Population Size Estimation Using Multiple Incomplete Lists with Overcoverage

Abstract

The quantity and quality of administrative information available to National Statistical Institutes have been constantly increasing over the past several years. However, different sources of administrative data are not expected to each have the same population coverage, so that estimating the true population size from the collective set of data poses several methodological challenges that set the problem apart from a classical capture-recapture setting. In this article, we consider two specific aspects of this problem: (1) misclassification of the units, leading to lists with both overcoverage and undercoverage; and (2) lists focusing on a specific subpopulation, leaving a proportion of the population with null probability of being captured. We propose an approach to this problem that employs a class of capturerecapture methods based on Latent Class models. We assess the proposed approach via a simulation study, then apply the method to five sources of empirical data to estimate the number of active local units of Italian enterprises in 2011.

Multi‐source Statistics: Basic Situations and Methods

“…Assumption (e) is violated in the presence of overcoverage in one or more data sets. Di Cecco et al () have developed an extended capture–recapture method that can account for overcoverage as well as data sets that contain certain specific subpopulations only (so that not all units in the target population have a positive probability of being observed in each of the data sets, and assumption (c) is violated). This approach is based on an LC model, with erroneous captures indicated by a latent variable.…”

“…For instance, a population register may suffer from overcoverage due to delayed de‐registration of inactive units. In practice, overcoverage and duplicated records are often handled by clerical review or by applying deterministic rules (Di Cecco et al , ). Assessing the amount of overcoverage and its effects on estimates may be difficult in some applications, in particular, when overcoverage is caused by false positive linkage errors (Bakker, ).…”

Latent Class Analysis for Estimating an Unknown Population Size – with Application to Censuses

“…Hagenaars (1993) suggests either including an additional latent variable or alternatively adding association terms between manifest variables. Within the capture-recapture literature, these latent variable models have been used in Biggeri et al (1999) and Stanghellini and Van der Heijden (2004), and more relevant to the current article, Gerritse et al (2015) and Di Cecco et al (2018) have advocated a similar approach in the use of multiple administrative lists for population estimation.…”

Multiple System Estimation using Covariates having Missing Values and Measurement Error: Estimating the Size of the Māori Population in New Zealand

“…This would give a final estimate of 768,479, corresponding to an estimated probability of 768,479/4,422,962 = 0.174. A statistical approach to measurement error is to make use of a latent class model (McCutcheon, 1987), a technique that has also been applied to evaluate census-related multiple system estimation by Biemer et al (2001), see for comparable work Biggeri et al (1999), di Cecco et al (2018). See also Boeschoten et al (2019), for a comparison of the latent class model with the ad hoc approach described in the preceding paragraph.…”

“…We also show under what conditions this is true in general. An alternative modelling approach is presented bySutherland et al (2007), and related work is found in diCecco et al (2018), van der Heijden and Smith (2020), and diCecco et al (2020).…”