Author: Stan Development Team
Date: 2018-01-19

# 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