# Accessing the contents of a stanfit object

#### Stan Development Team

#### 2023-09-07

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 1 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]  2.447580  9.418657 15.031435  6.649415  5.107273  6.397837

    head(list_of_draws$tau)

    [1] 11.417342  8.720120 19.049094  7.807759  5.871701  5.689897

    head(list_of_draws$theta)

    iterations      [,1]        [,2]        [,3]      [,4]       [,5]      [,6]
          [1,] 29.102315  -6.8352772  1.23356314  8.976819 -2.8839518  1.865264
          [2,] 17.078375   8.6445358 -3.23158464 15.926286  4.6678079 18.680604
          [3,] 27.852589 -10.4130976 -7.61875190  8.524452 -0.1367373  4.948742
          [4,] 12.382813  16.6561818  9.54715182  9.853305  4.8246508 11.056800
          [5,]  5.845018   5.8791792 -3.83363100  3.290390  5.0624421 -3.871691
          [6,]  7.617909   0.3362016  0.04841452  7.687758  9.0632974  3.331856

    iterations      [,7]      [,8]
          [1,] 23.561906  9.542693
          [2,]  5.875668 14.785823
          [3,] 18.845638 26.807357
          [4,] 18.420371  5.660821
          [5,] 19.235571  5.490098
          [6,]  6.831372 18.526726

#### 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,] 6.396282 6.354773
          [2,] 7.662356 7.568286
          [3,] 5.021843 4.966370
          [4,] 9.521256 9.710008
          [5,] 7.401199 5.294640
          [6,] 5.616735 5.596601

## 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         8.190493020 0.10094285 5.0348597  -1.3684385   4.8798182
    tau        6.285897792 0.13946786 5.2226912   0.1791174   2.3471887
    eta[1]     0.389103775 0.01389046 0.9405289  -1.5505938  -0.2054586
    eta[2]     0.003440379 0.01394031 0.8728298  -1.7514717  -0.5826758
    eta[3]    -0.169140344 0.01414622 0.9374580  -1.9415179  -0.8225351
    eta[4]    -0.068875026 0.01369500 0.9015124  -1.8099156  -0.6674928
    eta[5]    -0.338904184 0.01530117 0.8845929  -2.0306160  -0.9335687
    eta[6]    -0.206333574 0.01406427 0.9140670  -1.9834252  -0.8101284
    eta[7]     0.315543688 0.01418088 0.8983463  -1.5092330  -0.2846886
    eta[8]     0.043423175 0.01437340 0.9330859  -1.7953530  -0.5579193
    theta[1]  11.266248104 0.16214590 7.8788866  -2.1082879   6.1615017
    theta[2]   8.079353246 0.08886517 6.2005540  -4.3028936   4.2950385
    theta[3]   6.526529901 0.11547740 7.4404528  -9.5282541   2.6028216
    theta[4]   7.623234850 0.09258236 6.4698649  -5.6261091   3.6433675
    theta[5]   5.431031450 0.10679264 6.3159180  -8.1187846   1.7478471
    theta[6]   6.351951997 0.10774051 6.8250987  -8.4484326   2.6317519
    theta[7]  10.548337152 0.10476329 6.5956453  -1.0543288   5.9443021
    theta[8]   8.547837597 0.14417203 7.7267428  -6.7253719   3.9902413
    lp__     -39.659671566 0.07993048 2.6468184 -45.4316415 -41.2455374
                      50%         75%      97.5%    n_eff      Rhat
    mu         8.07115584  11.2487511  18.520587 2487.847 1.0001926
    tau        5.01773253   8.8707562  19.998788 1402.298 1.0049815
    eta[1]     0.41760281   1.0085123   2.205133 4584.704 0.9991427
    eta[2]    -0.01420980   0.6019420   1.705852 3920.256 0.9991851
    eta[3]    -0.17329615   0.4738874   1.641107 4391.601 1.0000856
    eta[4]    -0.08897772   0.5046882   1.792725 4333.305 0.9998628
    eta[5]    -0.35930807   0.2478095   1.456381 3342.240 0.9997310
    eta[6]    -0.23573517   0.3955700   1.654451 4223.979 0.9994896
    eta[7]     0.32238654   0.9253870   2.046694 4013.111 0.9992923
    eta[8]     0.05363753   0.6605782   1.855477 4214.286 0.9995499
    theta[1]  10.23376978  15.4109486  30.143158 2361.118 1.0010100
    theta[2]   8.05420013  11.8427249  20.318133 4868.530 0.9997838
    theta[3]   7.01749339  11.0652904  20.460197 4151.497 1.0003605
    theta[4]   7.66750650  11.4617651  20.774681 4883.530 0.9996923
    theta[5]   5.79340833   9.5746062  16.998168 3497.762 1.0004061
    theta[6]   6.71726075  10.5998817  19.127611 4012.914 0.9994485
    theta[7]   9.98507347  14.5519171  24.896658 3963.660 1.0000578
    theta[8]   8.27251798  12.7664163  25.330121 2872.307 0.9999784
    lp__     -39.48362883 -37.7752727 -35.141510 1096.537 1.0033910

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  8.190493 0.1009429 5.034860 2.063252 14.60106 2487.847 1.000193
    tau 6.285898 0.1394679 5.222691 0.885754 13.26074 1402.298 1.004981

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  2.063252 14.60106
    tau 0.885754 13.26074

## 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] 0.9335954 0.8281076 0.9218277 0.8700841

    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] -0.8768214

    $tau
    [1] 5.6757

    $eta
    [1]  1.6005474  1.3092637  0.8760021  1.1847391  0.6396777 -1.0579591 -1.9268414
    [8]  1.8571407

    $theta
    [1]   8.207405   6.554166   4.095104   5.847402   2.753797  -6.881480 -11.812995
    [8]   9.663752

## (P)RNG seed

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

    print(get_seed(fit))

    [1] 542726306

## 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  0.034  0.036
    chain:2  0.033  0.027
    chain:3  0.033  0.036
    chain:4  0.031  0.033