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Model Selection via Focused Information Criteria for Complex Data in Ecology and Evolution

Gerda Claeskens, Céline Cunen, Nils Lid Hjort

Abstract

Datasets encountered when examining deeper issues in ecology and evolution are often complex. This calls for careful strategies for both model building, model selection, and model averaging. Our paper aims at motivating, exhibiting, and further developing focused model selection criteria. In contexts involving precisely formulated interest parameters, these versions of FIC, the focused information criterion, typically lead to better final precision for the most salient estimates, confidence intervals, etc. as compared to estimators obtained from other selection methods. Our methods are illustrated with real case studies in ecology; one related to bird species abundance and another to the decline in body condition for the Antarctic minke whale.

Model Selection via Focused Information Criteria for Complex Data in Ecology and Evolution

Abstract

Datasets encountered when examining deeper issues in ecology and evolution are often complex. This calls for careful strategies for both model building, model selection, and model averaging. Our paper aims at motivating, exhibiting, and further developing focused model selection criteria. In contexts involving precisely formulated interest parameters, these versions of FIC, the focused information criterion, typically lead to better final precision for the most salient estimates, confidence intervals, etc. as compared to estimators obtained from other selection methods. Our methods are illustrated with real case studies in ecology; one related to bird species abundance and another to the decline in body condition for the Antarctic minke whale.
Paper Structure (14 sections, 45 equations, 2 figures, 2 tables)

This paper contains 14 sections, 45 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Focused information criteria
  3. General FIC scheme
  4. AFIC, the averaged-weighted selection scheme
  5. FIC within a fixed wide model framework
  6. General regression models
  7. FIC for generalised linear models, with a fixed wide model
  8. FIC for linear mixed effects models
  9. Application: The slimming of minke whales
  10. Discussion
  11. Appendix: Derivations and technical details
  12. FIC within a local asymptotic framework
  13. FIC for generalised linear models, via local asymptotics
  14. Details and derivations for the fixed wide model FIC

Figures (2)

  • Figure 1: The two plots give values for a total of 113 Poisson regression models, related to two different focused questions. (a) FIC plot for estimating the expected number of bird species for the Chiles region. (b) AFIC plot for estimating the probability of observing over 30 species, averaging over all 14 islands. The red dot and line indicate the selected value, the blue triangle and line are for the wide model.
  • Figure 2: (a) Estimates of the yearly decline in fat-weight focus parameter, for the Antarctic minke whale population (vertical axis), along with root-FIC scores (horizontal axis), for the wide model $M_0$, marked in blue, and five additional candidate models $M_1,\ldots,M_5$. The scale is in kilograms of fat. (b) Root-FIC scores and estimates of the probability of observing a whale with more than 1.5 tonnes of fat for the wide model (marked in blue) and the five candidate models.