Discussion to “The central role of the identifying assumption in population size estimation”

Summary: In this discussion response we consider some practical implications of the authors’ consideration of the no highest order interaction model for multiple systems estimation which permits the authors to derive the explicit (albeit untestable) identifying assumption related to the unobserved (or missing) individuals. In particular, we discuss several aspects, from the standard process of model selection to potential poor predictive performance due to over- fitting and the implications of data reduction. We discuss these aspects in relation to the case study presented by the authors relating to the number of civilian casualties within the Kosovo war, and conduct further preliminary simulations to investigate these issues further. The results suggest that the no highest order interaction models considered, despite having a potentially useful theoretical result in relation to the underlying identifying assumption, may perform poorly in practice.