State-space models' dirty little secrets: even simple linear Gaussian models can have estimation problems

TL;DR

This paper reveals that even simple linear Gaussian state-space models can face significant estimation issues, especially when measurement error exceeds biological variability, potentially misleading ecological inferences.

Contribution

It demonstrates the occurrence of estimation problems in simple SSMs through simulations and real data, highlighting the need for careful parameter assessment.

Findings

Estimation problems are common when measurement error is large.

Biased estimates can lead to incorrect ecological conclusions.

Potential solutions are discussed but remain challenging.

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 (\textit{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.