Accessing the contents of a stanfit object

Stan Development Team

2016-06-24

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) function 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$mu)
[1] -2.084350  3.260267  8.745208  6.170586 11.195565 11.152329
head(list_of_draws$tau)
[1]  8.370224 12.943845 19.370003  3.120488 14.901105  1.290637
head(list_of_draws$theta)
          
iterations      [,1]      [,2]        [,3]       [,4]       [,5]
      [1,] 15.210256 -1.852729  0.66484946  3.0329038 -12.015565
      [2,] 14.358175  1.825837 -9.32030583  0.9541714  -2.354849
      [3,] 25.853763  7.747521 13.92746846  2.3013293  -8.742198
      [4,]  3.701011  9.017647  0.08693733  6.0868513   8.065210
      [5,] 15.504647 -3.415650  5.34605564 15.9829446   2.784469
      [6,] 12.401836 10.325730 10.05556904 11.1593639  10.976051
          
iterations       [,6]      [,7]      [,8]
      [1,]   2.055806  0.372758  2.568031
      [2,] -10.415389 29.835874  3.545465
      [3,]  -3.997713 19.977181 10.521570
      [4,]   7.581508  5.717939  9.269729
      [5,]   7.911253 10.967054 -6.481475
      [6,]   8.690259 11.083815 10.537022


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,]  3.477189 10.516983
      [2,] 10.279402  6.357327
      [3,]  9.991988  6.532370
      [4,]  5.648669  6.544317
      [5,] 15.432545  9.488765
      [6,]  3.772203  6.452969


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         7.660630530 0.12670159 4.8986649  -1.9012523   4.4740177
tau        6.378119795 0.15381056 5.4170982   0.2127316   2.3287640
eta[1]     0.376734130 0.01664676 0.9243349  -1.5254877  -0.2353968
eta[2]     0.011411499 0.01412896 0.8566048  -1.7152716  -0.5371076
eta[3]    -0.179014908 0.01453097 0.9190193  -2.0064361  -0.7948001
eta[4]     0.003489828 0.01499329 0.8659118  -1.6707630  -0.5583425
eta[5]    -0.316543779 0.01570160 0.8583787  -2.0146666  -0.8730942
eta[6]    -0.210541272 0.01497987 0.8593656  -1.8802686  -0.7843831
eta[7]     0.337534699 0.01643547 0.8630937  -1.4379886  -0.2373123
eta[8]     0.048367864 0.01620119 0.9239220  -1.7298459  -0.5694289
theta[1]  10.948680427 0.16137617 7.9471018  -1.9321403   5.8146691
theta[2]   7.780490561 0.09862214 6.2374120  -4.3974203   3.8500355
theta[3]   6.033941343 0.14495472 7.6297296 -11.3226605   1.9074771
theta[4]   7.513045436 0.11229283 6.4397480  -5.5255597   3.5428951
theta[5]   5.086693879 0.09889334 6.2545641  -8.5810771   1.4726241
theta[6]   6.016150530 0.11288859 6.4588830  -7.8911233   2.2079590
theta[7]  10.234893232 0.11511377 6.4599922  -1.3880187   5.9217927
theta[8]   8.113033994 0.12655558 7.4593450  -6.8547356   3.8413985
lp__     -39.407715347 0.07611112 2.5483874 -45.2178690 -40.9161446
                  50%         75%      97.5%    n_eff      Rhat
mu         7.61294100  10.7289393  17.428330 1494.828 1.0025865
tau        5.20555343   8.9588378  20.226884 1240.398 1.0045107
eta[1]     0.38686554   1.0050612   2.164465 3083.181 1.0007988
eta[2]     0.01101529   0.5780660   1.691733 3675.702 0.9996258
eta[3]    -0.18790317   0.4148696   1.668176 4000.000 0.9998477
eta[4]    -0.02209771   0.5634043   1.718963 3335.442 1.0012894
eta[5]    -0.32233547   0.2240705   1.431428 2988.617 0.9996588
eta[6]    -0.22579288   0.3611567   1.496558 3291.093 1.0001976
eta[7]     0.36179695   0.9123188   1.999456 2757.730 1.0012209
eta[8]     0.04790445   0.6744077   1.857211 3252.197 0.9999573
theta[1]   9.89797009  14.9031719  29.555109 2425.151 1.0012430
theta[2]   7.82695756  11.4363461  20.993767 4000.000 0.9998802
theta[3]   6.57483454  10.7139365  20.583467 2770.471 1.0021669
theta[4]   7.72119996  11.4672507  20.154463 3288.772 1.0009829
theta[5]   5.55722333   9.3457024  16.218718 4000.000 1.0004978
theta[6]   6.45955803  10.3485025  17.712019 3273.518 1.0008193
theta[7]   9.67721824  14.0474831  24.879937 3149.267 1.0012385
theta[8]   7.97749869  12.1665368  23.872224 3474.072 0.9994894
lp__     -39.17676469 -37.6529163 -35.129276 1121.075 1.0046112

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  7.660631 0.1267016 4.898665 1.4446260 13.89384 1494.828 1.002586
tau 6.378120 0.1538106 5.417098 0.9553664 13.16897 1240.398 1.004511

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  1.4446260 13.89384
tau 0.9553664 13.16897


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] 0.9004148 0.9079614 0.8067289 0.8771056
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] 0.3266236

$tau
[1] 0.2621781

$eta
[1] -1.1920366 -1.3056395 -0.8993741  0.7011695  0.6477077 -0.2637617
[7]  1.8353844  1.9857074

$theta
[1]  0.01409769 -0.01568647  0.09082741  0.51045481  0.49643832  0.25747104
[7]  0.80782109  0.84723250


(P)RNG seed

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

print(get_seed(fit))
[1] 311726855


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 0.029005 0.034145
chain:2 0.026610 0.054124
chain:3 0.043405 0.027770
chain:4 0.035490 0.032698