Comparison of Akaike information criterion and consistent Akaike information criterion for model selection and statistical inference from capture-recapture studies

Abstract

Summary We compare properties of parameter estimators under Akaike information criterion (AIC) and 'consistent' AIC (CAIC) model selection in a nested sequence of open population capture-recapture models. These models consist of product multinomials, where the cell probabilities are parameterized in terms of survival ( ) and capture ( p ) i i probabilities for each time interval i . The sequence of models is derived from 'treatment' effects that might be (1) absent, model H ; (2) only acute, model H ; or (3) acute and 0 2 p chronic, lasting several time intervals, model H . Using a 35 factorial design, 1000 3 repetitions were simulated for each of 243 cases. The true number of parameters ranged from 7 to 42, and the sample size ranged from approximately 470 to 55 000 per case. We focus on the quality of the inference about the model parameters and model structure that results from the two selection criteria. We use achieved confidence interval coverage as an integrating metric to judge what constitutes a 'properly parsimonious' model, and contrast the performance of these two model selection criteria for a wide range of models, sample sizes, parameter values and study interval lengths. AIC selection resulted in models in which the parameters were estimated with relatively little bias. However, these models exhibited asymptotic sampling variances that were somewhat too small, and achieved confidence interval coverage that was somewhat below the nominal level. In contrast, CAIC…