title: State-space models' dirty little secrets: even simple linear Gaussian models can have estimation problems.
abstract: State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results.
authors.affiliation: Dalhousie University, Department of Mathematics and Statistics, Halifax, B3H 4R2, Canada.
authors.forename: Marie
authors.initials: M
authors.lastname: Auger-Méthé
authors.affiliation: Dalhousie University, Department of Mathematics and Statistics, Halifax, B3H 4R2, Canada.
authors.forename: Chris
authors.initials: C
authors.lastname: Field
authors.affiliation: Technical University of Denmark, National Institute of Aquatic Resources, Charlottenlund, 2920, Denmark.
authors.forename: Christoffer M
authors.initials: CM
authors.lastname: Albertsen
authors.affiliation: University of Alberta, Department of Biological Sciences, Edmonton, T6G 2E9, Canada.
authors.forename: Andrew E
authors.initials: AE
authors.lastname: Derocher
authors.affiliation: University of Alberta, Department of Biological Sciences, Edmonton, T6G 2E9, Canada.|University of Alberta, Department of Mathematical and Statistical Sciences, Edmonton, T6G 2G1, Canada.
authors.forename: Mark A
authors.initials: MA
authors.lastname: Lewis
authors.affiliation: Macquarie University, Department of Biological Sciences, Sydney, 2109, Australia.
authors.forename: Ian D
authors.initials: ID
authors.lastname: Jonsen
authors.affiliation: Dalhousie University, Department of Mathematics and Statistics, Halifax, B3H 4R2, Canada.
authors.forename: Joanna
authors.initials: J
authors.lastname: Mills Flemming