Author: Stan Development Team
Date: 2022-09-07

# Accessing the contents of a stanfit object

#### Stan Development Team

#### 2022-09-07

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 2 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]  7.369312  4.738791 12.186492 13.760985 17.112781  1.973161

    head(list_of_draws$tau)

    [1]  7.978171  1.089728  4.125323  5.601477 14.917425  6.435649

    head(list_of_draws$theta)

    iterations      [,1]      [,2]        [,3]      [,4]      [,5]      [,6]
          [1,] 20.771861  3.149816  6.84929626 17.202170 -1.491638 10.045561
          [2,]  4.235975  5.702351  5.46369584  4.647449  3.069896  4.836850
          [3,] 17.183456  8.058508 18.94757288 13.566894 11.428894 10.165681
          [4,]  9.680666  5.659564 14.75438928  9.747233  2.466835 18.354298
          [5,] 30.503290 14.097343  4.04705241 13.009119 13.570706  5.266705
          [6,]  6.010498 10.157953 -0.04061875  9.479760  4.169078  5.132693

    iterations      [,7]      [,8]
          [1,]  5.098211 -1.811097
          [2,]  5.265172  5.240903
          [3,] 15.043956 12.889617
          [4,]  8.417942  9.487148
          [5,] 29.271447  8.762275
          [6,] 14.529463 13.972027

#### 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,]  7.704581  7.310924
          [2,] 12.866489 21.274948
          [3,]  4.309980  4.978919
          [4,] 10.220344 13.042346
          [5,]  5.926049 11.841887
          [6,]  8.239194 12.268610

## 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         7.990476551 0.13638519 5.1607569  -1.8706588   4.6142060
    tau        6.762924820 0.13661467 5.4197384   0.3484975   2.6328173
    eta[1]     0.393503508 0.01539995 0.9361409  -1.5431178  -0.2108019
    eta[2]     0.005466482 0.01500633 0.8610708  -1.7042092  -0.5641638
    eta[3]    -0.206593495 0.01482551 0.9200078  -2.0183803  -0.8318383
    eta[4]    -0.034381263 0.01478586 0.8765419  -1.7340930  -0.6170551
    eta[5]    -0.368965166 0.01601678 0.8459114  -1.9996973  -0.9223153
    eta[6]    -0.213887751 0.01593222 0.8658979  -1.8989164  -0.7896156
    eta[7]     0.346944146 0.01477211 0.8930023  -1.5434491  -0.2129022
    eta[8]     0.060572448 0.01556258 0.9238299  -1.7814491  -0.5605957
    theta[1]  11.492856487 0.17703365 8.5085143  -2.3852731   5.8827308
    theta[2]   7.884966432 0.10176589 6.2150845  -4.7042486   4.0611059
    theta[3]   6.055576626 0.14408116 7.8464805 -12.1349414   2.1179796
    theta[4]   7.634462419 0.10896845 6.6941906  -6.1531274   3.5807990
    theta[5]   5.113826435 0.10114357 6.2508747  -8.5167406   1.4106055
    theta[6]   6.078937379 0.11529981 6.6690209  -7.8732431   2.3053587
    theta[7]  10.887935413 0.12535706 6.8580137  -0.9037645   6.2793789
    theta[8]   8.571310149 0.14189270 7.9603919  -7.6927459   3.9250264
    lp__     -39.379967490 0.07099875 2.5284606 -44.8113092 -41.0042906
                       50%         75%      97.5%    n_eff      Rhat
    mu        7.863686e+00  11.2037379  18.480531 1431.833 1.0011095
    tau       5.476201e+00   9.4529232  20.659966 1573.845 0.9999193
    eta[1]    4.169561e-01   1.0184377   2.181095 3695.251 1.0001351
    eta[2]    1.429393e-04   0.5854696   1.714123 3292.521 1.0003660
    eta[3]   -2.215231e-01   0.4264461   1.627305 3850.912 1.0021652
    eta[4]   -4.863008e-02   0.5340422   1.688879 3514.406 0.9998232
    eta[5]   -3.795160e-01   0.1678531   1.343664 2789.325 0.9994925
    eta[6]   -2.298394e-01   0.3336712   1.510450 2953.796 1.0009000
    eta[7]    3.840260e-01   0.9205111   2.057795 3654.432 0.9995959
    eta[8]    7.830821e-02   0.6840637   1.873693 3523.876 0.9995864
    theta[1]  1.032506e+01  15.9741691  31.922405 2309.914 0.9995204
    theta[2]  7.887766e+00  11.7688342  20.417707 3729.835 1.0004593
    theta[3]  6.549406e+00  10.8138304  20.722800 2965.756 1.0009363
    theta[4]  7.645091e+00  11.7227322  20.953045 3773.936 1.0003973
    theta[5]  5.424388e+00   9.2542199  16.548798 3819.487 0.9997135
    theta[6]  6.461682e+00  10.3308785  18.448228 3345.546 0.9999136
    theta[7]  1.016331e+01  14.8221071  26.725688 2992.948 0.9994907
    theta[8]  8.234690e+00  12.8046889  26.076766 3147.377 0.9995999
    lp__     -3.917174e+01 -37.6267299 -34.995963 1268.268 1.0016461

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  7.990477 0.1363852 5.160757 1.662045 14.57341 1431.833 1.0011095
    tau 6.762925 0.1366147 5.419738 1.075565 14.21973 1573.845 0.9999193

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  1.662045 14.57341
    tau 1.075565 14.21973

## 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] 0.7625438 0.7829519 0.8700801 0.8734198

    max_treedepth_by_chain <- sapply(sampler_params, function(x) max(x[, "treedepth__"]))
    print(max_treedepth_by_chain)

    [1] 4 5 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] 1.083532

    $tau
    [1] 6.267349

    $eta
    [1] -0.5314910 -0.6480376  0.5977603 -0.6206335  0.5769578 -1.7231283 -1.0818183
    [8]  1.9134495

    $theta
    [1] -2.247508 -2.977946  4.829904 -2.806195  4.699528 -9.715915 -5.696601
    [8] 13.075788

## (P)RNG seed

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

    print(get_seed(fit))

    [1] 1730641227

## 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 0.036806 0.022088
    chain:2 0.045345 0.032371
    chain:3 0.033602 0.032454
    chain:4 0.032642 0.032313