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:
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
[1] "stanfit"
attr(,"package")
[1] "rstan"
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.
The extract
function (with its default arguments) returns a list with named components corresponding to the model parameters.
[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:
[1] 5.383476 4.259927 3.773597 5.466592 6.588603 13.404230
[1] 3.4376655 3.8935749 21.2406208 1.0448334 0.0428121 0.1155494
iterations [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 4.073177 4.784386 5.980737 5.431588 6.7625026 -1.7959618
[2,] -5.478766 -2.610753 5.670680 2.879631 5.1155202 -0.1764268
[3,] 30.829292 7.974888 7.947629 4.284104 -0.3401116 16.7858948
[4,] 5.696482 7.297221 4.605994 6.486964 6.1890079 5.1381530
[5,] 6.504383 6.618376 6.610435 6.579370 6.5386955 6.6227491
[6,] 13.421515 13.463637 13.422910 13.271886 13.4840941 13.4339324
iterations [,7] [,8]
[1,] 3.064505 1.695676
[2,] 7.233268 -0.929307
[3,] 12.418555 12.867065
[4,] 5.527287 8.000315
[5,] 6.686698 6.625466
[6,] 13.321305 13.466787
The as.matrix
, as.data.frame
, and as.array
functions can also be used to retrieve the posterior draws from a stanfit object:
[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__"
[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__"
$iterations
NULL
$chains
[1] "chain:1" "chain:2" "chain:3" "chain:4"
$parameters
[1] "mu" "tau" "eta[1]" "eta[2]" "eta[3]" "eta[4]"
[7] "eta[5]" "eta[6]" "eta[7]" "eta[8]" "theta[1]" "theta[2]"
[13] "theta[3]" "theta[4]" "theta[5]" "theta[6]" "theta[7]" "theta[8]"
[19] "lp__"
The as.matrix
and as.data.frame
methods essentially return the same thing except in matrix and data frame form, respectively. The as.array
method returns the draws from each chain separately and so has an additional dimension:
[1] 4000 19
[1] 4000 19
[1] 1000 4 19
By default all of the functions for retrieving the posterior draws return the draws for all parameters (and generated quantities). The optional argument pars
(a character vector) can be used if only a subset of the parameters is desired, for example:
parameters
iterations mu theta[1]
[1,] 12.294436 10.2946760
[2,] 8.083146 7.2673147
[3,] 7.050771 24.2162877
[4,] 9.663047 11.2475908
[5,] 7.068416 5.9276186
[6,] -2.398115 0.9736401
Summary statistics are obtained using the summary
function. The object returned is a list with two components:
[1] "summary" "c_summary"
In fit_summary$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
).
mean se_mean sd 2.5% 25% 50%
mu 8.12522362 0.10543295 4.9418227 -1.6916254 4.8892048 8.07321948
tau 6.58614056 0.13328284 5.3510302 0.3028005 2.5433639 5.33964019
eta[1] 0.39724794 0.01513050 0.9543864 -1.5419715 -0.2031095 0.41086420
eta[2] -0.01075482 0.01530338 0.8483966 -1.7073219 -0.5758459 -0.02502340
eta[3] -0.22081500 0.01677053 0.9275588 -2.0440687 -0.8354153 -0.22846245
eta[4] -0.03561663 0.01484608 0.8959867 -1.8110925 -0.6209377 -0.02911226
eta[5] -0.38864870 0.01489854 0.8891847 -2.1672920 -0.9612040 -0.40092400
eta[6] -0.19644806 0.01520503 0.8923989 -1.9271772 -0.7897538 -0.21008728
eta[7] 0.36064597 0.01511057 0.8727346 -1.4024953 -0.1905596 0.36105649
eta[8] 0.05628648 0.01545371 0.9486657 -1.7995728 -0.5671822 0.05449893
theta[1] 11.78534121 0.16684539 8.5954849 -1.5310472 6.1435927 10.40794080
theta[2] 7.96961129 0.09413415 6.2626214 -4.8075733 4.2037808 7.96903459
theta[3] 6.09287412 0.13829410 7.7266011 -11.8098608 2.0036229 6.61427388
theta[4] 7.62404665 0.10095742 6.6220885 -5.8614275 3.5185197 7.66786315
theta[5] 5.08963645 0.10133845 6.4625099 -9.0375331 1.2950346 5.67086449
theta[6] 6.30804934 0.10871398 6.8057938 -8.6100492 2.2471665 6.63691149
theta[7] 10.80131200 0.11700021 6.7325358 -1.0770481 6.2887084 10.25576210
theta[8] 8.62092983 0.14475281 8.1621693 -6.8275700 3.9479337 8.26511019
lp__ -39.54481281 0.07849596 2.6604631 -45.6436033 -41.1301979 -39.29168235
75% 97.5% n_eff Rhat
mu 11.4339051 17.962924 2196.957 1.0006081
tau 9.2721739 20.020787 1611.856 1.0005018
eta[1] 1.0157440 2.234923 3978.708 0.9999563
eta[2] 0.5353172 1.721535 3073.427 0.9993953
eta[3] 0.3833220 1.663098 3059.068 1.0000438
eta[4] 0.5619414 1.736866 3642.333 0.9996340
eta[5] 0.1840037 1.415889 3562.020 1.0017262
eta[6] 0.3957598 1.635603 3444.635 0.9999902
eta[7] 0.9309946 2.103064 3335.819 1.0008580
eta[8] 0.6739109 1.931676 3768.433 0.9993490
theta[1] 16.0149389 33.139961 2654.070 1.0005255
theta[2] 11.8857421 20.546013 4426.066 0.9995913
theta[3] 10.7650010 20.444246 3121.546 1.0005744
theta[4] 11.8440778 20.968700 4302.426 0.9997326
theta[5] 9.5195398 16.565089 4066.811 0.9996950
theta[6] 10.7773185 18.676699 3919.104 1.0002833
theta[7] 14.7056071 25.422768 3311.190 1.0004802
theta[8] 12.8273735 26.781811 3179.488 0.9994721
lp__ -37.6681294 -35.074027 1148.735 1.0016283
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 8.125224 0.1054329 4.941823 1.927823 14.34993 2196.957 1.000608
tau 6.586141 0.1332828 5.351030 1.018044 13.78748 1611.856 1.000502
Since mu_tau_summary
is a matrix we can pull out columns using their names:
10% 90%
mu 1.927823 14.34993
tau 1.018044 13.78748
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] 0.8946750 0.8043410 0.8784134 0.7977858
max_treedepth_by_chain <- sapply(sampler_params, function(x) max(x[, "treedepth__"]))
print(max_treedepth_by_chain)
[1] 5 4 4 4
The Stan program itself is also stored in the stanfit object and can be accessed using get_stancode
:
The object code
is a single string and is not very intelligible when printed:
[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
:
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);
}
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:
$mu
[1] 0.9807931
$tau
[1] 3.772335
$eta
[1] -1.5529622 -0.8238692 -1.2685297 -1.0187685 -0.3050989 1.7212214 1.6778877
[8] 0.2406339
$theta
[1] -4.8775012 -2.1271178 -3.8045261 -2.8623432 -0.1701422 7.4738173 7.3103483
[8] 1.8885450
The get_seed
function returns the (P)RNG seed as an integer:
[1] 1349966339
The get_elapsed_time
function returns a matrix with the warmup and sampling times for each chain:
warmup sample
chain:1 0.085 0.064
chain:2 0.043 0.037
chain:3 0.041 0.034
chain:4 0.065 0.057