Information-theoretic model selection and model averaging for closed-population capture-recapture studies

Specification of an appropriate model is critical to valid statistical inference. Given the “true model” for the data is unknown, the goal of model selection is to select a plausible approximating model that balances model bias and sampling variance. Model selection based on information criteria such as AIC or its variant AIC_c, or criteria like CAIC, has proven useful in a variety of contexts including the analysis of open-population capture-recapture data. These criteria have not been intensively evaluated for closed-population capture-recapture models, which are integer parameter models used to estimate population size (N), and there is concern that they will not perform well. To address this concern, we evaluated AIC, AIC_c, and CAIC model selection for closed-population capture-recapture models by empirically assessing the quality of inference for the population size parameter N. We found that AIC-, AIC_c-, and CAIC-selected models had smaller relative mean squared errors than randomly selected models, but that confidence interval coverage on N was poor unless unconditional variance estimates (which incorporate model uncertainty) were used to compute confidence intervals. Overall, AIC and AIC_c outperformed CAIC, and are preferred to CAIC for selection among the closed-population capture-recapture models we investigated. A model averaging approach to estimation, using AIC, AIC_c, or CAIC to estimate weights, was also investigated and proved superior to estimation using AIC-, AIC_c-, or CAIC-selected models. Our results suggested that, for model averaging, AIC or AIC_c should be favored over CAIC for estimating weights.