The Annals of Applied Statistics

A multi-state conditional logistic regression model for the analysis of animal movement

Aurélien Nicosia, Thierry Duchesne, Louis-Paul Rivest, and Daniel Fortin

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A multi-state version of an animal movement analysis method based on conditional logistic regression, called Step Selection Function (SSF), is proposed. In ecology SSF is developed from a comparison between the observed location of an animal and randomly sampled locations at each time step. Interpretation of the parameters in the multi-state model and the impact of different sampling schemes for the random locations are discussed. We prove the relationship between the new model, called HMM-SSF, and a random walk model on the plane. This relationship allows one to use both movement characteristics and local discrete choice behaviors when identifying the model’s hidden states. The new HMM-SSF is used to model the movement behavior of GPS-collared bison in Prince Albert National Park, Canada, where it successfully teases apart areas used to forage and to travel. The analysis thus provides valuable insights into how bison adjust their movement to habitat features, thereby revealing spatial determinants of functional connectivity in heterogeneous landscapes.

Article information

Ann. Appl. Stat., Volume 11, Number 3 (2017), 1537-1560.

Received: November 2016
Revised: April 2017
First available in Project Euclid: 5 October 2017

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Zentralblatt MATH identifier

Animal movement biased correlated random walk conditional logistic regression GPS hidden Markov model Step Selection Function


Nicosia, Aurélien; Duchesne, Thierry; Rivest, Louis-Paul; Fortin, Daniel. A multi-state conditional logistic regression model for the analysis of animal movement. Ann. Appl. Stat. 11 (2017), no. 3, 1537--1560. doi:10.1214/17-AOAS1045.

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Supplemental materials

  • A: Relationship between methods when applied to bison trajectory. Comparison of the multi-state SSF and random walk models using real bison movement data.
  • B: Proofs of the relationship between the proposed multi-state SSF model and the multi-state random walk model. Theoretical proofs that the multi-state random walk model can be fitted using the proposed multi-state SSF model.
  • C: R code. R code to fit the proposed HMM-SSF and the multi-state random walk model.
  • D: Bison data set. Data of the bison trajectory and its habitat attributes used in Section 4.