Imputation Approaches for Animal Movement Modeling

  • Henry Scharf
  • Mevin B. Hooten
  • Devin S. Johnson


The analysis of telemetry data is common in animal ecological studies. While the collection of telemetry data for individual animals has improved dramatically, the methods to properly account for inherent uncertainties (e.g., measurement error, dependence, barriers to movement) have lagged behind. Still, many new statistical approaches have been developed to infer unknown quantities affecting animal movement or predict movement based on telemetry data. Hierarchical statistical models are useful to account for some of the aforementioned uncertainties, as well as provide population-level inference, but they often come with an increased computational burden. For certain types of statistical models, it is straightforward to provide inference if the latent true animal trajectory is known, but challenging otherwise. In these cases, approaches related to multiple imputation have been employed to account for the uncertainty associated with our knowledge of the latent trajectory. Despite the increasing use of imputation approaches for modeling animal movement, the general sensitivity and accuracy of these methods have not been explored in detail. We provide an introduction to animal movement modeling and describe how imputation approaches may be helpful for certain types of models. We also assess the performance of imputation approaches in two simulation studies. Our simulation studies suggests that inference for model parameters directly related to the location of an individual may be more accurate than inference for parameters associated with higher-order processes such as velocity or acceleration. Finally, we apply these methods to analyze a telemetry data set involving northern fur seals (Callorhinus ursinus) in the Bering Sea. Supplementary materials accompanying this paper appear online.


Animal movement models Hierarchical models Telemetry data Multiple imputation 



The authors thank Ephraim Hanks for early insights and discussions about the research. Funding for this research was provided by NOAA (RWO 103), CPW (TO 1304), and NSF (DMS 1614392). Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the US Government.

Supplementary material

13253_2017_294_MOESM1_ESM.pdf (3.9 mb)
Supplement A: Implementation details This document contains implementation details and additional results for both simulation studies and the appllication to the movement of a Northern fur seal. (PDF 3.91MB) (3.4 mb)
Supplement B: Application vignette This vignette shows how the two-stage process imputation procedure was implemented for the application to the movement of a Norther fur seal. (ZIP 3.38MB)


  1. Brillinger, D. R. Modeling spatial trajectories. In Gelfand, A. E., P. J. Diggle, M. Fuentes, and P. Guttorp, editors, Handbook of Spatial Statistics, chapter 26, pages 463—-475. Chapman & Hall/CRC, Boca Raton, Florida, USA, 2010.CrossRefGoogle Scholar
  2. Brillinger, D. R. and B. S. Stewart. 1998. Elephant-seal movements: Modelling migration. Canadian Journal of Statistics, 26(3):431–443.CrossRefzbMATHGoogle Scholar
  3. Brost, B. M., M. B. Hooten, E. M. Hanks, and R. J. Small. 2015. Animal movement constraints improve resource selection inference in the presence of telemetry error. Ecology, 96(10):2590–2597.CrossRefPubMedGoogle Scholar
  4. Buderman, F. E., M. B. Hooten, J. S. Ivan, and T. M. Shenk. 2016. A functional model for characterizing long-distance movement behaviour. Methods in Ecology and Evolution, 7(3):264–273.CrossRefGoogle Scholar
  5. Fleming, C. H., W. F. Fagan, T. Mueller, K. A. Olson, P. Leimgruber, and J. M. Calabrese. 2015. Estimating where and how animals travel: An optimal framework for path reconstruction from autocorrelated tracking data. Ecology, pages 15–1607.1.Google Scholar
  6. Gelfand, A. E. and A. F. M. Smith. 1990. Sampling-Based Approaches to Calculating Marginal Densities. Journal of the American Statistical Association, 85(410):398–409.MathSciNetCrossRefzbMATHGoogle Scholar
  7. Hanks, E. M., M. B. Hooten, and M. W. Alldredge. 2015. Continuous-time discrete-space models for animal movement. The Annals of Applied Statistics, 9(1):145–165.MathSciNetCrossRefzbMATHGoogle Scholar
  8. Hanks, E. M., M. B. Hooten, D. S. Johnson, and J. T. Sterling. 2011. Velocity-Based movement modeling for individual and population level inference. PLoS ONE, 6(8):e22795.ADSCrossRefPubMedPubMedCentralGoogle Scholar
  9. Hanks, E. M. and D. A. Hughes. 2016. Flexible discrete space models of animal movement.Google Scholar
  10. Hefley, T. J., K. M. Broms, B. M. Brost, F. E. Buderman, S. L. Kay, H. R. Scharf, J. R. Tipton, P. J. Williams, and M. B. Hooten. 2017. The basis function approach for modeling autocorrelation in ecological data. Ecology, 98(3):632–6446.CrossRefPubMedGoogle Scholar
  11. Hooten, M. B., F. E. Buderman, B. M. Brost, E. M. Hanks, and J. S. Ivan. 2016. Hierarchical animal movement models for population-level inference. Environmetrics, 27(6):322–333.MathSciNetCrossRefGoogle Scholar
  12. Hooten, M. B. and D. S. Johnson. In Press. Basis function models for animal movement. Journal of the American Statistical Association.Google Scholar
  13. Hooten, M. B., D. S. Johnson, E. M. Hanks, and J. H. Lowry. 2010. Agent-based inference for animal movement and selection. Journal of Agricultural, Biological, and Environmental Statistics, 15(4):523–538.MathSciNetCrossRefzbMATHGoogle Scholar
  14. Hooten, M. B., D. S. Johnson, B. T. McClintock, and J. M. Morales. 2017. Animal Movement: Statistical Models for Telemetry Data. Chapman & Hall/CRC, Boca Raton, Florida, USA.CrossRefGoogle Scholar
  15. Johnson, D. S., M. B. Hooten, and C. E. Kuhn. 2013. Estimating animal resource selection from telemetry data using point process models. Journal of Animal Ecology, 82(6):1155–1164.CrossRefPubMedGoogle Scholar
  16. Johnson, D. S., J. M. London, M.-A. Lea, and J. W. Durban. 2008. Continuous-time correlated random walk model for animal telemetry data. Ecology, 89(5):1208–15.CrossRefPubMedGoogle Scholar
  17. Kays, R., M. C. Crofoot, W. Jetz, and M. Wikelski. 2015. Terrestrial animal tracking as an eye on life and planet. Science, 348(6240).Google Scholar
  18. Langrock, R., R. King, J. Matthiopoulos, L. Thomas, D. Fortin, and J. M. Morales. 2012. Flexible and practical modeling of animal telemetry data: Hidden Markov models and extensions. Ecology, 93(11):2336–2342.CrossRefPubMedGoogle Scholar
  19. Little, R. J. A. and D. B. Rubin. 1987. Statistical Analysis with Missing Data. John Wiley & Sons, New York, New York, USA.zbMATHGoogle Scholar
  20. McClintock, B. T. 2017. Incorporating Telemetry Error into Hidden Markov Models of Animal Movement Using Multiple Imputation. Journal of Agricultural, Biological and Environmental Statistics.Google Scholar
  21. McClintock, B. T., D. S. Johnson, M. B. Hooten, J. M. Ver Hoef, and J. M. Morales. 2014. When to be discrete: the importance of time formulation in understanding animal movement. Movement Ecology, 2(1):21.CrossRefPubMedPubMedCentralGoogle Scholar
  22. McClintock, B. T., J. M. London, M. F. Cameron, and P. L. Boveng. 2015. Modelling animal movement using the Argos satellite telemetry location error ellipse. Methods in Ecology and Evolution, 6(3):266–277.CrossRefGoogle Scholar
  23. McClintock, B. T., D. J. F. Russell, J. Matthiopoulos, and R. King. 2013. Combining individual animal movement and ancillary biotelemetry data to investigate population-level activity budgets. Ecology, 94(4):838–849.CrossRefGoogle Scholar
  24. Nelson, E. 1967. Dynamical Theories of Brownian Motion. Princeton University Press, Princeton, New Jersey.zbMATHGoogle Scholar
  25. Ormerod, J. T. and M. P. Wand. 2010. Explaining variational approximations. The American Statistician, 64(2):140–153.MathSciNetCrossRefzbMATHGoogle Scholar
  26. Rubin, D. B. 1996. Multiple imputation after 18+ years. Journal of the American Statistical Association, 91(434):473–489.CrossRefzbMATHGoogle Scholar
  27. —— 2004. Multiple Imputation for Nonresponse in Surveys.John Wiley & Sons, New York, New York, USA.zbMATHGoogle Scholar
  28. Scharf, H. R., M. B. Hooten, B. K. Fosdick, D. S. Johnson, J. M. London, and J. W. Durban. 2016. Dynamic social networks based on movement. Annals of Applied Statistics, 10(4):2182–2202.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© International Biometric Society 2017

Authors and Affiliations

  1. 1. Department of StatisticsColorado State UniversityFort CollinsUSA
  2. 2.U.S. Geological Survey, Colorado Cooperative Fish and Wildlife Research Unit, Department of Fish, Wildlife, and Conservation Biology, Department of Statistics, Colorado State UniversityFort CollinsUSA
  3. 3.Alaska Fisheries Science Center, NOAA FisheriesSeattleUSA

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