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 3 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"
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.
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$mu)
[1] 0.1918428 2.7525145 2.9338555 2.4851729 2.9938300 6.4762800
head(list_of_draws$tau)
[1] 4.958288 8.162640 5.123909 5.402533 3.523353 13.594075
head(list_of_draws$theta)
iterations [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 3.781077 0.9461683 -0.66575821 6.3953394 -7.7761697 2.792552
[2,] 3.483947 3.9612480 8.05559747 -1.9883135 0.1219574 9.607624
[3,] 1.627558 4.4237801 -0.04246828 -0.6903147 0.9148411 4.019601
[4,] 9.488085 7.8098342 -3.31569480 -1.0968917 8.3659423 6.063906
[5,] 3.520259 4.9659016 -1.68729992 7.0645555 9.1705344 3.103952
[6,] 20.978418 11.0378340 16.24589496 8.5292676 5.2703316 1.893699
iterations [,7] [,8]
[1,] 0.05130667 -1.3863444
[2,] -2.12527682 2.9931911
[3,] 16.58203560 3.3411102
[4,] 9.03247509 0.5086259
[5,] 5.12634253 4.5176642
[6,] 6.63218539 2.2184181
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"
$parameters
[1] "mu" "tau" "eta[1]" "eta[2]" "eta[3]" "eta[4]"
[7] "eta[5]" "eta[6]" "eta[7]" "eta[8]" "theta[1]" "theta[2]"
[13] "theta[3]" "theta[4]" "theta[5]" "theta[6]" "theta[7]" "theta[8]"
[19] "lp__"
The as.matrix
and as.data.frame
methods essentially return the same thing except in matrix and data frame form, respectively. The as.array
method returns the draws from each chain separately and so has an additional dimension:
print(dim(matrix_of_draws))
print(dim(df_of_draws))
print(dim(array_of_draws))
[1] 4000 19
[1] 4000 19
[1] 1000 4 19
By default all of the functions for retrieving the posterior draws return the draws for all parameters (and generated quantities). The optional argument pars
(a character vector) can be used if only a subset of the parameters is desired, for example:
mu_and_theta1 <- as.matrix(fit, pars = c("mu", "theta[1]"))
head(mu_and_theta1)
parameters
iterations mu theta[1]
[1,] 9.9517932 15.2384913
[2,] 11.4724031 11.9530087
[3,] 16.1433788 17.9815749
[4,] -0.5957746 0.7019507
[5,] 2.3457693 0.2228519
[6,] 5.4070436 17.0271083
Summary statistics are obtained using the summary
function. The object returned is a list with two components:
fit_summary <- summary(fit)
print(names(fit_summary))
[1] "summary" "c_summary"
In fit_summary$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 7.86799800 0.10662963 4.9217422 -1.8354272 4.6332082
tau 6.27764968 0.16113273 5.3965473 0.1959559 2.3914635
eta[1] 0.37674896 0.01640885 0.9473873 -1.5506912 -0.2526270
eta[2] -0.00323991 0.01380036 0.8619471 -1.7479182 -0.5699341
eta[3] -0.17614796 0.01640252 0.9307869 -1.9240390 -0.8267083
eta[4] -0.02970133 0.01473376 0.8951438 -1.7647504 -0.6199526
eta[5] -0.32765396 0.01566645 0.9112051 -2.0833248 -0.9462620
eta[6] -0.17648594 0.01556463 0.8938928 -1.9036378 -0.7679067
eta[7] 0.33584465 0.01699721 0.8940393 -1.4871514 -0.2245970
eta[8] 0.04264788 0.01474508 0.9325608 -1.7244342 -0.5931117
theta[1] 11.07381121 0.15387741 8.0601096 -2.5417886 5.8516865
theta[2] 7.97221659 0.09810210 6.2045216 -4.6116895 4.1905999
theta[3] 6.20342501 0.16359209 7.8829909 -11.6570612 2.2628827
theta[4] 7.67135311 0.10052734 6.3579075 -5.1289342 3.8030840
theta[5] 5.35676102 0.10275590 6.4988538 -9.6296949 1.6926472
theta[6] 6.28540642 0.10503208 6.6428123 -8.6823092 2.6027384
theta[7] 10.69707537 0.11851290 6.7923297 -0.9302766 6.1573982
theta[8] 8.32350693 0.14681495 7.9347566 -7.9072642 3.7736639
lp__ -39.64678810 0.07627834 2.6172068 -45.4797958 -41.2508943
50% 75% 97.5% n_eff Rhat
mu 7.87116112 11.0337688 17.833674 2130.502 1.0006856
tau 5.02653345 8.7631542 19.274861 1121.668 1.0024870
eta[1] 0.39533129 1.0300437 2.156344 3333.488 1.0005870
eta[2] 0.01841221 0.5727731 1.648863 3901.041 0.9998967
eta[3] -0.19196360 0.4370510 1.651364 3220.175 0.9997577
eta[4] -0.03592233 0.5524715 1.782602 3691.121 1.0002275
eta[5] -0.33393119 0.2693459 1.540539 3382.915 0.9995419
eta[6] -0.20301303 0.4074410 1.679429 3298.324 1.0020175
eta[7] 0.36057610 0.9193941 1.996400 2766.674 0.9998384
eta[8] 0.03356431 0.6835376 1.884688 4000.000 0.9996460
theta[1] 9.92166484 15.0903456 30.473599 2743.672 1.0006287
theta[2] 7.95860025 11.7499337 20.233027 4000.000 0.9999558
theta[3] 6.82238754 10.9143105 20.695641 2321.974 1.0004085
theta[4] 7.54896551 11.5844618 20.451921 4000.000 0.9999093
theta[5] 5.84314303 9.5750732 16.965198 4000.000 0.9996760
theta[6] 6.69842266 10.5520154 18.708159 4000.000 1.0003362
theta[7] 9.95171026 14.6551619 26.037501 3284.780 0.9992323
theta[8] 7.99340717 12.6743689 26.061404 2920.967 1.0007071
lp__ -39.39738459 -37.8189882 -35.223695 1177.263 1.0011848
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 7.867998 0.1066296 4.921742 1.7927700 14.02136 2130.502 1.000686
tau 6.277650 0.1611327 5.396547 0.9095436 12.86726 1121.668 1.002487
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 1.7927700 14.02136
tau 0.9095436 12.86726
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] 0.8295204 0.7994754 0.8420772 0.8765889
max_treedepth_by_chain <- sapply(sampler_params, function(x) max(x[, "treedepth__"]))
print(max_treedepth_by_chain)
[1] 5 4 5 4
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);
}
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] -0.5629321
$tau
[1] 0.2903741
$eta
[1] 0.4795601 0.4850170 -0.8729951 0.5627613 -0.3524287 -1.7468493
[7] -0.7472970 1.8054111
$theta
[1] -0.42368026 -0.42209569 -0.81642720 -0.39952076 -0.66526822 -1.07017180
[7] -0.77992774 -0.03868748
The get_seed
function returns the (P)RNG seed as an integer:
print(get_seed(fit))
[1] 331435434
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 0.033336 0.025449
chain:2 0.032405 0.021598
chain:3 0.030668 0.034357
chain:4 0.030953 0.031631