Accessing the contents of a stanfit object

Stan Development Team

2018-11-06

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 5 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$mu)
[1]  0.5447095  4.7252417  3.2569470 -0.8286781  9.6219050  8.2216086
head(list_of_draws$tau)
[1]  8.5346787 17.9086457  0.6533242  7.6947293  0.4868406  0.1776437
head(list_of_draws$theta)
          
iterations      [,1]      [,2]      [,3]      [,4]      [,5]     [,6]
      [1,]  6.418424  2.377951 -7.457418 -4.285390  6.260707 4.035662
      [2,] 16.200762 20.996226 13.522734 10.804684 -5.715024 1.373639
      [3,]  2.730646  2.906606  3.566164  4.272856  3.946449 3.156987
      [4,] -9.516586  3.419058  2.609175  2.106274  1.168186 2.333335
      [5,] 10.649391  9.347813  8.845197  9.312305 10.572009 8.837870
      [6,]  7.779830  8.059589  8.098960  8.071455  8.152695 8.439963
          
iterations       [,7]       [,8]
      [1,] -10.233530 -0.2492004
      [2,]   2.659190 20.2856562
      [3,]   2.915854  1.8150799
      [4,]  10.873250 -8.2252264
      [5,]   9.736105  9.5069306
      [6,]   8.829198  8.4036264


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,] 7.834656 14.658213
      [2,] 8.602845  8.707589
      [3,] 6.683328  6.059371
      [4,] 1.136996 16.144736
      [5,] 3.099223 12.282279
      [6,] 9.837489  9.743201


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         7.863884583 0.13700508 5.2321964  -2.0422915   4.6269794
tau        6.599095132 0.16046573 5.7085456   0.2345065   2.4116847
eta[1]     0.375229911 0.01514060 0.9381203  -1.5313749  -0.2151492
eta[2]     0.004147385 0.01559322 0.8790939  -1.7521281  -0.5766739
eta[3]    -0.199061848 0.01522928 0.9134201  -1.9233541  -0.8049536
eta[4]    -0.039406372 0.01362912 0.8479632  -1.7511187  -0.6066509
eta[5]    -0.370246352 0.01655953 0.8932633  -2.0846894  -0.9660010
eta[6]    -0.204209067 0.01498057 0.8799825  -1.9172993  -0.7788366
eta[7]     0.348635042 0.01697559 0.9111550  -1.4979758  -0.2043391
eta[8]     0.062709382 0.01502139 0.9282725  -1.7781836  -0.5482978
theta[1]  11.335275863 0.15664699 8.4281621  -2.2940551   5.8620102
theta[2]   7.883719928 0.10284132 6.3925801  -5.1356249   3.9948330
theta[3]   6.036301960 0.15676490 7.8803570 -12.3008577   1.8278046
theta[4]   7.575273541 0.10199717 6.4364544  -5.3897602   3.6837216
theta[5]   4.886665484 0.10579500 6.4088014  -9.6346894   1.1328775
theta[6]   6.251944264 0.10720494 6.5528113  -7.7144651   2.3897055
theta[7]  10.610438309 0.12460629 6.9284417  -1.4690289   6.0211123
theta[8]   8.514287880 0.14635666 7.9547517  -7.1063146   3.9007457
lp__     -39.537150705 0.07642424 2.6232606 -45.3329098 -41.1098461
                  50%         75%      97.5%    n_eff      Rhat
mu         7.77626346  11.0972178  18.581425 1458.461 1.0039599
tau        5.28591218   9.1108242  21.028160 1265.571 1.0041627
eta[1]     0.39427914   0.9970109   2.247871 3839.112 1.0009535
eta[2]     0.01655031   0.5600328   1.726874 3178.329 1.0029754
eta[3]    -0.22392990   0.4167847   1.647382 3597.346 1.0011706
eta[4]    -0.03390189   0.5365456   1.591477 3870.958 0.9998946
eta[5]    -0.39030913   0.2051930   1.449781 2909.800 1.0006403
eta[6]    -0.21086457   0.3779280   1.597726 3450.575 1.0007759
eta[7]     0.34287287   0.9354712   2.147667 2880.942 1.0003174
eta[8]     0.06297143   0.6578275   1.961969 3818.832 1.0007991
theta[1]  10.18327621  15.4053555  31.995808 2894.820 1.0005149
theta[2]   7.84386632  11.8243242  20.981496 3863.822 1.0001433
theta[3]   6.63421295  10.8045881  20.371353 2526.935 1.0009286
theta[4]   7.63718913  11.4798972  20.620087 3982.146 1.0001086
theta[5]   5.41247224   9.1606172  16.289103 3669.639 1.0011515
theta[6]   6.65775950  10.4060349  18.794605 3736.162 1.0004816
theta[7]   9.97535487  14.5480351  26.003608 3091.656 1.0004385
theta[8]   8.17189454  12.5817082  25.800651 2954.121 1.0009291
lp__     -39.27056233 -37.6887982 -35.097643 1178.204 1.0064082

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  7.863885 0.1370051 5.232196 1.6079465 14.39235 1458.461 1.003960
tau 6.599095 0.1604657 5.708546 0.9589362 13.54728 1265.571 1.004163

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  1.6079465 14.39235
tau 0.9589362 13.54728


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] 0.8623579 0.8631091 0.8363789 0.8016998
max_treedepth_by_chain <- sapply(sampler_params, function(x) max(x[, "treedepth__"]))
print(max_treedepth_by_chain)
[1] 5 5 5 6


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] 1.001

$tau
[1] 0.1748375

$eta
[1] -0.96097895 -0.48769618  0.53046695  0.90459315 -0.04889237  1.22326686
[7] -0.88752200  1.48297866

$theta
[1] 0.8329847 0.9157323 1.0937454 1.1591567 0.9924517 1.2148728 0.8458278
[8] 1.2602802


(P)RNG seed

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

print(get_seed(fit))
[1] 699847790


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 0.038175 0.029291
chain:2 0.037047 0.033903
chain:3 0.033255 0.032134
chain:4 0.030956 0.026188