A regression estimator for mixed binomial capture–recapture data

Mixed binomial models are frequently used to provide estimates for the unknown size of a partially observed population when capture–recapture data are available through a known, finite, number of identification (sampling) sources. In this context, inherently major problems may be the lack of identifiability of the mixing distribution (Link, 2003) and boundary problems in ML estimation for mixed binomial models (such as the beta-binomial or finite mixture of binomials), see e.g. Dorazio and Royle (2003, 2005). To solve these problems, we introduce a novel regression estimator based on observed ratios of successive capture frequencies. Both simulations and real data examples show that the proposed estimator frequently leads to under-estimate the true population size, but with a smaller bias and a lower variability when compared to other well-known estimators.