Fit models for use in examples
(string) The name of the example. The currently available examples are
"logistic": logistic regression with intercept and 3 predictors.
"schools": the so-called "eight schools" model, a hierarchical
meta-analysis. Fitting this model will result in warnings about
divergences.
"schools_ncp": non-centered parameterization of the "eight schools"
model that fixes the problem with divergences.
To print the Stan code for a given example use
print_example_program(example).
(string) Which fitting method should be used? The default is
the "sample" method (MCMC).
Arguments passed to the chosen method. See the help pages for
the individual methods for details.
(logical) If TRUE (the default) then fitting the model is
wrapped in utils::capture.output().
The fitted model object returned by the selected method.
# \dontrun{
print_example_program("logistic")
#> data {
#> int<lower=0> N;
#> int<lower=0> K;
#> array[N] int<lower=0, upper=1> y;
#> matrix[N, K] X;
#> }
#> parameters {
#> real alpha;
#> vector[K] beta;
#> }
#> model {
#> target += normal_lpdf(alpha | 0, 1);
#> target += normal_lpdf(beta | 0, 1);
#> target += bernoulli_logit_glm_lpmf(y | X, alpha, beta);
#> }
#> generated quantities {
#> vector[N] log_lik;
#> for (n in 1 : N) {
#> log_lik[n] = bernoulli_logit_lpmf(y[n] | alpha + X[n] * beta);
#> }
#> }
fit_logistic_mcmc <- cmdstanr_example("logistic", chains = 2)
fit_logistic_mcmc$summary()
#> # A tibble: 105 × 10
#> variable mean median sd mad q5 q95 rhat ess_bulk
#> <chr> <num> <num> <num> <num> <num> <num> <num> <num>
#> 1 lp__ -65.9 -65.6 1.40 1.25 -68.6 -64.3 1.00 1066.
#> 2 alpha 0.381 0.385 0.216 0.223 0.0256 0.732 1.00 1952.
#> 3 beta[1] -0.667 -0.657 0.250 0.249 -1.09 -0.266 1.00 1902.
#> 4 beta[2] -0.275 -0.271 0.223 0.222 -0.655 0.0809 1.00 2026.
#> 5 beta[3] 0.691 0.680 0.272 0.261 0.257 1.14 1.00 2036.
#> 6 log_lik[1] -0.516 -0.508 0.100 0.0986 -0.696 -0.364 1.00 2121.
#> 7 log_lik[2] -0.399 -0.376 0.146 0.142 -0.665 -0.195 1.00 2027.
#> 8 log_lik[3] -0.496 -0.463 0.218 0.204 -0.895 -0.205 0.999 2110.
#> 9 log_lik[4] -0.448 -0.433 0.154 0.149 -0.731 -0.227 1.00 1978.
#> 10 log_lik[5] -1.19 -1.17 0.276 0.277 -1.65 -0.776 1.00 2176.
#> # ℹ 95 more rows
#> # ℹ 1 more variable: ess_tail <num>
fit_logistic_optim <- cmdstanr_example("logistic", method = "optimize")
fit_logistic_optim$summary()
#> # A tibble: 105 × 2
#> variable estimate
#> <chr> <num>
#> 1 lp__ -63.9
#> 2 alpha 0.364
#> 3 beta[1] -0.632
#> 4 beta[2] -0.259
#> 5 beta[3] 0.649
#> 6 log_lik[1] -0.515
#> 7 log_lik[2] -0.394
#> 8 log_lik[3] -0.469
#> 9 log_lik[4] -0.442
#> 10 log_lik[5] -1.14
#> # ℹ 95 more rows
fit_logistic_vb <- cmdstanr_example("logistic", method = "variational")
fit_logistic_vb$summary()
#> # A tibble: 106 × 7
#> variable mean median sd mad q5 q95
#> <chr> <num> <num> <num> <num> <num> <num>
#> 1 lp__ -66.7 -66.3 1.91 1.73 -70.5 -64.4
#> 2 lp_approx__ -2.03 -1.75 1.37 1.23 -4.66 -0.332
#> 3 alpha 0.519 0.518 0.223 0.224 0.153 0.895
#> 4 beta[1] -0.690 -0.687 0.234 0.244 -1.06 -0.298
#> 5 beta[2] -0.296 -0.297 0.262 0.251 -0.720 0.144
#> 6 beta[3] 0.546 0.548 0.309 0.310 0.0501 1.06
#> 7 log_lik[1] -0.454 -0.448 0.0931 0.0926 -0.622 -0.311
#> 8 log_lik[2] -0.530 -0.498 0.215 0.215 -0.951 -0.244
#> 9 log_lik[3] -0.488 -0.446 0.238 0.228 -0.906 -0.178
#> 10 log_lik[4] -0.535 -0.516 0.191 0.180 -0.875 -0.267
#> # ℹ 96 more rows
print_example_program("schools")
#> data {
#> int<lower=1> J;
#> vector<lower=0>[J] sigma;
#> vector[J] y;
#> }
#> parameters {
#> real mu;
#> real<lower=0> tau;
#> vector[J] theta;
#> }
#> model {
#> target += normal_lpdf(tau | 0, 10);
#> target += normal_lpdf(mu | 0, 10);
#> target += normal_lpdf(theta | mu, tau);
#> target += normal_lpdf(y | theta, sigma);
#> }
fit_schools_mcmc <- cmdstanr_example("schools")
#> Warning: 391 of 4000 (10.0%) transitions ended with a divergence.
#> See https://mc-stan.org/misc/warnings for details.
fit_schools_mcmc$summary()
#> # A tibble: 11 × 10
#> variable mean median sd mad q5 q95 rhat ess_bulk ess_tail
#> <chr> <num> <num> <num> <num> <num> <num> <num> <num> <num>
#> 1 lp__ -55.6 -56.0 6.40 7.14 -65.7 -45.9 1.14 19.4 333.
#> 2 mu 6.95 7.68 4.20 3.72 -0.0865 14.5 1.07 246. 40.2
#> 3 tau 4.24 3.19 3.55 3.11 0.592 11.2 1.18 15.7 9.70
#> 4 theta[1] 9.05 7.63 6.17 5.01 -0.247 20.1 1.11 575. 1129.
#> 5 theta[2] 7.29 7.96 5.17 4.40 -1.33 15.6 1.06 383. 660.
#> 6 theta[3] 6.04 7.16 6.37 5.11 -4.96 15.8 1.05 345. 591.
#> 7 theta[4] 7.16 7.85 5.55 4.64 -2.09 16.3 1.04 287. 330.
#> 8 theta[5] 5.44 6.31 5.68 4.65 -4.51 14.3 1.02 185. 57.9
#> 9 theta[6] 6.24 7.03 5.68 4.70 -3.84 15.5 1.02 162. 83.5
#> 10 theta[7] 8.94 7.77 5.69 4.69 0.261 18.8 1.15 489. 1084.
#> 11 theta[8] 7.45 8.18 6.27 5.20 -2.53 16.9 1.06 527. 1455.
print_example_program("schools_ncp")
#> data {
#> int<lower=1> J;
#> vector<lower=0>[J] sigma;
#> vector[J] y;
#> }
#> parameters {
#> real mu;
#> real<lower=0> tau;
#> vector[J] theta_raw;
#> }
#> transformed parameters {
#> vector[J] theta = mu + tau * theta_raw;
#> }
#> model {
#> target += normal_lpdf(tau | 0, 10);
#> target += normal_lpdf(mu | 0, 10);
#> target += normal_lpdf(theta_raw | 0, 1);
#> target += normal_lpdf(y | theta, sigma);
#> }
fit_schools_ncp_mcmc <- cmdstanr_example("schools_ncp")
fit_schools_ncp_mcmc$summary()
#> # A tibble: 19 × 10
#> variable mean median sd mad q5 q95 rhat ess_bulk
#> <chr> <num> <num> <num> <num> <num> <num> <num> <num>
#> 1 lp__ -46.9 -46.7 2.45 2.37 -51.5 -43.4 1.00 1390.
#> 2 mu 6.45 6.53 4.16 4.02 -0.486 13.3 1.00 3299.
#> 3 tau 4.63 3.83 3.59 3.39 0.324 11.6 1.00 1997.
#> 4 theta_raw[1] 0.343 0.373 0.968 0.963 -1.26 1.90 0.999 3956.
#> 5 theta_raw[2] 0.0288 0.0326 0.919 0.900 -1.49 1.54 1.00 4784.
#> 6 theta_raw[3] -0.150 -0.150 0.930 0.871 -1.70 1.39 1.00 4594.
#> 7 theta_raw[4] 0.0241 0.0138 0.929 0.917 -1.51 1.53 1.00 3987.
#> 8 theta_raw[5] -0.254 -0.266 0.923 0.936 -1.77 1.29 1.00 4286.
#> 9 theta_raw[6] -0.138 -0.151 0.936 0.911 -1.69 1.44 1.00 4732.
#> 10 theta_raw[7] 0.354 0.386 0.935 0.917 -1.22 1.88 1.00 4376.
#> 11 theta_raw[8] 0.0685 0.0563 0.960 0.955 -1.47 1.65 1.00 4469.
#> 12 theta[1] 8.82 8.19 6.70 5.73 -0.854 21.4 1.00 3878.
#> 13 theta[2] 6.71 6.68 5.47 4.95 -2.08 15.8 1.00 4371.
#> 14 theta[3] 5.58 5.85 6.23 5.28 -4.90 15.2 1.00 4089.
#> 15 theta[4] 6.54 6.57 5.71 5.16 -2.62 16.0 1.00 4307.
#> 16 theta[5] 4.90 5.24 5.62 5.24 -5.14 13.5 1.00 3910.
#> 17 theta[6] 5.65 5.84 5.75 5.24 -4.27 14.7 1.00 4570.
#> 18 theta[7] 8.69 8.23 5.89 5.49 0.0330 19.2 1.00 4332.
#> 19 theta[8] 7.00 6.80 6.39 5.51 -2.89 17.5 1.00 3804.
#> # ℹ 1 more variable: ess_tail <num>
# optimization fails for hierarchical model
cmdstanr_example("schools", "optimize", quiet = FALSE)
#> Initial log joint probability = -52.1838
#> Iter log prob ||dx|| ||grad|| alpha alpha0 # evals Notes
#> 99 122.653 0.275645 9.62182e+09 0.14 0.3154 173
#> Iter log prob ||dx|| ||grad|| alpha alpha0 # evals Notes
#> 187 258.482 0.227211 1.52288e+17 1e-12 0.001 402 LS failed, Hessian reset
#> Optimization terminated with error:
#> Line search failed to achieve a sufficient decrease, no more progress can be made
#> Finished in 0.1 seconds.
#> variable estimate
#> lp__ 258.48
#> mu 0.28
#> tau 0.00
#> theta[1] 0.28
#> theta[2] 0.28
#> theta[3] 0.28
#> theta[4] 0.28
#> theta[5] 0.28
#> theta[6] 0.28
#> theta[7] 0.28
#>
#> # showing 10 of 11 rows (change via 'max_rows' argument or 'cmdstanr_max_rows' option)
# }