# Multiple Systems Estimation for Sparse Capture Data: Inferential Challenges when there are Non-Overlapping Lists

## TL;DR

This paper develops inference methods for multiple systems estimation with sparse or non-overlapping lists, addressing challenges in model fitting and providing stable estimates for hard-to-reach populations.

## Contribution

It introduces a Poisson log-linear regression approach with a stepwise parameter selection and bootstrap confidence intervals for sparse data with non-overlapping lists.

## Key findings

- Stable estimates for trafficking populations in US regions
- Effective handling of data sparsity and non-overlap issues
- Public R software implementation available

## 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 data sets 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.