Validation of ecological state space models using the Laplace approximation

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Abstract

Many statistical models in ecology follow the state space paradigm. For such models, the important step of model validation rarely receives as much attention as estimation or hypothesis testing, perhaps due to lack of available algorithms and software. Model validation is often based on a naive adaptation of Pearson residuals, i.e. the difference between observations and posterior means, even if this approach is flawed. Here, we consider validation of state space models through one-step prediction errors, and discuss principles and practicalities arising when the model has been fitted with a tool for estimation in general mixed effects models. Implementing one-step predictions in the R package Template Model Builder, we demonstrate that it is possible to perform model validation with little effort, even if the ecological model is multivariate, has non-linear dynamics, and whether observations are continuous or discrete. With both simulated data, and a real data set related to geolocation of seals, we demonstrate both the potential and the limitations of the techniques. Our results fill a need for convenient methods for validating a state space model, or alternatively, rejecting it while indicating useful directions in which the model could be improved.
Original languageEnglish
JournalEnvironmental and Ecological Statistics
Volume24
Issue number2
Pages (from-to)317-339
ISSN1352-8505
DOIs
Publication statusPublished - 2017

Keywords

  • Life Sciences
  • Ecology
  • Statistics, general
  • Mathematical and Computational Biology
  • Evolutionary Biology
  • SC3
  • Maximum likelihood estimation
  • Model validation
  • Residual analysis
  • Statistical ecology
  • State space methods
  • Time series analysis

Cite this

@article{a9be3dcca816445489754406ba9d7a1f,
title = "Validation of ecological state space models using the Laplace approximation",
abstract = "Many statistical models in ecology follow the state space paradigm. For such models, the important step of model validation rarely receives as much attention as estimation or hypothesis testing, perhaps due to lack of available algorithms and software. Model validation is often based on a naive adaptation of Pearson residuals, i.e. the difference between observations and posterior means, even if this approach is flawed. Here, we consider validation of state space models through one-step prediction errors, and discuss principles and practicalities arising when the model has been fitted with a tool for estimation in general mixed effects models. Implementing one-step predictions in the R package Template Model Builder, we demonstrate that it is possible to perform model validation with little effort, even if the ecological model is multivariate, has non-linear dynamics, and whether observations are continuous or discrete. With both simulated data, and a real data set related to geolocation of seals, we demonstrate both the potential and the limitations of the techniques. Our results fill a need for convenient methods for validating a state space model, or alternatively, rejecting it while indicating useful directions in which the model could be improved.",
keywords = "Life Sciences, Ecology, Statistics, general, Mathematical and Computational Biology, Evolutionary Biology, SC3, Maximum likelihood estimation, Model validation, Residual analysis, Statistical ecology, State space methods, Time series analysis",
author = "Thygesen, {Uffe H{\o}gsbro} and Albertsen, {Christoffer Moesgaard} and Berg, {Casper Willestofte} and Kasper Kristensen and Anders Nielsen",
year = "2017",
doi = "10.1007/s10651-017-0372-4",
language = "English",
volume = "24",
pages = "317--339",
journal = "Environmental and Ecological Statistics",
issn = "1352-8505",
publisher = "Springer New York",
number = "2",

}

TY - JOUR

T1 - Validation of ecological state space models using the Laplace approximation

AU - Thygesen, Uffe Høgsbro

AU - Albertsen, Christoffer Moesgaard

AU - Berg, Casper Willestofte

AU - Kristensen, Kasper

AU - Nielsen, Anders

PY - 2017

Y1 - 2017

N2 - Many statistical models in ecology follow the state space paradigm. For such models, the important step of model validation rarely receives as much attention as estimation or hypothesis testing, perhaps due to lack of available algorithms and software. Model validation is often based on a naive adaptation of Pearson residuals, i.e. the difference between observations and posterior means, even if this approach is flawed. Here, we consider validation of state space models through one-step prediction errors, and discuss principles and practicalities arising when the model has been fitted with a tool for estimation in general mixed effects models. Implementing one-step predictions in the R package Template Model Builder, we demonstrate that it is possible to perform model validation with little effort, even if the ecological model is multivariate, has non-linear dynamics, and whether observations are continuous or discrete. With both simulated data, and a real data set related to geolocation of seals, we demonstrate both the potential and the limitations of the techniques. Our results fill a need for convenient methods for validating a state space model, or alternatively, rejecting it while indicating useful directions in which the model could be improved.

AB - Many statistical models in ecology follow the state space paradigm. For such models, the important step of model validation rarely receives as much attention as estimation or hypothesis testing, perhaps due to lack of available algorithms and software. Model validation is often based on a naive adaptation of Pearson residuals, i.e. the difference between observations and posterior means, even if this approach is flawed. Here, we consider validation of state space models through one-step prediction errors, and discuss principles and practicalities arising when the model has been fitted with a tool for estimation in general mixed effects models. Implementing one-step predictions in the R package Template Model Builder, we demonstrate that it is possible to perform model validation with little effort, even if the ecological model is multivariate, has non-linear dynamics, and whether observations are continuous or discrete. With both simulated data, and a real data set related to geolocation of seals, we demonstrate both the potential and the limitations of the techniques. Our results fill a need for convenient methods for validating a state space model, or alternatively, rejecting it while indicating useful directions in which the model could be improved.

KW - Life Sciences

KW - Ecology

KW - Statistics, general

KW - Mathematical and Computational Biology

KW - Evolutionary Biology

KW - SC3

KW - Maximum likelihood estimation

KW - Model validation

KW - Residual analysis

KW - Statistical ecology

KW - State space methods

KW - Time series analysis

U2 - 10.1007/s10651-017-0372-4

DO - 10.1007/s10651-017-0372-4

M3 - Journal article

VL - 24

SP - 317

EP - 339

JO - Environmental and Ecological Statistics

JF - Environmental and Ecological Statistics

SN - 1352-8505

IS - 2

ER -