Assessing individual heterogeneity using model selection criteria: how many mixture components in capture-recapture models?

• Published in: Methods in Ecology and Evolution
• Main Authors: Cubaynes, Sarah, Lavergne, Christian, Gimenez, Olivier, Marboutin, Eric
• Other Authors: Centre d’Ecologie Fonctionnelle et Evolutive (CEFE), Université Paul-Valéry - Montpellier 3 (UPVM)-Institut National de la Recherche Agronomique (INRA)-Centre international d'études supérieures en sciences agronomiques (Montpellier SupAgro)-École Pratique des Hautes Études (EPHE), Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD France-Sud )-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut de Mathématiques et de Modélisation de Montpellier (I3M), Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Université Paul-Valéry - Montpellier 3 (UPVM), Oncfs, ONCFS
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2012
• Subjects: capture-recapture; individual heterogeneity; classification; information criteria; mixture models; simulation experiment; [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]; [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]; [SDE.BE]Environmental Sciences/Biodiversity and Ecology; Canis lupus
• Online Access: https://hal.science/hal-00707466; https://doi.org/10.1111/j.2041-210X.2011.00175.x

International audience 1. Capture-recapture mixture models are important tools in evolution and ecology to estimate demographic parameters and abundance while accounting for individual heterogeneity. A key step is to select the correct number of mixture components i) to provide unbiased estimates that can be used as reliable proxies of fitness or ingredients in management strategies and ii) classify individuals into biologically meaningful classes. However, there is no consensus method in the statistical literature for selecting the number of components. 2. In ecology, most studies rely on the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) that has recently gained attention in ecology. The Integrated Completed Likelihood criterion (ICL; IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22, 719) was specifically developed to favour well-separated components, but its use has never been investigated in ecology. 3. We compared the performance of AIC, BIC and ICL for selecting the number of components with regard to a) bias and accuracy of survival and detection estimates and b) success in selecting the true number of components using extensive simulations and data on wolf (Canis lupus) that were used for management through survival and abundance estimation. 4. Bias in survival and detection estimates was <0.02 for both AIC and BIC, and more than 0.09 for ICL, while mean square error was <0.05 for all criteria. As expected, bias increased as heterogeneity increased. Success rates of AIC and BIC in selecting the 'true' number of components were better than ICL (68% for AIC, 58% for BIC, and 16% for ICL). As the degree of heterogeneity increased, AIC (and BIC in a lesser extent) overestimated the number of components, while ICL often underestimated this number. For the wolf study, the 2-class model was selected by BIC and ICL, while AIC could not decide between the 2- and 3-class models. 5. We recommend using AIC or BIC when the aim is to estimate parameters. ...