Silverman 2020 - Data Sets for Multiple Systems Estimation
Summary
Four real multi-list data sets drive the whole comparison: UK 2013 potential trafficking victims (6 lists, 2744 cases), Netherlands 2010-2015 (6 lists, 8234 cases), Greater New Orleans 2016 (8 lists, 185 cases) and Kosovo 1999 killings (4 lists, 4400 cases). The modern-slavery tables are sparse with many non-overlapping list pairs; Kosovo is dense with strong dependence.
Overview
Each data set is a table of counts for each observed combination of lists (an incomplete contingency table without the all-zero cell). Combinations with zero observed count are left out of the printed tables but kept in the analysis. Cell patterns are in the paper (Tables 1-4) and for Kosovo in the R package LCMCR.
Main Content
UK 2013 (Table 1; Bales et al. 2015)
Lists: LA (local authorities), NG (non-government organisations), PF (police forces), GO (government organisations, e.g. Border Force, GLAA), GP (general public), NCA (National Crime Agency). 26 observed list combinations. Single-list-only counts: LA 54, NG 463, PF 907, GO 695, GP 316, NCA 57. Overlaps are small: e.g. LA and NG only: 15; one case on LA, NG, PF and GO only. Total observed: 2744 (6 or 5 lists), 2428 (4 lists).
Derived UK variants
Five-list: PF and NCA merged (NCA is not strictly police but has similar powers). Four-list: also omit GP (cases on this list may not be specified enough to match reliably). The variants test robustness of any method to merging or dropping lists.
Netherlands 2010-2015 (Table 2; van Dijk et al. 2017; Cruyff et al. 2017)
Lists: P (National Police), K (Border Police), I (Inspectorate SZW), R (regional coordinators), O (residential treatment centres and shelters), Z (others). Single-list-only counts: I 352, K 1299, O 403, P 4466, R 650, Z 632. Total observed 8234. Five-list variant merges the two smallest lists (I and O).
Greater New Orleans 2016 (Table 3; Bales et al. 2019)
Eight agencies, 185 individuals; lists labelled A to H for confidentiality (no other information was available). Counts are tiny (largest single list 70); none of the overlap sets contains more than two cases. Five-list variant merges the four lists with smallest counts into one list “BEFG”.
Kosovo, 20 March-22 June 1999 (Table 4; Ball et al. 2002, via LCMCR)
Four lists: EXH (exhumations), ABA (American Bar Association CEELI), OSCE, HRW. All 15 observable combinations have non-zero counts; 4400 known victims; large counts in higher-order overlaps. “This is in the nature of the particular application and is highly unlikely to occur in any modern slavery data set.”
Table 4 reproduced (cell patterns decoded from the column positions of the PDF)
EXH ABA OSCE HRW Count 1 0 0 0 1131 0 1 0 0 845 0 0 1 0 936 0 0 0 1 306 1 1 0 0 177 1 0 1 0 228 1 0 0 1 106 0 1 1 0 217 0 1 0 1 31 0 0 1 1 123 1 1 1 0 181 1 1 0 1 18 1 0 1 1 42 0 1 1 1 32 1 1 1 1 27 The counts sum to 4400 (check: singles 3218, pairs 882, triples 273, quadruple 27).
| Data set | Lists | Observed cases | Character |
|---|---|---|---|
| UK 2013 | 6 (5, 4) | 2744 (2744, 2428) | sparse, non-overlapping pairs |
| Netherlands 2010-15 | 6 (5) | 8234 | sparse, small lists |
| New Orleans 2016 | 8 (5) | 185 | very sparse, overlaps |
| Kosovo 1999 | 4 | 4400 | dense, strong dependence |
Examples
Why zero overlaps matter
UK: no case is on both LA and GP, and none on both LA and NCA. New Orleans five-list: 3 of 10 pair overlaps are empty; in the eight-list data 18 of 28 pairwise overlaps are empty. Maximum-likelihood interaction parameters for empty overlaps run to (Silverman 2020 - Existence, Identifiability and Empty Overlaps).
Connections
- The PyMC E109 example uses Kosovo (via LCMCR) and UK (via SparseMSE) data.
- Modelling approach: Silverman 2020 - Poisson Log-Linear Model for Multiple Lists.