seed(fit))

[1] 806056744

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  0.024  0.028
chain:2  0.024  0.020
chain:3  0.024  0.026
chain:4  0.026  0.026