Author: Stan Development Team
Date: 2018-11-06

# Accessing the contents of a stanfit object

#### Stan Development Team

#### 2018-11-06

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 5 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]  0.5447095  4.7252417  3.2569470 -0.8286781  9.6219050  8.2216086

    head(list_of_draws$tau)

    [1]  8.5346787 17.9086457  0.6533242  7.6947293  0.4868406  0.1776437

    head(list_of_draws$theta)

    iterations      [,1]      [,2]      [,3]      [,4]      [,5]     [,6]
          [1,]  6.418424  2.377951 -7.457418 -4.285390  6.260707 4.035662
          [2,] 16.200762 20.996226 13.522734 10.804684 -5.715024 1.373639
          [3,]  2.730646  2.906606  3.566164  4.272856  3.946449 3.156987
          [4,] -9.516586  3.419058  2.609175  2.106274  1.168186 2.333335
          [5,] 10.649391  9.347813  8.845197  9.312305 10.572009 8.837870
          [6,]  7.779830  8.059589  8.098960  8.071455  8.152695 8.439963

    iterations       [,7]       [,8]
          [1,] -10.233530 -0.2492004
          [2,]   2.659190 20.2856562
          [3,]   2.915854  1.8150799
          [4,]  10.873250 -8.2252264
          [5,]   9.736105  9.5069306
          [6,]   8.829198  8.4036264

#### 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,] 7.834656 14.658213
          [2,] 8.602845  8.707589
          [3,] 6.683328  6.059371
          [4,] 1.136996 16.144736
          [5,] 3.099223 12.282279
          [6,] 9.837489  9.743201

## 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         7.863884583 0.13700508 5.2321964  -2.0422915   4.6269794
    tau        6.599095132 0.16046573 5.7085456   0.2345065   2.4116847
    eta[1]     0.375229911 0.01514060 0.9381203  -1.5313749  -0.2151492
    eta[2]     0.004147385 0.01559322 0.8790939  -1.7521281  -0.5766739
    eta[3]    -0.199061848 0.01522928 0.9134201  -1.9233541  -0.8049536
    eta[4]    -0.039406372 0.01362912 0.8479632  -1.7511187  -0.6066509
    eta[5]    -0.370246352 0.01655953 0.8932633  -2.0846894  -0.9660010
    eta[6]    -0.204209067 0.01498057 0.8799825  -1.9172993  -0.7788366
    eta[7]     0.348635042 0.01697559 0.9111550  -1.4979758  -0.2043391
    eta[8]     0.062709382 0.01502139 0.9282725  -1.7781836  -0.5482978
    theta[1]  11.335275863 0.15664699 8.4281621  -2.2940551   5.8620102
    theta[2]   7.883719928 0.10284132 6.3925801  -5.1356249   3.9948330
    theta[3]   6.036301960 0.15676490 7.8803570 -12.3008577   1.8278046
    theta[4]   7.575273541 0.10199717 6.4364544  -5.3897602   3.6837216
    theta[5]   4.886665484 0.10579500 6.4088014  -9.6346894   1.1328775
    theta[6]   6.251944264 0.10720494 6.5528113  -7.7144651   2.3897055
    theta[7]  10.610438309 0.12460629 6.9284417  -1.4690289   6.0211123
    theta[8]   8.514287880 0.14635666 7.9547517  -7.1063146   3.9007457
    lp__     -39.537150705 0.07642424 2.6232606 -45.3329098 -41.1098461
                      50%         75%      97.5%    n_eff      Rhat
    mu         7.77626346  11.0972178  18.581425 1458.461 1.0039599
    tau        5.28591218   9.1108242  21.028160 1265.571 1.0041627
    eta[1]     0.39427914   0.9970109   2.247871 3839.112 1.0009535
    eta[2]     0.01655031   0.5600328   1.726874 3178.329 1.0029754
    eta[3]    -0.22392990   0.4167847   1.647382 3597.346 1.0011706
    eta[4]    -0.03390189   0.5365456   1.591477 3870.958 0.9998946
    eta[5]    -0.39030913   0.2051930   1.449781 2909.800 1.0006403
    eta[6]    -0.21086457   0.3779280   1.597726 3450.575 1.0007759
    eta[7]     0.34287287   0.9354712   2.147667 2880.942 1.0003174
    eta[8]     0.06297143   0.6578275   1.961969 3818.832 1.0007991
    theta[1]  10.18327621  15.4053555  31.995808 2894.820 1.0005149
    theta[2]   7.84386632  11.8243242  20.981496 3863.822 1.0001433
    theta[3]   6.63421295  10.8045881  20.371353 2526.935 1.0009286
    theta[4]   7.63718913  11.4798972  20.620087 3982.146 1.0001086
    theta[5]   5.41247224   9.1606172  16.289103 3669.639 1.0011515
    theta[6]   6.65775950  10.4060349  18.794605 3736.162 1.0004816
    theta[7]   9.97535487  14.5480351  26.003608 3091.656 1.0004385
    theta[8]   8.17189454  12.5817082  25.800651 2954.121 1.0009291
    lp__     -39.27056233 -37.6887982 -35.097643 1178.204 1.0064082

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  7.863885 0.1370051 5.232196 1.6079465 14.39235 1458.461 1.003960
    tau 6.599095 0.1604657 5.708546 0.9589362 13.54728 1265.571 1.004163

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  1.6079465 14.39235
    tau 0.9589362 13.54728

## 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] 0.8623579 0.8631091 0.8363789 0.8016998

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

    [1] 5 5 5 6

## 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] 1.001

    $tau
    [1] 0.1748375

    $eta
    [1] -0.96097895 -0.48769618  0.53046695  0.90459315 -0.04889237  1.22326686
    [7] -0.88752200  1.48297866

    $theta
    [1] 0.8329847 0.9157323 1.0937454 1.1591567 0.9924517 1.2148728 0.8458278
    [8] 1.2602802

## (P)RNG seed

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

    print(get_seed(fit))

    [1] 699847790

## 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 0.038175 0.029291
    chain:2 0.037047 0.033903
    chain:3 0.033255 0.032134
    chain:4 0.030956 0.026188