On comparison of mixture models for closed population capture-recapture studies.

A mixture model is a natural choice to deal with individual heterogeneity in capture-recapture studies. Pledger (2000, Biometrics 56, 434-442; 2005, Biometrics 61, 868-876) advertised the use of the two-point mixture model. Dorazio and Royle (2003, Biometrics 59, 351-364; 2005, Biometrics 61, 874-876) suggested that the beta-binomial model has advantages. The controversy is related to the nonidentifiability of the population size (Link, 2003, Biometrics 59, 1123-1130) and certain boundary problems. The total bias is decomposed into an intrinsic bias, an approximation bias, and an estimation bias. We propose to assess the approximation bias, the estimation bias, and the variance, with the intrinsic bias excluded when comparing different estimators. The boundary problems in both models and their impacts are investigated. Real epidemiological and ecological examples are analyzed.