Behavioral Ecology and Sociobiology

, Volume 65, Issue 1, pp 103–116

Model averaging, missing data and multiple imputation: a case study for behavioural ecology

Original Paper

DOI: 10.1007/s00265-010-1044-7

Cite this article as:
Nakagawa, S. & Freckleton, R.P. Behav Ecol Sociobiol (2011) 65: 103. doi:10.1007/s00265-010-1044-7

Abstract

Model averaging, specifically information theoretic approaches based on Akaike’s information criterion (IT-AIC approaches), has had a major influence on statistical practices in the field of ecology and evolution. However, a neglected issue is that in common with most other model fitting approaches, IT-AIC methods are sensitive to the presence of missing observations. The commonest way of handling missing data is the complete-case analysis (the complete deletion from the dataset of cases containing any missing values). It is well-known that this results in reduced estimation precision (or reduced statistical power), biased parameter estimates; however, the implications for model selection have not been explored. Here we employ an example from behavioural ecology to illustrate how missing data can affect the conclusions drawn from model selection or based on hypothesis testing. We show how missing observations can be recovered to give accurate estimates for IT-related indices (e.g. AIC and Akaike weight) as well as parameters (and their standard errors) by utilizing ‘multiple imputation’. We use this paper to illustrate key concepts from missing data theory and as a basis for discussing available methods for handling missing data. The example is intended to serve as a practically oriented case study for behavioural ecologists deciding on how to handle missing data in their own datasets and also as a first attempt to consider the problems of conducting model selection and averaging in the presence of missing observations.

Keywords

Data augmentation Data deletion Estimation bias The rate of missing information Expectation maximization QAIC EPP MCMC House sparrows 

Supplementary material

265_2010_1044_MOESM1_ESM.doc (254 kb)
S1(DOC 253 kb)
265_2010_1044_MOESM2_ESM.zip (27 kb)
S2(ZIP 26.9 kb)

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of ZoologyUniversity of OtagoDunedinNew Zealand
  2. 2.Department of Animal and Plant SciencesUniversity of SheffieldSheffieldUK