Accessing the contents of a stanfit object

Stan Development Team

2017-07-03

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 4 divergent transitions after warmup. Increasing adapt_delta above 0.8 may help. See
http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
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.

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$mu)
[1] 4.178689 7.896903 5.230637 9.477452 5.166316 5.575505
head(list_of_draws$tau)
[1]  1.8210255  0.3198835  3.5427238 10.9788963  1.5416283  6.5294129
head(list_of_draws$theta)
          
iterations      [,1]      [,2]      [,3]      [,4]      [,5]     [,6]
      [1,]  4.328065  2.035497  2.687295  4.830606  2.591323 3.415279
      [2,]  7.701131  8.079618  7.415463  8.012570  7.721320 8.004710
      [3,] 12.080879  6.458229  4.256499  3.626688  6.189494 7.787423
      [4,] 15.436545 15.575352 -1.666966  8.823516 -6.225512 6.897776
      [5,]  5.427178  5.698364  5.923378  4.087328  5.174217 2.535239
      [6,] 14.797413  2.227443  1.963443 13.695857 13.611430 3.288641
          
iterations      [,7]      [,8]
      [1,]  5.631401  4.327563
      [2,]  7.843496  7.791768
      [3,]  3.987610  1.214433
      [4,]  8.292774 13.447035
      [5,]  6.470211  8.030746
      [6,] 13.736938  2.483708


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,]  8.7078861  7.698465
      [2,]  0.8769045  3.818568
      [3,] 14.8421405 12.974890
      [4,] 13.2551953 21.464781
      [5,] 10.9892924  4.396455
      [6,]  1.0052114 28.014937


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         8.048679487 0.10855021 4.8844478  -1.5270458   4.7956486
tau        6.557081758 0.14082445 5.4953624   0.2443783   2.4172257
eta[1]     0.352512349 0.01456519 0.9211836  -1.4828920  -0.2395504
eta[2]     0.001035813 0.01391937 0.8803384  -1.7609156  -0.5578358
eta[3]    -0.210298411 0.01451442 0.9179728  -2.0459843  -0.8182240
eta[4]    -0.046330692 0.01399663 0.8852245  -1.7858954  -0.6395271
eta[5]    -0.354773627 0.01389684 0.8789130  -2.0387730  -0.9241866
eta[6]    -0.242147628 0.01406086 0.8892870  -1.9917021  -0.8297227
eta[7]     0.344116861 0.01528489 0.9006204  -1.4912825  -0.2527849
eta[8]     0.054117112 0.01476876 0.9340583  -1.7048651  -0.5703094
theta[1]  11.179939131 0.14049641 7.9699140  -2.5322883   6.0314217
theta[2]   8.139112021 0.10033489 6.3457354  -4.0253160   4.1476907
theta[3]   6.157855087 0.11955944 7.5616029 -10.4333424   2.0474438
theta[4]   7.706870487 0.10183980 6.4409143  -5.4322317   3.8157935
theta[5]   5.169066290 0.10015811 6.3345549  -8.7036114   1.5443474
theta[6]   6.109612619 0.10500089 6.6408396  -8.5017959   2.3172212
theta[7]  10.811708319 0.10782097 6.8191970  -0.9882565   6.0876259
theta[8]   8.424636902 0.12081343 7.6409122  -7.2523268   4.0548291
lp__     -39.503782098 0.07847223 2.6924066 -45.5837397 -41.1328365
                   50%         75%      97.5%    n_eff      Rhat
mu         7.994847396  11.2254151  17.658561 2024.741 1.0019591
tau        5.356981530   9.0604728  20.124940 1522.778 1.0033007
eta[1]     0.359401600   0.9678725   2.151131 4000.000 1.0007800
eta[2]    -0.005405507   0.5806379   1.754201 4000.000 1.0013342
eta[3]    -0.194855108   0.3980163   1.574262 4000.000 1.0002214
eta[4]    -0.050960318   0.5300522   1.681861 4000.000 1.0004579
eta[5]    -0.373137019   0.2164363   1.431801 4000.000 0.9999436
eta[6]    -0.242018489   0.3228345   1.507530 4000.000 1.0007736
eta[7]     0.377271785   0.9532751   2.046999 3471.835 1.0013864
eta[8]     0.033099352   0.6799525   1.875869 4000.000 0.9992675
theta[1]  10.046211535  15.3792620  29.470367 3217.932 1.0012703
theta[2]   7.999553815  12.0080307  21.110053 4000.000 0.9996522
theta[3]   6.698712608  10.8766773  20.326054 4000.000 0.9999629
theta[4]   7.775685400  11.6781117  20.492719 4000.000 0.9998420
theta[5]   5.542552626   9.4562901  16.385787 4000.000 0.9998813
theta[6]   6.499023855  10.2922662  18.184320 4000.000 0.9996696
theta[7]  10.172402385  14.7617284  26.181687 4000.000 1.0000294
theta[8]   8.302620439  12.6568257  24.369944 4000.000 1.0001679
lp__     -39.297076824 -37.5638248 -35.020254 1177.198 1.0035031

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  8.048679 0.1085502 4.884448 1.987987 14.03885 2024.741 1.001959
tau 6.557082 0.1408245 5.495362 1.030037 13.46754 1522.778 1.003301

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  1.987987 14.03885
tau 1.030037 13.46754


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] 0.9503392 0.6811747 0.8134112 0.9048823
max_treedepth_by_chain <- sapply(sampler_params, function(x) max(x[, "treedepth__"]))
print(max_treedepth_by_chain)
[1] 4 5 5 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] -1.461743

$tau
[1] 0.1964472

$eta
[1] -0.8751053 -1.7047613 -0.9337199  1.3190496  0.4229845 -0.7018442
[7]  0.2604412  1.1808317

$theta
[1] -1.633655 -1.796638 -1.645169 -1.202619 -1.378649 -1.599618 -1.410580
[8] -1.229772


(P)RNG seed

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

print(get_seed(fit))
[1] 308838208


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 0.059357 0.061835
chain:2 0.051969 0.034312
chain:3 0.059145 0.053630
chain:4 0.058807 0.057540