mvgam
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 Stan
as the backend. 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). An introduction to the package and some worked examples are shown in this seminar: Ecological Forecasting with Dynamic Generalized Additive Models.
Installation
Install the stable version from CRAN using: install.packages('mvgam')
, or install the development version from GitHub
using: devtools::install_github("nicholasjclark/mvgam")
. Note that to actually condition models with MCMC sampling, 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 Stan
with rstan
here, or for Stan
with cmdstandr
here. You will need a fairly recent version of Stan
(preferably 2.29 or above) to ensure all the model syntax is recognized. 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 nonnegative integervalued data (counts). These data are traditionally challenging to analyse with existing timeseries 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 realvalued data 
student_t()
for heavytailed realvalued data 
lognormal()
for nonnegative realvalued data 
Gamma()
for nonnegative realvalued data 
betar()
for proportional data on(0,1)

bernoulli()
for binary data 
poisson()
for count data 
nb()
for overdispersed count data 
binomial()
for count data with known number of trials 
beta_binomial()
for overdispersed count data with known number of trials 
nmix()
for count data with imperfect detection (unknown number of trials)
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$data_train, series = 'all')
Fit a DGAM to these series that uses a hierarchical cyclic seasonal smooth term to capture variation in seasonality among series. The model also includes seriesspecific latent Gaussian Processes with squared exponential covariance functions to capture temporal dynamics
mod < mvgam(y ~ s(season, bs = 'cc', k = 7) +
s(season, by = series, m = 1, k = 5),
trend_model = GP(),
data = data$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.
Vignettes
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 https://nicholasjclark.github.io/mvgam/articles/
Other resources
A number of case studies have been compiled to highlight how GAMs and DGAMs can be useful for working with time series data:
 Ecological Forecasting with Dynamic Generalized Additive Models
 StateSpace Vector Autoregressions in
mvgam
 How to interpret and report nonlinear effects from Generalized Additive Models
 Phylogenetic smoothing using mgcv
 Distributed lags (and hierarchical distributed lags) using mgcv and mvgam
 Incorporating timevarying seasonality in forecast models
The package can also be used to generate all necessary data structures, initial value functions and modelling code necessary to fit DGAMs using Stan
. This can be helpful if users wish to make changes to the model to better suit their own bespoke research / analysis goals.