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Generalizing residual analysis for complex, stochastic animal movement models

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### Generalizing residual analysis for complex, stochastic animal movement models

Jonathan Potts, Marie Auger-Méthé, Mark Lewis

How good is our best model?

Potts JR, Harris S & Giuggioli L. (2013) Quantifying behavioural changes in territorial animals caused by sudden population declines. Am Nat 182:E73-E82

Check: look at the residuals

“Residual”: the distance between the model prediction and the data

Zuur et al. (2009) Mixed effects models and extensions in ecology with R. Springer Verlag

How do we extend these ideas to movement models?

Generic movement model: probability of moving to x at a time τ in the future given that the agent is currently at y and arrived there on a bearing θand is travelling through environment E is

Earth mover`s distance: a generalised residual

- is the actual place the animal moves to

A scheme for testing how close your model is to data

- Suppose you have N data points

A scheme for testing how close your model is to data

- Suppose you have N data points
- Simulate your model for N steps and repeat M times, where M is nice and big

A scheme for testing how close your model is to data

- Suppose you have N data points
- Simulate your model for N steps and repeat M times, where M is nice and big
- For each simulation, generate the Earth Movers distance (EMD)

A scheme for testing how close your model is to data

- Suppose you have N data points
- Simulate your model for N steps and repeat M times, where M is nice and big
- For each simulation, generate the Earth Movers distance (EMD)
- This gives a distribution of simulation EMDs

A scheme for testing how close your model is to data

- Suppose you have N data points
- Simulate your model for N steps and repeat M times, where M is nice and big
- For each simulation, generate the Earth Movers distance (EMD)
- This gives a distribution of simulation EMDs
- Also calculate EMD between data and model ED

A scheme for testing how close your model is to data

- Suppose you have N data points
- Simulate your model for N steps and repeat M times, where M is nice and big
- For each simulation, generate the Earth Movers distance (EMD)
- This gives a distribution of simulation EMDs
- Also calculate EMD between data and model ED
- If ED is not within 95% confidence intervals of the distribution of simulation EMDs then reject null hypothesis that model describes the data well

Power test on simulated data

Potts JR, Auger-Méthé M, Mokross K, Lewis MA. A generalized residual technique for analyzing complex movement models using earth mover's distance. In review for Methods EcolEvol arxiv:1402.1805

Acknowledgements

Mark Lewis (University of Alberta)

Marie Auger-Méthé (UofA)

Members of the Lewis Lab

Conclusion

- Want to know how good your model is in an absolute rather than relative sense?

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