Connecting Correction Methods for Linkage Error in Capture-Recapture

Abstract

A commonly known problem in population size estimation using registers, is that registers do not necessarily cover the whole population. This may be because they intend to cover part of the population (e.g., students), due to administrative delay or because part of the target population is not registered by default (e.g., illegal persons). One of the methods to estimate the population size in the presence of undercount is the capture-recapture method that combines the information of two or more samples. In the context of census estimation registers are used instead of samples. However, the method assumes that perfect linkage between the registers can be achieved. It is known that this assumption is often violated. In the setting of evaluating the population coverage of a census using a post-enumeration survey, a correction for linkage error was proposed. That correction was later generalized by relaxing some of the newly introduced conditions. However, the new correction method still implicitly assumed that the two registers are of equal size. We introduce a further generalization that includes both previously mentioned correction methods and at the same time deals with registers of different sizes. Specific parameter settings will correspond to the different correction methods. We show that the parameters of each method can be chosen such that the resulting estimates all equal the traditional Petersen estimate (1896) that would theoretically be obtained under truly perfect linkage.

A General Framework for Multiple-Recapture Estimation that Incorporates Linkage Error Correction

“…In this article we derived and tested the WMR model for population size estimation corrected for linkage error. The model is derived from the D&F model and is a more general extension than the models developed by DC&T (2015DC&T ( , 2018 and De Wolf et al (2019) because it includes three or more sources and covariates, which are often necessary to correct for other sources of bias. The linkage error correction model we developed is incorporated in the more general family of log-linear regression models.…”

Linkage Free Dual System Estimation

“…Usually, the practical difficulty of achieving perfect linkage is recognised by setting some admissible level for linkage errors and accepting the consequent small bias. However, procedures to adjust the DSE to account for the linkage have been developed [8,6], although they require independent estimates of the linkage errors.…”

“…Hereafter, we refer to our approach as the linkage free dual system estimation (LFDSE). Note that in contrast to linkage error corrected DSE methods [8,6], which need estimates of the linkage error rates, the LFDSE does not require any additional data.…”

“…Thus, capture-recapture methods are closely related to the fields of record linkage [9,10,4] and estimation of the linkage error [2,18]. The linkage error adjusted population size estimation [8,6] combines together capture-recapture, record linage and estimation of the linkage error. In order to correct for the linkage errors in capture-recapture estimation, existing methods require an estimate of the linkage errors that occurred at the linkage stage.…”

Multi‐source Statistics: Basic Situations and Methods

“…De Wolf et al . () provide a synthesis and further generalisation of these extensions. These methods work under probabilistic record linkage, by correcting the observed counts for bias due to erroneous and missed links.…”