A general framework for multiple-recapture estimation that incorporates linkage error correction

The size of a partly observed population is often estimated with the capture – recapture (for two sources) or multiple – recapture (for multiple sources) estimation method. An important assumption of these modelsis that recordsin different sources can be identified such that it is known whether these records belong to the same unit or not, i.e. records can be perfectly linked between sources. This assumption of perfect linkage is of particular relevance if identification is not obtained by some perfect identifier (like a tag or id-code) but by indirect identifiers (like name and address or animal’s skin patterns). In that case the perfect linkage assumption is often violated, which in general leads to biased population size estimates. A solution to this problem was provided by Ding and Fienberg (1994), Di Consiglio and Tuoto (2015) and De Wolf et al. (2018). These authors show how to use linkage probabilities to correct the capture - recapture estimator for linkage errors. Recently, Di Consiglio and Tuoto (2018) extended their method to three sources. In this paper we provide a general framework that allows us to extend this work further in two ways. First, we extend this work further to any number of sources. Second, our framework allows to incorporate covariates in a better way. We do this by generalising the standard log - linear modelling approach used in multiple - recapture estimation such that it incorporates linkage error correction. We show how the method performs in a simulation study with data that resemble real data.