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Fit a Bayesian dynamic multivariate panel model (DMPM) using Stan for Bayesian inference. The dynamite package supports a wide range of distributions and allows the user to flexibly customize the priors for the model parameters. The dynamite model is specified using standard R formula syntax via dynamiteformula(). For more information and examples, see 'Details' and the package vignettes.

The formula method returns the model definition as a quoted expression.

Information on the estimated dynamite model can be obtained via print including the following: The model formula, the data, the smallest effective sample sizes, largest Rhat and summary statistics of the time- and group-invariant model parameters.

The summary() method provides statistics of the posterior samples of the model; this is an alias of with summary = TRUE.


  group = NULL,
  priors = NULL,
  backend = "rstan",
  verbose = TRUE,
  verbose_stan = FALSE,
  stanc_options = list("O0"),
  threads_per_chain = 1L,
  grainsize = NULL,
  custom_stan_model = NULL,
  debug = NULL,

# S3 method for dynamitefit
formula(x, ...)

# S3 method for dynamitefit
print(x, full_diagnostics = FALSE, ...)

# S3 method for dynamitefit
summary(object, ...)



The model formula. See dynamiteformula() and 'Details'.


[data.frame, tibble::tibble, or data.table::data.table]
The data that contains the variables in the model in long format. Supported column types are integer, logical, double, and factor. Columns of type character will be converted to factors. Unused factor levels will be dropped. The data can contain missing values which will simply be ignored in the estimation in a case-wise fashion (per time-point and per channel). Input data is converted to channel specific matrix representations via stats::model.matrix.lm().


A column name of data that denotes the time index of observations. If this variable is a factor, the integer representation of its levels are used internally for defining the time indexing.


A column name of data that denotes the unique groups or NULL corresponding to a scenario without any groups. If group is NULL, a new column .group is created with constant value 1L is created indicating that all observations belong to the same group. In case of name conflicts with data, see the group_var element of the return object to get the column name of the new variable.


An optional data frame with prior definitions. See get_priors() and 'Details'.


Defines the backend interface to Stan, should be either "rstan" (the default) or "cmdstanr". Note that cmdstanr needs to be installed separately as it is not on CRAN. It also needs the actual CmdStan software. See for details.


All warnings and messages are suppressed if set to FALSE. Defaults to TRUE. Setting this to FALSE will also disable checks for perfect collinearity in the model matrix.


This is the verbose argument for rstan::sampling(). Defaults to FALSE.


This is the stanc_options argument passed to the compile method of a CmdStanModel object via cmdstanr::cmdstan_model() when backend = "cmdstanr". Defaults to list("O0"). To enable level one compiler optimizations, use list("O1").


A Positive integer defining the number of parallel threads to use within each chain. Default is 1. See rstan::rstan_options() and cmdstanr::sample() for details.


A positive integer defining the suggested size of the partial sums when using within-chain parallelization. Default is number of time points divided by threads_per_chain. Setting this to 1 leads the workload division entirely to the internal scheduler. The performance of the within-chain parallelization can be sensitive to the choice of grainsize, see Stan manual on reduce-sum for details.


An optional character string that either contains a customized Stan model code or a path to a .stan file that contains the code. Using this will override the generated model code. For expert users only.


A named list of form name = TRUE indicating additional objects in the environment of the dynamite function which are added to the return object. Additionally, values no_compile = TRUE and no_sampling = TRUE can be used to skip the compilation of the Stan code and sampling steps respectively. This can be useful for debugging when combined with model_code = TRUE, which adds the Stan model code to the return object.


For dynamite(), additional arguments to rstan::sampling() or cmdstanr::sample(), such as chains and cores (chains and parallel_chains in cmdstanr). For summary(), additional arguments to For print(), further arguments to the print method for tibbles (see tibble::formatting). Not used for formula().


The model fit object.


By default, the effective sample size (ESS) and Rhat are computed only for the time- and group-invariant parameters (full_diagnostics = FALSE). Setting this to TRUE computes ESS and Rhat values for all model parameters, which can take some time for complex models.


The model fit object.


dynamite returns a dynamitefit object which is a list containing the following components:

  • stanfit
    A stanfit object, see rstan::sampling() for details.

  • dformulas
    A list of dynamiteformula objects for internal use.

  • data
    A processed version of the input data.

  • data_name
    Name of the input data object.

  • stan
    A list containing various elements related to Stan model construction and sampling.

  • group_var
    Name of the variable defining the groups.

  • time_var
    Name of the variable defining the time index.

  • priors
    Data frame containing the used priors.

  • backend
    Either "rstan" or "cmdstanr" indicating which package was used in sampling.

  • call
    Original function call as an object of class call.

formula returns a quoted expression.

print returns x invisibly.

summary returns a data.frame.


The best-case scalability of dynamite in terms of data size should be approximately linear in terms of number of time points and and number of groups, but as wall-clock time of the MCMC algorithms provided by Stan can depend on the discrepancy of the data and the model (and the subsequent shape of the posterior), this can vary greatly.


Santtu Tikka and Jouni Helske (2023). dynamite: An R Package for Dynamic Multivariate Panel Models. arXiv preprint,

Jouni Helske and Santtu Tikka (2022). Estimating Causal Effects from Panel Data with Dynamic Multivariate Panel Models. SocArxiv preprint,


data.table::setDTthreads(1) # For CRAN
# \donttest{
# Please update your rstan and StanHeaders installation before running
# on Windows
if (!identical(.Platform$OS.type, "windows")) {
  fit <- dynamite(
    dformula = obs(y ~ -1 + varying(~x), family = "gaussian") +
      lags(type = "varying") +
      splines(df = 20),
    chains = 1,
    refresh = 0
# }

data.table::setDTthreads(1) # For CRAN
#> obs(y ~ -1 + z + varying(~x + lag(y)) + random(~1), family = "gaussian") + 
#>     splines(df = 20, degree = 3, lb_tau = 0, noncentered = FALSE, 
#>         override = FALSE) + random_spec(correlated = FALSE, noncentered = TRUE)

data.table::setDTthreads(1) # For CRAN
#> Model:
#>   Family   Formula                                       
#> y gaussian y ~ -1 + z + varying(~x + lag(y)) + random(~1)
#> Correlated random effects added for response(s): y
#> Data: gaussian_example (Number of observations: 1450)
#> Grouping variable: id (Number of groups: 50)
#> Time index variable: time (Number of time points: 30)
#> NUTS sampler diagnostics:
#> No divergences, saturated max treedepths or low E-BFMIs.
#> Smallest bulk-ESS: 178 (sigma_y)
#> Smallest tail-ESS: 156 (tau_alpha_y)
#> Largest Rhat: 1.018 (beta_y_z)
#> Elapsed time (seconds):
#>         warmup sample
#> chain:1  6.313  3.086
#> chain:2  6.472  3.322
#> Summary statistics of the time- and group-invariant parameters:
#> # A tibble: 6 × 10
#>   variable      mean median      sd     mad     q5   q95  rhat ess_bulk ess_tail
#>   <chr>        <dbl>  <dbl>   <dbl>   <dbl>  <dbl> <dbl> <dbl>    <dbl>    <dbl>
#> 1 beta_y_z    1.97   1.97   0.0112  0.0113  1.95   1.98  1.02      230.     175.
#> 2 sigma_nu_y… 0.0955 0.0940 0.0117  0.0103  0.0791 0.120 1.00      195.     157.
#> 3 sigma_y     0.198  0.198  0.00404 0.00401 0.192  0.205 0.995     178.     188.
#> 4 tau_alpha_y 0.200  0.193  0.0463  0.0440  0.139  0.283 0.999     211.     156.
#> 5 tau_y_x     0.364  0.348  0.0770  0.0746  0.253  0.497 1.01      198.     187.
#> 6 tau_y_y_la… 0.105  0.102  0.0208  0.0195  0.0764 0.140 1.01      231.     186.

data.table::setDTthreads(1) # For CRAN
  types = "beta",
  probs = c(0.05, 0.1, 0.9, 0.95)
#> # A tibble: 1 × 12
#>   parameter  mean     sd    q5   q10   q90   q95  time group category response
#>   <chr>     <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <int> <int> <chr>    <chr>   
#> 1 beta_y_z   1.97 0.0112  1.95  1.95  1.98  1.98    NA    NA NA       y       
#> # ℹ 1 more variable: type <chr>