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A generalization of Chao's estimator for covariate information

A generalization of Chao's estimator for covariate information
A generalization of Chao's estimator for covariate information
This note generalizes Chao's estimator of population size for closed capture–recapture studies if covariates are available. Chao's estimator was developed under unobserved heterogeneity in which case it represents a lower bound of the population size. If observed heterogeneity is available in form of covariates we show how this information can be used to reduce the bias of Chao's estimator. The key element in this development is the understanding and placement of Chao's estimator in a truncated Poisson likelihood. It is shown that a truncated Poisson likelihood (with log-link) with all counts truncated besides ones and twos is equivalent to a binomial likelihood (with logit-link). This enables the development of a generalized Chao estimator as the estimated, expected value of the frequency of zero counts under a truncated (all counts truncated except ones and twos) Poisson regression model. If the regression model accounts for the heterogeneity entirely, the generalized Chao estimator is asymptotically unbiased. A simulation study illustrates the potential in gain of bias reduction. Comparisons of the generalized Chao estimator with the homogeneous zero-truncated Poisson regression approach are supplied as well. The method is applied to a surveillance study on the completeness of farm submissions in Great Britain.
1033-1042
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Vidal-Diez, Alberto
ad93ccb8-1ace-434b-96c9-6959df389490
Lerdsuwansri, Rattana
56aa3b31-c2d9-412d-9769-0be3831a9334
Vivatwongkasem, Chukiat
17d01d7c-1118-4222-a0af-281bd7753828
Arnold, Mark
d718648f-7432-4927-b7e8-f40e36d24580
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Vidal-Diez, Alberto
ad93ccb8-1ace-434b-96c9-6959df389490
Lerdsuwansri, Rattana
56aa3b31-c2d9-412d-9769-0be3831a9334
Vivatwongkasem, Chukiat
17d01d7c-1118-4222-a0af-281bd7753828
Arnold, Mark
d718648f-7432-4927-b7e8-f40e36d24580

Böhning, Dankmar, Vidal-Diez, Alberto, Lerdsuwansri, Rattana, Vivatwongkasem, Chukiat and Arnold, Mark (2013) A generalization of Chao's estimator for covariate information. Biometrics, 69 (4), 1033-1042. (doi:10.1111/biom.12082).

Record type: Article

Abstract

This note generalizes Chao's estimator of population size for closed capture–recapture studies if covariates are available. Chao's estimator was developed under unobserved heterogeneity in which case it represents a lower bound of the population size. If observed heterogeneity is available in form of covariates we show how this information can be used to reduce the bias of Chao's estimator. The key element in this development is the understanding and placement of Chao's estimator in a truncated Poisson likelihood. It is shown that a truncated Poisson likelihood (with log-link) with all counts truncated besides ones and twos is equivalent to a binomial likelihood (with logit-link). This enables the development of a generalized Chao estimator as the estimated, expected value of the frequency of zero counts under a truncated (all counts truncated except ones and twos) Poisson regression model. If the regression model accounts for the heterogeneity entirely, the generalized Chao estimator is asymptotically unbiased. A simulation study illustrates the potential in gain of bias reduction. Comparisons of the generalized Chao estimator with the homogeneous zero-truncated Poisson regression approach are supplied as well. The method is applied to a surveillance study on the completeness of farm submissions in Great Britain.

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More information

Published date: December 2013
Organisations: Statistics, Southampton Law School, Statistical Sciences Research Institute, Primary Care & Population Sciences

Identifiers

Local EPrints ID: 361660
URI: https://eprints.soton.ac.uk/id/eprint/361660
PURE UUID: 7c561a89-8969-4368-a981-e8ef1aadcc2e
ORCID for Dankmar Böhning: ORCID iD orcid.org/0000-0003-0638-7106

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Date deposited: 29 Jan 2014 16:52
Last modified: 20 Jul 2019 00:44

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