Multivariate (Dynamic) Generalized Additive Models • mvgam

MultiVariate (Dynamic) Generalized Additive Models

The goal of the mvgam 📦 is to fit Bayesian Dynamic Generalized Additive Models (DGAMs) that can include highly flexible nonlinear predictor effects for both process and observation components. The package does this by relying on functionalities from the impressive brms and mgcv packages. Parameters are estimated using the probabilistic programming language Stan, giving users access to the most advanced Bayesian inference algorithms available. This allows mvgam to fit a very wide range of models, including:

Installation

Install the stable version from CRAN using: install.packages('mvgam'), or install the development version from GitHub using: devtools::install_github("nicholasjclark/mvgam"). You will also need a working version of Stan installed (along with either rstan and/or cmdstanr). Please refer to installation links for Stan with rstan here, or for Stan with cmdstandr here.

Introductory seminar

Cheatsheet

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)
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:

set.seed(100)
data <- sim_mvgam(
  family = betar(),
  T = 80,
  trend_model = GP(),
  prop_trend = 0.5, 
  seasonality = 'shared'
)

Plot the series to see how they evolve over time

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

Visualizing multivariate proportional time series using the mvgam R package #rstats

Fit a State-Space GAM 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

library(patchwork)
fc <- forecast(mod)
wrap_plots(
  plot(fc, series = 1), 
  plot(fc, series = 2), 
  plot(fc, series = 3), 
  ncol = 2
)

Forecasting multivariate time series with Dynamic Generalized Additive Models

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 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/

Citing `mvgam` and related software

When using any software please make sure to appropriately acknowledge the hard work that developers and maintainers put into making these packages available. Citations are currently the best way to formally acknowledge this work (but feel free to ⭐ the repo as well), so we highly encourage you to cite any packages that you rely on for your research.

When using mvgam, please cite the following:

Clark, N.J. and Wells, K. (2023). Dynamic Generalized Additive Models (DGAMs) for forecasting discrete ecological time series. Methods in Ecology and Evolution. DOI: https://doi.org/10.1111/2041-210X.13974

As mvgam acts as an interface to Stan, please additionally cite:

Carpenter B., Gelman A., Hoffman M. D., Lee D., Goodrich B., Betancourt M., Brubaker M., Guo J., Li P., and Riddell A. (2017). Stan: A probabilistic programming language. Journal of Statistical Software. 76(1). DOI: https://doi.org/10.18637/jss.v076.i01

mvgam relies on several other R packages and, of course, on R itself. To find out how to cite R and its packages, use citation(). There are some features of mvgam which specifically rely on certain packages. The most important of these is the generation of data necessary to estimate smoothing splines and Gaussian Processes, which rely on the mgcv, brms and splines2 packages. The rstan and cmdstanr packages together with Rcpp makes Stan conveniently accessible in R. If you use some of these features, please also consider citing the related packages.

Other resources

A number of case studies and step-by-step webinars have been compiled to highlight how GAMs and DGAMs can be useful for analysing multivariate data:

Getting help

If you encounter a clear bug, please file an issue with a minimal reproducible example on GitHub. Please also feel free to use the mvgam Discussion Board to hunt for or post other discussion topics related to the package, and do check out the mvgam changelog for any updates about recent upgrades that the package has incorporated.

Interested in contributing?

I’m actively seeking PhD students and other researchers to work in the areas of ecological forecasting, multivariate model evaluation and development of mvgam. Please reach out if you are interested (n.clark’at’uq.edu.au). Other contributions are also very welcome, but please see The Contributor Instructions for general guidelines. Note that by participating in this project you agree to abide by the terms of its Contributor Code of Conduct.

mvgam