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MultiVariate (Dynamic) Generalized Addivite Models

The goal of mvgam is to use a Bayesian framework to estimate parameters of Dynamic Generalized Additive Models (DGAMs) for time series with dynamic trend components. The package provides an interface to fit Bayesian DGAMs using either JAGS or Stan as the backend, but note that users are strongly encouraged to opt for Stan over JAGS. The formula syntax is based on that of the package mgcv to provide a familiar GAM modelling interface. The motivation for the package and some of its primary objectives are described in detail by Clark & Wells 2022 (published in Methods in Ecology and Evolution).


Install the development version from GitHub using: devtools::install_github("nicholasjclark/mvgam"). Note that to actually condition models with MCMC sampling, either the JAGS software must be installed (along with the R packages rjags and runjags) or the Stan software must be installed (along with either rstan and/or cmdstanr). Only rstan is listed as a dependency of mvgam to ensure that installation is less difficult. If users wish to fit the models using mvgam, please refer to installation links for JAGS here, for Stan with rstan here, or for Stan with cmdstandr here. You will need a fairly recent version of Stan to ensure all the model syntax is recognized. If you see warnings such as variable "array" does not exist, this is usually a sign that you need to update your version of Stan. We highly recommend you use Cmdstan through the cmdstanr interface as the backend. This is because Cmdstan is easier to install, is more up to date with new features, and uses less memory than Rstan. See this documentation from the Cmdstan team for more information.

Getting started

mvgam was originally designed to analyse and forecast non-negative integer-valued data (counts). These data are traditionally challenging to analyse with existing time-series analysis packages. But further development of mvgam has resulted in support for a growing number of observation families that extend to other types of data. Currently, the package can handle data for the following families:

  • gaussian() for real-valued data
  • student_t() for heavy-tailed real-valued data
  • lognormal() for non-negative real-valued data
  • Gamma() for non-negative real-valued data
  • betar() for proportional data on (0,1)
  • poisson() for count data
  • nb() for overdispersed count data
  • tweedie() for overdispersed count data

Note that only poisson(), nb(), and tweedie() are available if using JAGS. All families, apart from tweedie(), are supported if using Stan. See ??mvgam_families for more information. Below is a simple example for simulating and modelling proportional data with Beta observations over a set of seasonal series with independent Gaussian Process dynamic trends:

data <- sim_mvgam(family = betar(),
                 T = 80,
                 trend_model = 'GP',
                 trend_rel = 0.5, 
                 seasonality = 'shared')

Plot the series to see how they evolve over time

plot_mvgam_series(data = data$data_train, series = 'all')

Fit a DGAM to these series that uses a hierarchical cyclic seasonal smooth term to capture variation in seasonality among series. The model also includes series-specific latent Gaussian Processes with squared exponential covariance functions to capture temporal dynamics

mod <- mvgam(y ~ s(season, bs = 'cc', k = 7) +
               s(season, by = series, m = 1, k = 5),
             trend_model = 'GP',
             data = data$data_train,
             newdata = data$data_test,
             family = betar())

Plot the estimated posterior hindcast and forecast distributions for each series

layout(matrix(1:4, nrow = 2, byrow = TRUE))
for(i in 1:3){
  plot(mod, type = 'forecast', series = i)

Various S3 functions can be used to inspect parameter estimates, plot smooth functions and residuals, and evaluate models through posterior predictive checks or forecast comparisons. Please see the package documentation for more detailed examples.


You can set build_vignettes = TRUE when installing with either devtools::install_github or remotes::install_github, but be aware this will slow down the installation drastically. Instead, you can always access the vignette htmls online at

Other resources

A number of case studies have been compiled to highlight how DGAMs can be estimated using MCMC sampling. These are hosted currently on RPubs at the following links:

The package can also be used to generate all necessary data structures, initial value functions and modelling code necessary to fit DGAMs using Stan or JAGS. This can be helpful if users wish to make changes to the model to better suit their own bespoke research / analysis goals. The following resources can be helpful to troubleshoot: