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?.

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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

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


A hypothetical data set

A hypothetical data set


High school data analysis best fit line

High-school data analysis: best fit line


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


Try again best fit quadratic

Try again: best fit quadratic


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


Generalizing residual analysis for complex stochastic animal movement models

e.g. food distribution

e.g. topography

Actual move


Earth mover s distance a generalised residual

Earth mover`s distance: a generalised residual


Earth mover s distance a generalised residual1

Earth mover`s distance: a generalised residual

  • is the actual place the animal moves to


Standardised earth mover s distance

Standardised earth mover`s distance


A scheme for testing how close your model is to data

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 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


Generalizing residual analysis for complex stochastic animal movement models

Power test on simulated data

F(x)

T(x)


Generalizing residual analysis for complex stochastic animal movement models

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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