A comparison of marginal and conditional models for capture-recapture data with application to human rights...

Human rights data presents challenges for capture-recapture methodology. Lists of violent acts provided by many different groups create large, sparse tables of data for which saturated models are difficult to fit and for which simple models may be misspecified. We analyze data on killings and disappearances in Casanare, Colombia during years 1998 to 2007. Our estimates differ whether we choose to model marginal reporting probabilities and odds ratios, versus modeling the full reporting pattern in a conditional (log-linear) model. With 2629 observed killings, a marginal model we consider estimates over 9000 killings, while conditional models we consider estimate 6000-7000 killings. The latter agree with previous estimates, also from a conditional model. We see a twofold difference between the high sample coverage estimate of over 10,000 killings and low sample coverage lower bound estimate of 5200 killings. We use a simulation study to compare marginal and conditional models with at most two-way interactions and sample coverage estimators. The simulation results together with model selection criteria lead us to believe the previous estimates of total killings in Casanare may have been biased downward, suggesting that the violence was worse than previously thought. Model specification is an important consideration when interpreting population estimates from capture recapture analysis and the Casanare data is a protypical example of how that manifests.