# Accessing the contents of a stanfit object

#### Stan Development Team

#### 2016-09-11

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 11 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) function 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] 12.486875  5.076899  9.406396  8.214410  9.929440 14.989116

    head(list_of_draws$tau)

    [1]  6.7132847  0.2337698  8.1825272  1.3028420 14.3867909  2.4507864

    head(list_of_draws$theta)

    iterations      [,1]      [,2]      [,3]      [,4]       [,5]      [,6]
          [1,]  9.461048 23.908189 16.826486  9.975644  14.560703  6.616533
          [2,]  5.094057  4.990376  4.955423  5.057209   4.919296  5.049225
          [3,] 14.899391 16.278589 16.229008 16.409987 -10.024558  5.523476
          [4,] 10.628681  8.395092  8.203159  9.064492   7.313150 10.330872
          [5,] 15.056341  2.778215  4.305036  9.798058   3.036702  2.766697
          [6,]  9.229407 15.113267 18.209782 14.809398  16.568487 15.118246

    iterations      [,7]      [,8]
          [1,]  6.753117  2.048181
          [2,]  5.037592  5.288633
          [3,] 15.001986 12.521378
          [4,]  9.422001  7.701444
          [5,] 11.612728 17.645587
          [6,] 14.912755 13.051368

#### 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,] -0.4539793  4.607627
          [2,] -0.4539793  4.607627
          [3,]  0.2655726  3.693130
          [4,]  2.3952512 13.605032
          [5,]  7.4405332  7.229162
          [6,]  5.8874078  2.259399

## 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         7.729488267 0.12450562 4.6831183  -1.7261778   4.5427491
    tau        6.283030357 0.15340960 5.3516839   0.2703335   2.3083988
    eta[1]     0.391475980 0.01760641 0.9139955  -1.4168183  -0.2200949
    eta[2]     0.003125851 0.01684324 0.8645206  -1.6597507  -0.5748516
    eta[3]    -0.166296398 0.01683880 0.9159540  -1.9851784  -0.7853604
    eta[4]    -0.016487013 0.01580548 0.8783463  -1.7837110  -0.5982585
    eta[5]    -0.335417619 0.01718280 0.8778829  -2.0382564  -0.9156673
    eta[6]    -0.184483251 0.01735472 0.8774091  -1.8937820  -0.7810608
    eta[7]     0.335008451 0.01660627 0.8934875  -1.5166426  -0.2302950
    eta[8]     0.105440665 0.01672050 0.8861569  -1.6553779  -0.4666342
    theta[1]  11.249019199 0.18364455 7.9845803  -1.7567678   6.0185741
    theta[2]   7.712124731 0.10657145 6.1082910  -4.5840223   3.8721269
    theta[3]   6.350647750 0.14996509 7.3762234 -10.0852382   2.5356931
    theta[4]   7.661529731 0.11158905 6.3933654  -5.4326505   3.8688637
    theta[5]   5.092344387 0.11908738 6.2357212  -8.5015380   1.4423010
    theta[6]   6.265100788 0.11780219 6.4771635  -8.5515199   2.6335756
    theta[7]  10.412976094 0.12001533 6.5841921  -1.1144428   5.9238673
    theta[8]   8.519610689 0.15017011 7.3401927  -5.4383628   4.1354525
    lp__     -39.417253126 0.07685835 2.5365246 -44.8643049 -41.0132422
                      50%         75%      97.5%    n_eff      Rhat
    mu         7.65387977  10.8544748  17.174263 1414.791 1.0017393
    tau        5.03708068   9.0438523  19.284862 1216.959 1.0002056
    eta[1]     0.40600696   1.0278283   2.113588 2694.925 1.0010516
    eta[2]     0.01079158   0.5595116   1.719588 2634.507 1.0009476
    eta[3]    -0.17901291   0.4409814   1.642419 2958.863 0.9996343
    eta[4]    -0.01922742   0.5782290   1.672891 3088.277 1.0008058
    eta[5]    -0.35165801   0.2260518   1.534272 2610.268 1.0002202
    eta[6]    -0.18976760   0.3893553   1.559546 2556.048 0.9998816
    eta[7]     0.34196484   0.9261350   2.035984 2894.897 1.0006285
    eta[8]     0.11614203   0.6774195   1.837521 2808.811 1.0008682
    theta[1]   9.97486797  15.2540485  31.549272 1890.375 1.0003312
    theta[2]   7.70356438  11.4975334  20.220256 3285.169 1.0005471
    theta[3]   6.61458873  10.6455958  20.266667 2419.289 1.0023597
    theta[4]   7.66481619  11.5583562  20.594161 3282.585 1.0002896
    theta[5]   5.59835370   9.1837565  16.285756 2741.839 0.9995162
    theta[6]   6.64319811  10.3713008  18.227114 3023.173 1.0001929
    theta[7]   9.82056744  14.2065331  24.862031 3009.758 1.0006305
    theta[8]   8.09365175  12.5358561  24.651408 2389.175 1.0028142
    lp__     -39.23143185 -37.6057979 -35.011607 1089.171 1.0012956

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  7.729488 0.1245056 4.683118 1.9000236 13.57571 1414.791 1.001739
    tau 6.283030 0.1534096 5.351684 0.9346014 12.84918 1216.959 1.000206

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  1.9000236 13.57571
    tau 0.9346014 12.84918

## 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] 0.8420007 0.8495299 0.7739685 0.7506460

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

    [1] 3 4 3 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] 0.1088753

    $tau
    [1] 1.548756

    $eta
    [1] -0.2636909  1.8027576  1.0231196 -1.7044300 -1.9552741  0.8916144
    [7] -0.4864400 -1.0945375

    $theta
    [1] -0.2995176  2.9009068  1.6934378 -2.5308708 -2.9193672  1.4897684
    [7] -0.6445016 -1.5862962

## (P)RNG seed

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

    print(get_seed(fit))

    [1] 878857678

## 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 0.028499 0.022623
    chain:2 0.027020 0.026945
    chain:3 0.025327 0.019895
    chain:4 0.027118 0.021236