dynamite: Bayesian Modeling and Causal Inference for Multivariate Longitudinal Data

The dynamite R package provides an easy-to-use interface for Bayesian inference of complex panel (time series) data comprising of multiple measurements per multiple individuals measured in time via dynamic multivariate panel models (DMPM). The main features distinguishing the package and the underlying methodology from many other approaches are:

• Support for regular time-invariant effects, group-level random effects, and time-varying effects modeled via Bayesian P-splines.
• Joint modeling of multiple measurements per individual (multiple channels) based directly on the assumed data generating process. Individual channels can be univariate or multivariate.
• Support for various distributions: Currently Gaussian, Multivariate Gaussian, Student t, Categorical, Multinomial, Poisson, Bernoulli, Binomial, Negative Binomial, Gamma, Exponential, and Beta distributions are available, and these can be combined arbitrarily in multichannel models.
• Allows evaluating realistic long-term counterfactual predictions which take into account the dynamic structure of the model by posterior predictive distribution simulation.
• Transparent quantification of parameter and predictive uncertainty due to a fully Bayesian approach.
• User-friendly and efficient R interface with state-of-the-art estimation via Stan. Both rstan and cmdstanr backends are supported.

The dynamite package is developed with the support of Academy of Finland grant 331817 (PREDLIFE). For further information on DMPMs and the dynamite package, see the related arXiv and SocArXiv preprints.

Installation

You can install the most recent stable version of dynmite from CRAN or the development version from R-universe by running one the following lines:

install.packages("dynamite")
install.packages("dynamite", repos = "https://ropensci.r-universe.dev")

Example

A single-channel model with time-invariant effect of z, time-varying effect of x, lagged value of the response variable y and a group-specific random intercepts:

set.seed(1)
library("dynamite")
gaussian_example_fit <- dynamite(
  obs(y ~ -1 + z + varying(~ x + lag(y)) + random(~1), family = "gaussian") +
    splines(df = 20),
  data = gaussian_example, time = "time", group = "id",
  iter = 2000, chains = 2, cores = 2, refresh = 0
)

Summary of the model:

gaussian_example_fit
#> 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: 661 (sigma_nu_y_alpha)
#> Smallest tail-ESS: 1058 (sigma_nu_y_alpha)
#> Largest Rhat: 1.003 (sigma_y)
#> 
#> Elapsed time (seconds):
#>         warmup sample
#> chain:1  5.479  3.373
#> chain:2  5.966  3.770
#> 
#> 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   0.0116  0.0112  1.95   1.99   1.00    2815.    1434.
#> 2 sigma_nu_y… 0.0944 0.0933 0.0114  0.0107  0.0780 0.114  1.00     661.    1058.
#> 3 sigma_y     0.198  0.198  0.00373 0.00362 0.192  0.204  1.00    2580.    1254.
#> 4 tau_alpha_y 0.212  0.205  0.0483  0.0432  0.146  0.301  1.00    1731.    1606.
#> 5 tau_y_x     0.364  0.355  0.0740  0.0648  0.266  0.494  1.00    2812.    1504.
#> 6 tau_y_y_la… 0.107  0.105  0.0219  0.0213  0.0781 0.148  1.00    2387.    1682.

Posterior estimates of time-varying effects:

plot_deltas(gaussian_example_fit, scales = "free")

And group-specific intercepts:

plot_nus(gaussian_example_fit, groups = 1:10)

Traceplots and density plots:

plot(gaussian_example_fit, type = "beta")

Posterior predictive samples for the first 4 groups (samples based on the posterior distribution of model parameters and observed data on first time point):

library("ggplot2")
pred <- predict(gaussian_example_fit, n_draws = 100)
pred |>
  dplyr::filter(id < 5) |>
  ggplot(aes(time, y_new, group = .draw)) +
  geom_line(alpha = 0.25) +
  # observed values
  geom_line(aes(y = y), colour = "tomato") +
  facet_wrap(~id) +
  theme_bw()

For more examples, see the package vignette and the blog post about dynamite.

Related packages

• The dynamite package uses Stan via rstan and cmdstanr (see also https://mc-stan.org), which is a probabilistic programming language for general Bayesian modelling.
• The brms package also uses Stan, and can be used to fit various complex multilevel models.
• Regression modeling with time-varying coefficients based on kernel smoothing and least squares estimation is available in package tvReg. The tvem package provides similar functionality for gaussian, binomial and poisson responses with mgcv backend.
• plm contains various methods to estimate linear models for panel data, e.g., fixed effect models.
• lavaan provides tools for structural equation modeling, and as such can be used to model various panel data models as well.

Contributing

Contributions are very welcome, see CONTRIBUTING.md for general guidelines.