A generalized residual technique for analyzing complex movement models using earth mover's distance

Abstract

1. Complex systems of moving and interacting objects are ubiquitous in the natural and social sciences. Predicting their behavior often requires models that mimic these systems with sufficient accuracy, while accounting for their inherent stochasticity. Though tools exist to determine which of a set of candidate models is best relative to the others, there is currently no generic goodness-of-fit framework for testing how close the best model is to the real complex stochastic system. 2. We propose such a framework, using a novel application of the Earth mover's distance, also known as the Wasserstein metric. It is applicable to any stochastic process where the probability of the model's state at time $t$ is a function of the state at previous times. It generalizes the concept of a residual, often used to analyze 1D summary statistics, to situations where the complexity of the underlying model's probability distribution makes standard residual analysis too imprecise for practical use. 3. We give a scheme for testing the hypothesis that a model is an accurate description of a data set. We demonstrate the tractability and usefulness of our approach by application to animal movement models in complex, heterogeneous environments. We detail methods for visualizing results and extracting a variety of information on a given model's quality, such as whether there is any inherent bias in the model, or in which situations it is most accurate. We demonstrate our techniques by application to data on multi-species flocks of insectivore birds in the Amazon rainforest. 4. This work provides a usable toolkit to assess the quality of generic movement models of complex systems, in an absolute rather than a relative sense.

References in corpus (5)

• The Dynamics of Crowd Disasters: An Empirical Study
• The Golden Age of Statistical Graphics
• Predicting local and non-local effects of resources on animal space use using a mechanistic step selection model
• A unifying framework for quantifying the nature of animal interactions
• Step selection techniques uncover the environmental predictors of space use patterns in flocks of Amazonian birds

Cited by in corpus (3)

• The conditionally autoregressive hidden Markov model (CarHMM): Inferring behavioural states from animal tracking data exhibiting conditional autocorrelation
• Characterising menotactic behaviours in movement data using hidden Markov models
• Integrated step selection analysis: bridging the gap between resource selection and animal movement