Accessing the contents of a stanfit object

Stan Development Team

2018-01-19

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 6 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$mu)
[1] 16.7171106  7.0089327 13.8497856  8.1877739 16.2616201  0.2744798
head(list_of_draws$tau)
[1]  9.364586  5.827724  2.750543  5.755315 17.285360  6.519455
head(list_of_draws$theta)
          
iterations      [,1]      [,2]      [,3]       [,4]      [,5]      [,6]
      [1,] 28.453957 12.419106 15.516747  2.5574035  2.263467  8.472571
      [2,]  4.528674  6.499778  5.451932  9.0888057  7.729877 15.774053
      [3,] 12.771530 15.425695 14.692907 15.6969563 11.451342 13.361527
      [4,] 16.865500 10.286443  6.221658  3.1859018 10.620816  7.234169
      [5,]  6.162221 -2.495423  2.672620 11.7757129 11.302094  2.235750
      [6,] -1.771098  3.133499 -7.037659  0.4147378 -5.067782  7.350022
          
iterations      [,7]      [,8]
      [1,] 10.275118  7.109640
      [2,]  9.786837 13.275637
      [3,] 14.179742 16.037178
      [4,]  1.655779  8.505250
      [5,] 40.527431 39.129386
      [6,] -1.817790 -1.918773


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,]  0.6756168  5.195072
      [2,] -7.2571368  4.375244
      [3,] 15.3683884 23.374643
      [4,]  8.0645033  8.885693
      [5,] 17.1224076 18.788788
      [6,]  5.0349269  4.160703


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         7.867437257 0.15892994 5.2322650  -3.0169813   4.7147520
tau        6.626935741 0.19019763 5.7613092   0.1737095   2.4807924
eta[1]     0.396827865 0.01627226 0.9275331  -1.5256002  -0.2000294
eta[2]    -0.006368546 0.01328615 0.8402902  -1.6991468  -0.5450760
eta[3]    -0.191327564 0.01481920 0.9372484  -2.0228163  -0.8124606
eta[4]    -0.035986863 0.01656904 0.8881159  -1.7745613  -0.6244789
eta[5]    -0.332255738 0.01540108 0.8833728  -1.9872840  -0.9283984
eta[6]    -0.224296508 0.01463412 0.8984994  -1.9776206  -0.8261355
eta[7]     0.350649240 0.01609166 0.8699195  -1.4356473  -0.1846289
eta[8]     0.047486827 0.01480290 0.9208317  -1.7850992  -0.5754983
theta[1]  11.464238735 0.16626091 8.1151701  -1.6475632   6.2056897
theta[2]   7.915108292 0.09978144 6.3107324  -4.9134723   4.0150828
theta[3]   6.021132930 0.18111965 8.2309200 -13.3073636   1.8506294
theta[4]   7.596581797 0.10619192 6.7161669  -6.6137648   3.6826139
theta[5]   5.201923246 0.09964162 6.3018894  -8.6581500   1.4164270
theta[6]   6.062592547 0.10705827 6.7709598  -9.2353176   2.1205098
theta[7]  10.738499073 0.12872914 6.8079375  -1.2781340   6.2858491
theta[8]   8.356702760 0.15623191 8.0433969  -8.2129703   3.7558798
lp__     -39.535694262 0.08164855 2.6859544 -45.4302715 -41.1898997
                   50%         75%      97.5%     n_eff      Rhat
mu         7.942005114  11.2095766  17.572268 1083.8471 1.0031900
tau        5.281556602   9.1208956  21.038118  917.5551 1.0018634
eta[1]     0.412384312   1.0109350   2.185451 3249.1016 1.0005115
eta[2]    -0.005741722   0.5352601   1.681856 4000.0000 1.0001097
eta[3]    -0.195891532   0.4293761   1.720477 4000.0000 0.9991624
eta[4]    -0.035225155   0.5493171   1.755505 2873.0589 1.0008162
eta[5]    -0.340544223   0.2113004   1.498730 3289.9223 0.9998935
eta[6]    -0.252501676   0.3734116   1.588361 3769.6616 1.0002139
eta[7]     0.356383153   0.9084446   2.102802 2922.5146 0.9997448
eta[8]     0.065672990   0.6594844   1.874076 3869.6055 1.0001271
theta[1]  10.176985161  15.4002992  31.315389 2382.4016 1.0006378
theta[2]   7.948040116  11.8865137  20.772755 4000.0000 0.9992118
theta[3]   6.734007130  11.0056881  21.062308 2065.2167 1.0000704
theta[4]   7.708573058  11.6103918  21.004689 4000.0000 1.0001788
theta[5]   5.636407514   9.5517247  16.167929 4000.0000 0.9998475
theta[6]   6.415524998  10.4281735  18.544505 4000.0000 1.0000755
theta[7]  10.138860417  14.6122868  26.070278 2796.9029 0.9995220
theta[8]   8.171516672  12.5619846  25.653657 2650.5713 1.0003065
lp__     -39.295331540 -37.6222979 -35.046677 1082.1820 0.9994835

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  7.867437 0.1589299 5.232265 1.7343878 14.28952 1083.8471 1.003190
tau 6.626936 0.1901976 5.761309 0.8959336 14.01834  917.5551 1.001863

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  1.7343878 14.28952
tau 0.8959336 14.01834


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] 0.7646803 0.7679597 0.8134928 0.9248611
max_treedepth_by_chain <- sapply(sampler_params, function(x) max(x[, "treedepth__"]))
print(max_treedepth_by_chain)
[1] 5 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] -1.02428

$tau
[1] 1.65887

$eta
[1]  1.4258287  1.5160555 -1.1737508  0.7662169 -0.6876157 -1.9135261
[7]  0.6225471 -0.8279610

$theta
[1]  1.340984517  1.490659059 -2.971380411  0.246774095 -2.164945397
[6] -4.198571598  0.008444555 -2.397760033


(P)RNG seed

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

print(get_seed(fit))
[1] 1987613865


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 0.031084 0.031025
chain:2 0.030385 0.019742
chain:3 0.032238 0.025778
chain:4 0.032997 0.034627