Leveraging Relational Evidence: Population Size Estimation on Tree-Structured Data with the Weighted Multiplier Method

TL;DR

This paper introduces an extended multiplier method for estimating hidden population sizes using tree-structured data, comparing its performance with Bayesian models on simulated and real data to enhance accessible population estimation techniques.

Contribution

It develops a novel extension of the multiplier method for tree-structured data, enabling synthesis of multiple subpopulations for population size estimation.

Findings

The extended multiplier method provides accurate estimates comparable to Bayesian models.

The method is robust and feasible across different data scenarios.

Key data sources significantly influence estimation accuracy.

Abstract

Populations of interest are often hidden from data for a variety of reasons, though their magnitude remains important in determining resource allocation and appropriate policy. One popular approach to population size estimation, the multiplier method, is a back-calculation tool requiring only a marginal subpopulation size and an estimate of the proportion belonging to this subgroup. Another approach is to use Bayesian methods, which are inherently well-suited to incorporating multiple data sources. However, both methods have their drawbacks. A framework for applying the multiplier method which combines information from several known subpopulations has not yet been established; Bayesian models, though able to incorporate complex dependencies and various data sources, can be difficult for researchers in less technical fields to design and implement. Increasing data collection and linkage across diverse fields suggests accessible methods of estimating population size with synthesized data are needed. We propose an extension to the well-known multiplier method which is applicable to tree-structured data, where multiple subpopulations and corresponding proportions combine to generate a population size estimate via the minimum variance estimator. The methodology and resulting estimates are compared with those from a Bayesian hierarchical model, for both simulated and real world data. Subsequent analysis elucidates which data are key to estimation in each method, and examines robustness and feasibility of this new methodology.