Multiple Systems Estimation for Sparse Capture Data: Inferential Challenges When There Are Nonoverlapping Lists

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.

How many trafficked people are there in Greater New Orleans? Lessons in measurement

“…If the β ij parameter for such a pair of lists is included in the model, then its maximum likelihood estimator is −∞. Motivated by the New Orleans area data, Chan, Silverman, and Vincent (2019a) have developed theory and software to account for this aspect. It includes consideration of its impact on the choice of which interaction terms β ij are included in the model, whether or not any cases are actually observed in the overlap between lists i and j.…”

“…It is reassuring that the five-list and eight-list analyses give such similar results. Further details are given in Chan et al (2019a), which allows the analysis we have presented to be fully reproduced.…”

Misunderstandings of Multiple Systems Estimation: A Response to “On the Unreliability of Multiple Systems Estimation for Estimating the Number of Potential Victims of Modern Slavery in the UK” by Whitehead, Jackson, Balch, and Francis (2019)

“…We have collaborated with our American and Australian peers, and have also been diligent about transparently publishing efforts, findings, and challenges (Cruyff et al, 2017), as well as improvements to the application of the MSE method. Chan et al (2019Chan et al ( , 2020 published findings and an R (R is an open source statistical programming software and packages are downloadable programs that allow you to run specific analyses) package to address limitations of MSE applications based on sparse overlap counts and which consequently give rise to critical warnings in commonly used software programs. It is from this variety of applications of MSE over the past five years that we provide our collective thoughts on the inappropriate and incorrect conclusions of Whitehead et al (2019).…”

“…Whitehead et al opt to address non-overlapping lists via artificially inflating the corresponding counts by either 0.5 or 0.1. As noted earlier, recent developments show that the methods presented in Chan et al (2020Chan et al ( , 2019 are capable of preserving the original observations and provide correct inference (which may differ significantly from those based on current, limited methods). 7 Whitehead et al then base their simulation studies on applying the stepwise method outlined in Bales et al, along with the full two-and three-way interaction models, to data sets generated from such full models fitted to the original data set.…”

Parameter Redundancy and the Existence of Maximum Likelihood Estimates in Log-Linear Models

“…However, those algorithms are inefficient for a model with a large number of variables (Wang et al, 2016). The R packages eMLEloglin and SparseMSE utilize the EMLE approach to fit log-linear models (Chan et al, 2019;Friedlander, 2016).…”