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A flexible ratio regression approach for zero-truncated capture–recapture counts

A flexible ratio regression approach for zero-truncated capture–recapture counts
A flexible ratio regression approach for zero-truncated capture–recapture counts
Capture–recapture methods are used to estimate the size of a population of interest which is only partially observed. In such studies, each member of the population carries a count of the number of times it has been identified during the observational period. In real-life applications, only positive counts are recorded, and we get a truncated at zero-observed distribution. We need to use the truncated count distribution to estimate the number of unobserved units. We consider ratios of neighboring count probabilities, estimated by ratios of observed frequencies, regardless of whether we have a zero-truncated or an untruncated distribution. Rocchetti et al. (2011) have shown that, for densities in the Katz family, these ratios can be modeled by a regression approach, and Rocchetti et al. (2014) have specialized the approach to the beta-binomial distribution. Once the regression model has been estimated, the unobserved frequency of zero counts can be simply derived. The guiding principle is that it is often easier to find an appropriate regression model than a proper model for the count distribution. However, a full analysis of the connection between the regression model and the associated count distribution has been missing. In this manuscript, we fill the gap and show that the regression model approach leads, under general conditions, to a valid count distribution; we also consider a wider class of regression models, based on fractional polynomials. The proposed approach is illustrated by analyzing various empirical applications, and by means of a simulation study.
capture-recapture, miced binomal distributions, ratio regression estimator, zero-truncated model
1-10
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Rocchetti, Irene
860f3ca0-8363-4fb4-b306-9a70e74bb663
Alfo, Marco
75ba69b7-5c36-41d2-9f9b-207b8d93f614
Holling, Heinz
88d46f56-77ca-4d0e-b035-a51aff735435
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Rocchetti, Irene
860f3ca0-8363-4fb4-b306-9a70e74bb663
Alfo, Marco
75ba69b7-5c36-41d2-9f9b-207b8d93f614
Holling, Heinz
88d46f56-77ca-4d0e-b035-a51aff735435

Böhning, Dankmar, Rocchetti, Irene, Alfo, Marco and Holling, Heinz (2016) A flexible ratio regression approach for zero-truncated capture–recapture counts. Biometrics, 1-10. (doi:10.1111/biom.12485).

Record type: Article

Abstract

Capture–recapture methods are used to estimate the size of a population of interest which is only partially observed. In such studies, each member of the population carries a count of the number of times it has been identified during the observational period. In real-life applications, only positive counts are recorded, and we get a truncated at zero-observed distribution. We need to use the truncated count distribution to estimate the number of unobserved units. We consider ratios of neighboring count probabilities, estimated by ratios of observed frequencies, regardless of whether we have a zero-truncated or an untruncated distribution. Rocchetti et al. (2011) have shown that, for densities in the Katz family, these ratios can be modeled by a regression approach, and Rocchetti et al. (2014) have specialized the approach to the beta-binomial distribution. Once the regression model has been estimated, the unobserved frequency of zero counts can be simply derived. The guiding principle is that it is often easier to find an appropriate regression model than a proper model for the count distribution. However, a full analysis of the connection between the regression model and the associated count distribution has been missing. In this manuscript, we fill the gap and show that the regression model approach leads, under general conditions, to a valid count distribution; we also consider a wider class of regression models, based on fractional polynomials. The proposed approach is illustrated by analyzing various empirical applications, and by means of a simulation study.

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More information

Accepted/In Press date: 1 December 2015
e-pub ahead of print date: 10 February 2016
Keywords: capture-recapture, miced binomal distributions, ratio regression estimator, zero-truncated model
Organisations: Statistics, Statistical Sciences Research Institute

Identifiers

Local EPrints ID: 390262
URI: https://eprints.soton.ac.uk/id/eprint/390262
PURE UUID: 1ba9fe79-2b9e-448a-a7aa-882a175d9660
ORCID for Dankmar Böhning: ORCID iD orcid.org/0000-0003-0638-7106

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Date deposited: 23 Mar 2016 08:50
Last modified: 31 Jul 2019 00:36

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