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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?.

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generalizing residual analysis for complex stochastic animal movement models

Generalizing residual analysis for complex, stochastic animal movement models

Jonathan Potts, Marie Auger-Méthé, Mark Lewis

how good is our best model
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
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
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

slide8
e.g. food distribution

e.g. topography

Actual move

earth mover s distance a generalised residual1
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 data1
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 data2
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 data3
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 data4
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 data5
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
slide19
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
Acknowledgements

Mark Lewis (University of Alberta)

Marie Auger-Méthé (UofA)

Members of the Lewis Lab

conclusion
Conclusion
  • Want to know how good your model is in an absolute rather than relative sense?
conclusion1
Conclusion
  • Got a mathematical model and want to know how good it is?
  • Use EMD for the best results.

EMD

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