# Accessing the contents of a stanfit object

#### 2024-03-04

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 3 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
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$mu) [1] 0.4833887 11.6850005 -3.3141669 -1.1598781 3.3806820 12.5507635 head(list_of_draws$tau)
[1] 20.736801  6.002451 25.372611  2.666828  3.549650  1.078036
head(list_of_draws$theta)  iterations [,1] [,2] [,3] [,4] [,5] [,6] [1,] 38.990737 16.287114 -11.8025114 11.063405 -4.3885999 6.387578 [2,] 16.285434 5.575360 7.9333888 14.673914 10.4915338 1.639833 [3,] 8.857648 11.587368 -5.3230698 -7.071244 -2.1626789 8.525583 [4,] -4.051336 -3.206878 0.1157556 -9.633611 -0.6574029 -1.550585 [5,] 8.429137 8.525984 3.2993868 4.504439 4.9565802 -2.691472 [6,] 12.133429 12.197865 13.2499500 10.900420 12.2274181 13.234744 iterations [,7] [,8] [1,] 9.880457 13.516355 [2,] 7.966316 9.850148 [3,] -4.982988 14.041399 [4,] -3.021736 -2.028627 [5,] 6.112344 4.727819 [6,] 15.015829 13.191878 #### 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,]  7.680122  5.583360
[2,]  6.146427  8.391114
[3,]  3.345247  2.542456
[4,] 11.190611 11.095583
[5,]  7.331734 23.847581
[6,]  1.999966  3.777700

## 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 7.75110327 0.11134056 5.1990038 -2.2690969 4.5036953 7.80630187 tau 6.80641050 0.17855223 6.0449436 0.2290198 2.4957338 5.33699182 eta[1] 0.38292109 0.01558869 0.9436183 -1.5917143 -0.2250060 0.41195951 eta[2] 0.01411281 0.01322934 0.8296821 -1.6041115 -0.5396589 0.01679256 eta[3] -0.17201770 0.01307911 0.9337684 -1.9874583 -0.7838333 -0.17804855 eta[4] -0.03832025 0.01475776 0.8836022 -1.8015636 -0.6169327 -0.03233633 eta[5] -0.35330329 0.01488249 0.8715506 -2.0323830 -0.9046659 -0.37269697 eta[6] -0.21318850 0.01432068 0.9109311 -2.0291215 -0.8150952 -0.23610678 eta[7] 0.36716141 0.01439726 0.8720225 -1.4001385 -0.1821243 0.36158066 eta[8] 0.06580386 0.01476528 0.9218926 -1.7831869 -0.5582930 0.05984778 theta[1] 11.30444959 0.16160030 8.3047480 -1.9758066 5.9323694 10.14824454 theta[2] 7.87409595 0.09331812 6.4029748 -4.6162975 3.8291169 7.76465969 theta[3] 6.12071272 0.14485185 8.2006024 -12.7047078 1.8579539 6.71433061 theta[4] 7.51752790 0.10077931 6.6291889 -6.0346728 3.5520111 7.57325747 theta[5] 4.92856284 0.11424483 6.5009916 -9.3626269 1.3123434 5.40143868 theta[6] 5.95562792 0.10429274 6.8094646 -8.8829227 2.0466017 6.32496123 theta[7] 10.63617997 0.11707419 6.8528602 -1.2758797 6.1083484 10.05169282 theta[8] 8.43429294 0.13356869 7.9117638 -6.4603252 3.6971623 8.19147859 lp__ -39.53080073 0.07796845 2.6531224 -45.5173608 -41.1490148 -39.27273980 75% 97.5% n_eff Rhat mu 10.9648821 17.998741 2180.387 1.0008978 tau 9.3110793 21.826483 1146.183 1.0019109 eta[1] 1.0229613 2.181206 3664.151 0.9999360 eta[2] 0.5667655 1.639260 3933.211 0.9997361 eta[3] 0.4343433 1.688982 5097.084 0.9994307 eta[4] 0.5558925 1.738362 3584.862 0.9999318 eta[5] 0.1911258 1.480976 3429.526 0.9998895 eta[6] 0.3905723 1.634791 4046.167 1.0001813 eta[7] 0.9432225 2.084443 3668.563 0.9998580 eta[8] 0.6712317 1.886720 3898.316 0.9996972 theta[1] 15.3699317 31.735854 2641.001 0.9996094 theta[2] 11.8883959 20.818955 4707.948 0.9996209 theta[3] 11.0223594 20.971858 3205.114 1.0015387 theta[4] 11.6591670 20.769237 4326.912 0.9991702 theta[5] 9.2160925 16.331576 3238.069 0.9998848 theta[6] 10.2769144 18.871329 4263.024 0.9998840 theta[7] 14.6033579 26.065618 3426.269 0.9995218 theta[8] 12.6438700 25.611631 3508.628 0.9998167 lp__ -37.6609821 -35.118680 1157.915 1.0042178 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  7.751103 0.1113406 5.199004 1.3286256 14.03575 2180.387 1.000898
tau 6.806410 0.1785522 6.044944 0.9572097 14.48271 1146.183 1.001911

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  1.3286256 14.03575
tau 0.9572097 14.48271

## 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] 0.7871779 0.9503414 0.9439005 0.8549200
max_treedepth_by_chain <- sapply(sampler_params, function(x) max(x[, "treedepth__"]))
print(max_treedepth_by_chain)
[1] 4 4 4 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)
$mu [1] 1.465461$tau
[1] 0.4536848

$eta [1] 1.80765657 1.96017502 -1.64586306 -0.06034084 1.58046455 -1.08906201 [7] -1.02607606 0.73341405$theta
[1] 2.2855675 2.3547628 0.7187580 1.4380854 2.1824939 0.9713702 0.9999460
[8] 1.7982000

## (P)RNG seed

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

print(get_seed(fit))
[1] 2115685401

## 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  0.040  0.027
chain:2  0.037  0.043
chain:3  0.038  0.044
chain:4  0.038  0.035