Model fitting in Multiple Systems Analysis for the quantification of Modern Slavery: Classical and Bayesian approaches
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Multiple Systems Estimation is a key estimation approach for hidden populations such as the number of victims of Modern Slavery. The UK Government estimate of 10,000 to 13,000 victims was obtained by a multiple systems estimate based on six lists. A stepwise method was used to choose the terms in the model. Further investigation shows that a small proportion of models give rather different answers, and that other model fitting approaches may choose one of these. Three data sets collected in the Modern Slavery context, together with a data set about the death toll in the Kosovo conflict, are used to investigate the stability and robustness of various Multiple Systems Estimate approaches. The crucial aspect is the way that interactions between lists are modelled, because these can substantially affect the results. Model selection and Bayesian approaches are considered in detail, in particular to assess their stability and robustness when applied to real data sets in the Modern Slavery context. A new Markov Chain Monte Carlo Bayesian approach is developed; overall, this gives robust and stable results at least for the examples considered. The software and datasets are freely and publicly available to facilitate wider implementation and further research.
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