dynamite: An R Package for Dynamic Multivariate Panel Models

dynamite is an R package for Bayesian inference of intensive panel (time series) data comprising multiple measurements per multiple individuals measured in time. The package supports joint modeling of multiple response variables, time-varying and time-invariant effects, a wide range of discrete and continuous distributions, group-specific random effects, latent factors, and customization of prior distributions of the model parameters. Models in the package are defined via a user-friendly formula interface, and estimation of the posterior distribution of the model parameters takes advantage of state-of-the-art Markov chain Monte Carlo methods. The package enables efficient computation of both individual-level and aggregated predictions and offers a comprehensive suite of tools for visualization and model diagnostics.

💡 Research Summary

The paper introduces dynamite, an R package that implements a novel class of statistical models called Dynamic Multivariate Panel Models (DMPMs). DMPMs are designed for intensive panel data where many individuals (N) are observed over many time points (T) and each observation consists of multiple response variables (C). The model assumes that each response at time t for individual i, y_{c,t,i}, can depend on (i) its own past values, (ii) exogenous covariates, and (iii) other responses measured at the same time point that precede it in a user‑specified ordering π. This ordering guarantees a factorisation of the joint conditional distribution and enables a flexible representation of contemporaneous dependencies.

The linear predictor for each response is written as

η_{c,t,i}=α_{c,t}+u_{c,t,i}^{⊤}β_{c}+w_{c,t,i}^{⊤}δ_{c,t}+z_{c,t,i}^{⊤}ν_{c,i}+λ_{c,i}^{⊤}ψ_{c,t},

where α_{c,t}, δ_{c,t}, and ψ_{c,t} are time‑varying components, β_{c} are time‑invariant fixed effects, ν_{c,i} are individual‑specific random effects (Gaussian with either diagonal or full covariance), and λ_{c,i}ψ_{c,t} represents a latent factor structure that can be correlated across responses. Time‑varying coefficients (α, δ, ψ) are modelled with Bayesian P‑splines: a set of equally‑spaced B‑splines with a random‑walk prior on the spline coefficients, controlled by a smoothness hyper‑parameter τ. This construction yields smooth, data‑driven trajectories for effects such as intervention impacts that evolve over time.

Estimation is fully Bayesian using Stan. The package supports both the rstan and cmdstanr interfaces, employing the No‑U‑Turn Sampler (NUTS), an adaptive Hamiltonian Monte Carlo algorithm, to draw posterior samples efficiently even for high‑dimensional models. The authors leverage data.table for fast data handling, posterior and ggplot2 for summarisation and visualisation, and loo for approximate leave‑one‑out and leave‑future‑out cross‑validation. All dependencies are on CRAN except cmdstanr, which requires a C++ toolchain (Rtools on Windows).

Key functional features of dynamite include:

1. Joint modelling of multiple responses – the package can simultaneously estimate C outcomes, capturing their inter‑dependencies without resorting to separate univariate fits.
2. Time‑varying effects via Bayesian splines – smooth, penalised B‑splines with random‑walk priors allow the user to let coefficients evolve over time while controlling over‑fitting.
3. Broad distributional support – Gaussian, Poisson, binomial, categorical, and other exponential‑family families are available, making the framework suitable for count, binary, and multinomial data.
4. Group‑level random effects and latent factors – hierarchical structures (random intercepts/slopes) and latent dynamic factors can be added, enabling multilevel and factor‑analytic extensions.
5. Automated multi‑step forecasting – after fitting, dynamite can generate predictions for any future horizon at both the individual and aggregate level, handling the recursion required by lagged covariates automatically.
6. Formula‑based DSL – a user‑friendly syntax (e.g., y1 + y2 ~ 1 + x1 + s(time) + (1|id) + lfactor(~1|id)) lets analysts declare fixed effects, splines, random effects, and latent factors in a single line.

The paper demonstrates the package with two case studies. The first uses real traffic safety data (seat‑belt usage and traffic fatalities) to illustrate how a policy intervention’s effect can be captured as a smooth time‑varying coefficient while accounting for the contemporaneous relationship between the two outcomes via a latent factor. The second employs a synthetic dataset with 1,000 individuals, 500 time points, and five responses, showcasing the scalability of dynamite: memory consumption and runtime are reduced by roughly 30‑40 % compared with a naïve Stan implementation of a comparable multivariate model.

Model diagnostics are performed using posterior predictive checks, R̂ convergence statistics, and approximate LOO/LFO cross‑validation. The results indicate good mixing of the MCMC chains, reasonable predictive performance, and the ability to quantify uncertainty in both parameter estimates and forecasts.

In summary, dynamite fills a gap in the R ecosystem for Bayesian dynamic panel analysis. It extends the capabilities of existing packages (plm, fixest, panelr, brms, etc.) by allowing many time points, multiple interdependent outcomes, and flexible time‑varying structures within a coherent Bayesian framework. The authors argue that this makes dynamite especially valuable for social‑science, epidemiology, and any field where intensive longitudinal data with complex dependence structures are encountered. Future directions mentioned include non‑linear state‑space extensions, non‑Gaussian latent factors, and hybrid inference schemes that combine variational approximations with MCMC for even larger datasets.