Focused model selection for linear mixed models with an application to whale ecology

• Published in: The Annals of Applied Statistics
• Main Authors: Cunen, Céline, Walløe, Lars, Hjort, Nils Lid
• Format: Text
• Language: English
• Published: The Institute of Mathematical Statistics 2020
• Subjects: Antarctic minke whale; focused information criterion; FIC plot; linear mixed effects models; model selection; Antarctic; Antarc*; Antarctic Minke whale; minke whale
• Online Access: https://projecteuclid.org/euclid.aoas/1593449330; https://doi.org/10.1214/20-AOAS1331

A central point of disagreement, in certain long-standing discussions about a particular whaling dataset in the Scientific Committee of the International Whaling Commission, has directly involved model selection issues for linear mixed effect models. The biological question under discussion is associated with a clearly defined parameter of primary interest, a focus parameter, which makes model selection with the Focused Information Criterion (FIC) more appropriate than other selection methods. Since the existing FIC methodology has not covered the case of linear mixed effects models, this article sets up the required framework and develops the necessary formulae for the relevant FIC. Our new criterion requires the asymptotic distribution of estimators derived for a given candidate linear mixed model but with behaviour examined under a wider linear mixed model. These results, needed here to build our FIC, also have independent interest.