# Accessing the contents of a stanfit object

#### Stan Development Team

#### 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