Dynamic Generalised Additive Models (DGAM) for forecasting discrete ecological time series

Abstract

ABSTRACTGeneralised Additive Models (GAMs) are increasingly popular for describing smooth nonlinear relationships between predictors and response variables. GAMs are particularly relevant in ecology for representing hierarchical functions for discrete responses that encompass complex features including zero-inflation, bounding and uneven sampling. However, GAMs are less useful for producing forecasts as their smooth functions provide unstable predictions outside the range of training data.We introduce Dynamic Generalised Additive Models (DGAMs), where the GAM linear predictor is jointly estimated with unobserved dynamic components to model time series that evolve as a function of nonlinear predictor associations and latent temporal processes. These models are particularly useful for multivariate series, as they can estimate hierarchical smooths while learning complex temporal associations via dimension-reduced latent factor processes. We implement our models in the mvgam R package, which uses the mgcv and rjags packages to construct smoothing splines and estimate unobserved parameters in a probabilistic framework.Using simulations, we illustrate how our models outperform competing formulations in realistic ecological forecasting tasks while identifying important smooth predictor functions. We use a real-world case study to highlight some of mvgam’s key features, which include functions for: calculating correlations among series’ latent trends, performing model selection using rolling window forecasts, online data augmentation via a recursive particle filter, and visualising probabilistic uncertainties for smooths and predictions.Dynamic GAMs (DGAM) offer a solution to the challenge of forecasting discrete time series while estimating ecologically relevant nonlinear predictor associations. Our Bayesian latent factor approach will be particularly useful for exploring competing dynamic ecological models that encompass hierarchical smoothing structures while providing forecasts with robust uncertainties, tasks that are becoming increasingly important in applied ecology.