The Central Role of the Identifying Assumption in Population Size Estimation

TL;DR

This paper emphasizes the critical importance of the untestable identifying assumption in population size estimation using multiple-systems methods, proposing a new framework that separates data modeling from assumptions to improve transparency and sensitivity analysis.

Contribution

It introduces a novel approach that decouples data modeling from identifying assumptions in multiple-systems estimation, enhancing clarity and facilitating sensitivity analysis.

Findings

The new framework clarifies the role of assumptions in population size estimation.

Application to Kosovo war casualties demonstrates practical utility.

Software implementation supports broader adoption.

Abstract

The problem of estimating the size of a population based on a subset of individuals observed across multiple data sources is often referred to as capture-recapture or multiple-systems estimation. This is fundamentally a missing data problem, where the number of unobserved individuals represents the missing data. As with any missing data problem, multiple-systems estimation requires users to make an untestable identifying assumption in order to estimate the population size from the observed data. If an appropriate identifying assumption cannot be found for a data set, no estimate of the population size should be produced based on that data set, as models with different identifying assumptions can produce arbitrarily different population size estimates -- even with identical observed data fits. Approaches to multiple-systems estimation often do not explicitly specify identifying assumptions. This makes it difficult to decouple the specification of the model for the observed data from the identifying assumption and to provide justification for the identifying assumption. We present a re-framing of the multiple-systems estimation problem that leads to an approach which decouples the specification of the observed-data model from the identifying assumption, and discuss how common models fit into this framing. This approach takes advantage of existing software and facilitates various sensitivity analyses. We demonstrate our approach in a case study estimating the number of civilian casualties in the Kosovo war. Code used to produce this manuscript is available at https://github.com/aleshing/central-role-of-identifying-assumptions.