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.
Highlights
While the SSM framework is flexible, much of its theoretical foundation is based on simple linear Gaussian SSMs
While our main estimation approach consists of maximizing the likelihood numerically through Template Model Builder (TMB)[22], we show that these problems persist across a wide range of platforms and statistical frameworks, including when the parameters and states are estimated via Bayesian methods
By extending the range of measurement error to process stochasticity ratios beyond those explored by Dennis et al.[16] and Knape[19], we demonstrate that relatively high measurement error can have dramatic effects on process parameter and state estimates, even when the measurement error is known
Summary
While the SSM framework is flexible, much of its theoretical foundation is based on simple linear Gaussian SSMs (sometimes referred as normal dynamic linear models, see Newman et al.[4]). An example of a simple univariate linear Gaussian SSM is the one we will use to demonstrate parameter-estimability problems: Measurement eq yt = xt + εt , εt ~ N(0, σε2), where t ≥ 1, σε > 0. The existence of parameter estimation problems have been largely overlooked in the movement literature, and by those that use complex Bayesian SSMs. As SMMs are becoming the favoured framework for many ecological analyses[1,2,3,4], and are gaining popularity in other fields (e.g.21), it is timely to warn researchers of their weaknesses. We use simulations to show that simple SSMs can have severe parameter-estimability problems that in turn affect state estimates These problems are more frequent when the measurement error is large, the very condition under which SSMs are needed, and can persist even when we incorporate measurement error information. We discuss techniques to diagnose and, when possible, alleviate estimability problems
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