Abstract
Multiple systems estimation strategies have recently been applied to quantify hard-to-reach populations, particularly when estimating the number of victims of human trafficking and modern slavery. In such contexts, it is not uncommon to see sparse or even no overlap between some of the lists on which the estimates are based. These create difficulties in model fitting and selection, and we develop inference procedures to address these challenges. The approach is based on Poisson log-linear regression modeling. Issues investigated in detail include taking proper account of data sparsity in the estimation procedure, as well as the existence and identifiability of maximum likelihood estimates. A stepwise method for choosing the most suitable parameters is developed, together with a bootstrap approach to finding confidence intervals for the total population size. We apply the strategy to two empirical datasets of trafficking in US regions, and find that the approach results in stable, reasonable estimates. An accompanying R software implementation has been made publicly available. Supplementary materials for this article are available online.
Highlights
A generalization of the markrecapture approach (Petersen 1896; Schwarz and Seber 1999), is a class of methods that can be used to estimate the size of hard-to-reach populations in many contexts, including, in recent years, those comprising victims of human trafficking or modern slavery
In the administrative or law enforcement context, multiple systems estimation aims to read across from lists of observed or identified individuals from a study population to estimate the total population of interest
The reason for using this model as a basis for a simulation is that it is reasonable to suppose that it will display features likely to be seen when using the methods in the human trafficking context
Summary
A generalization of the markrecapture approach (Petersen 1896; Schwarz and Seber 1999), is a class of methods that can be used to estimate the size of hard-to-reach populations in many contexts, including, in recent years, those comprising victims of human trafficking or modern slavery. In the administrative or law enforcement context, multiple systems estimation aims to read across from lists of observed or identified individuals from a study population to estimate the total population of interest (see, e.g., Bales, Hesketh, and Silverman 2015; Cruyff, van Dijk, and van der Heijden 2017). Because the method estimates the number of victims including those that are not directly observed or detected, it plays an especially important role in making policy to help combat human trafficking and modern slavery. As set out in Bales, Hesketh, and Silverman (2015), a multiple systems estimate constructed from data collated by a government agency was a key component of the strategy (Home Office 2014) leading to the UK Modern Slavery Act 2015
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