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A covariate adjustment for zero-truncated approaches to estimating the size of hidden and elusive populations

A covariate adjustment for zero-truncated approaches to estimating the size of hidden and elusive populations
A covariate adjustment for zero-truncated approaches to estimating the size of hidden and elusive populations
In this paper we consider the estimation of population size from one-source capture–recapture data, that is, a list in which individuals can potentially be found repeatedly and where the question is how many individuals are missed by the list. As a typical example, we provide data from a drug user study in Bangkok from 2001 where the list consists of drug users who repeatedly contact treatment institutions. Drug users with 1, 2, 3, … contacts occur, but drug users with zero contacts are not present, requiring the size of this group to be estimated. Statistically, these data can be considered as stemming from a zero-truncated count distribution. We revisit an estimator for the population size suggested by Zelterman that is known to be robust under potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a locally truncated Poisson likelihood which is equivalent to a binomial likelihood. This result allows the extension of the Zelterman estimator by means of logistic regression to include observed heterogeneity in the form of covariates. We also review an estimator proposed by Chao and explain why we are not able to obtain similar results for this estimator. The Zelterman estimator is applied in two case studies, the first a drug user study from Bangkok, the second an illegal immigrant study in the Netherlands. Our results suggest the new estimator should be used, in particular, if substantial unobserved heterogeneity is present.
population size estimation, capture–recapture, estimation under model misspecification, truncated poisson and binomial likelihood, elusive population
1932-6157
595-610
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
van der Heijden, Peter
baff06a5-f58c-480c-9b14-da34d305a413
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
van der Heijden, Peter
baff06a5-f58c-480c-9b14-da34d305a413

Böhning, Dankmar and van der Heijden, Peter (2009) A covariate adjustment for zero-truncated approaches to estimating the size of hidden and elusive populations. The Annals of Applied Statistics, 3 (2), 595-610. (doi:10.1214/08-AOAS214).

Record type: Article

Abstract

In this paper we consider the estimation of population size from one-source capture–recapture data, that is, a list in which individuals can potentially be found repeatedly and where the question is how many individuals are missed by the list. As a typical example, we provide data from a drug user study in Bangkok from 2001 where the list consists of drug users who repeatedly contact treatment institutions. Drug users with 1, 2, 3, … contacts occur, but drug users with zero contacts are not present, requiring the size of this group to be estimated. Statistically, these data can be considered as stemming from a zero-truncated count distribution. We revisit an estimator for the population size suggested by Zelterman that is known to be robust under potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a locally truncated Poisson likelihood which is equivalent to a binomial likelihood. This result allows the extension of the Zelterman estimator by means of logistic regression to include observed heterogeneity in the form of covariates. We also review an estimator proposed by Chao and explain why we are not able to obtain similar results for this estimator. The Zelterman estimator is applied in two case studies, the first a drug user study from Bangkok, the second an illegal immigrant study in the Netherlands. Our results suggest the new estimator should be used, in particular, if substantial unobserved heterogeneity is present.

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More information

Published date: June 2009
Keywords: population size estimation, capture–recapture, estimation under model misspecification, truncated poisson and binomial likelihood, elusive population
Organisations: Statistics, Statistical Sciences Research Institute

Identifiers

Local EPrints ID: 210457
URI: http://eprints.soton.ac.uk/id/eprint/210457
ISSN: 1932-6157
PURE UUID: c1816941-93c4-4d96-8d39-deac45c1b497
ORCID for Dankmar Böhning: ORCID iD orcid.org/0000-0003-0638-7106

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Date deposited: 09 Feb 2012 11:21
Last modified: 15 Mar 2024 03:39

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Author: Peter van der Heijden

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