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)

Warning: There were 11 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

Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
Running the chains for more iterations may help. See
https://mc-stan.org/misc/warnings.html#tail-ess

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]  9.264387  7.532259  8.321515  5.063982 10.915901  7.068204

head(list_of_draws$tau)

[1] 4.3749946 6.6523166 8.1629323 3.7559417 0.7335339 7.0144202

head(list_of_draws$theta)

          
iterations      [,1]      [,2]      [,3]       [,4]       [,5]      [,6]
      [1,] 13.508123 12.927211  7.084756  4.4389547  1.0645882  4.302487
      [2,]  5.197941 10.263788  4.846419  4.6961940 -0.8791130  5.646958
      [3,]  5.197980  8.387341 11.082761 11.2908558 -0.9776036  6.858847
      [4,]  7.261789  4.234994 12.282606  6.5455962 -2.4357326  5.333933
      [5,] 11.392526 11.063745 11.492085 10.0636099 11.1234929 10.903826
      [6,] 15.417872 13.534648 12.431409  0.1939912  2.7519099  6.717547
          
iterations      [,7]      [,8]
      [1,]  8.013038  8.496487
      [2,]  7.149842 -6.239125
      [3,] 14.152487  5.466075
      [4,]  3.515676 -0.588059
      [5,] 12.211917 11.563312
      [6,]  6.500746 12.059947

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,] 10.438777 13.478654
      [2,] 11.899997 13.305585
      [3,]  6.643817  6.187893
      [4,] 10.217506  5.426754
      [5,]  2.984540  3.423543
      [6,] 11.299232 11.178555

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         8.08544776 0.32209123 5.6748607  -2.5918479   4.6318634   7.92964066
tau        7.01933763 0.18877506 6.1071511   0.2232951   2.5054145   5.55771763
eta[1]     0.41550731 0.01487660 0.9561075  -1.4997298  -0.2148951   0.44354619
eta[2]    -0.01685718 0.02124064 0.8696249  -1.7926319  -0.5700728  -0.01339714
eta[3]    -0.21022979 0.01609943 0.9029323  -1.9833995  -0.8059864  -0.22408078
eta[4]    -0.03443285 0.01607047 0.8837582  -1.7100056  -0.6272921  -0.02900023
eta[5]    -0.35470986 0.01711456 0.8787852  -2.0360756  -0.9386034  -0.36269568
eta[6]    -0.24150626 0.01879604 0.9178001  -1.9974791  -0.8418028  -0.25375199
eta[7]     0.33844628 0.01753914 0.9071545  -1.4909339  -0.2298367   0.34134105
eta[8]     0.05865807 0.01348561 0.9075872  -1.7366427  -0.5438963   0.07013935
theta[1]  11.97894788 0.30032352 8.8087747  -1.8607081   6.1719763  10.49446476
theta[2]   7.81461589 0.09970294 6.1058058  -4.2250125   4.0124304   7.86519069
theta[3]   5.98916039 0.16433131 8.0652537 -11.7258489   1.6939847   6.58373839
theta[4]   7.63439616 0.10233882 6.5850975  -6.2514380   3.7814608   7.71982588
theta[5]   4.90246034 0.11275064 6.5092552  -9.5066672   1.1063243   5.44789796
theta[6]   5.97410715 0.10278816 6.8256699  -9.0398858   2.1317648   6.41394148
theta[7]  10.78762539 0.13435774 6.7442684  -0.9500700   6.1573886  10.31260163
theta[8]   8.72068717 0.30464080 8.2737452  -6.9337489   3.6205341   8.28882436
lp__     -39.48940697 0.07674344 2.6688863 -45.4680362 -41.1234562 -39.18738069
                 75%      97.5%     n_eff      Rhat
mu        11.2560414  19.476027  310.4221 1.0117287
tau        9.9308854  21.944336 1046.6178 1.0018334
eta[1]     1.0394846   2.286120 4130.5329 0.9995223
eta[2]     0.5396902   1.760146 1676.2105 1.0014133
eta[3]     0.3789947   1.612031 3145.4982 1.0001675
eta[4]     0.5376120   1.684640 3024.1941 1.0018620
eta[5]     0.2049529   1.452015 2636.5380 1.0034160
eta[6]     0.3716703   1.593875 2384.3150 1.0019915
eta[7]     0.9418666   2.056268 2675.1349 1.0002056
eta[8]     0.6818988   1.790606 4529.3455 1.0004780
theta[1]  16.3747148  34.356536  860.3048 1.0037847
theta[2]  11.6544904  20.472616 3750.3349 0.9995593
theta[3]  10.7337357  20.651680 2408.7704 1.0012638
theta[4]  11.6196924  20.624632 4140.4122 0.9994396
theta[5]   9.3813162  16.114073 3332.9172 1.0002509
theta[6]  10.4107358  18.316474 4409.6524 0.9998224
theta[7]  14.8294773  25.389841 2519.6736 1.0002245
theta[8]  13.0356805  27.964255  737.6123 1.0041103
lp__     -37.5448195 -35.007517 1209.4214 0.9998492

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  8.085448 0.3220912 5.674861 1.4406346 14.50235  310.4221 1.011729
tau 7.019338 0.1887751 6.107151 0.9605613 14.60252 1046.6178 1.001833

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  1.4406346 14.50235
tau 0.9605613 14.60252

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] 0.9014808 0.8052644 0.8094257 0.9168968

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

[1] 4 4 5 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] 1.139419

$tau
[1] 1.135551

$eta
[1] -0.2816226  0.8839261  0.1348173  1.1142563  0.5333998 -1.6239508  0.6269902
[8]  0.6529137

$theta
[1]  0.8196216  2.1431620  1.2925104  2.4047137  1.7451214 -0.7046610  1.8513981
[8]  1.8808355

(P)RNG seed

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

print(get_seed(fit))

[1] 757216720

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  0.026  0.028
chain:2  0.023  0.019
chain:3  0.023  0.024
chain:4  0.024  0.028