A regression estimator for mixed binomial capture–recapture data

• We extend the approach by Rocchetti et al. (2011) to situations where the number of sampling occasions is known and fixed.
• We propose an estimator based on a novel weighted regression model for (log) ratios of successive capture frequencies.
• The proposed estimator prevents identifiability and boundary problems which are quite standard in ML estimation.
• The observed frequency data are used to provide estimates for the number of unregistered individuals.
• The results from simulation and three benchmark datasets are encouraging.

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 and Dorazio and Royle, 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.