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.