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Population Size Estimation Using Zero-Truncated Poisson Regression with Measurement Error

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Abstract

Population size estimation is an important research field in biological sciences. In practice, covariates are often measured upon capture on individuals sampled from the population. However, some biological measurements, such as body weight, may vary over time within a subject’s capture history. This can be treated as a population size estimation problem in the presence of covariate measurement error. We show that if the unobserved true covariate and measurement error are both normally distributed, then a naïve estimator without taking into account measurement error will under-estimate the population size. We then develop new methods to correct for the effect of measurement errors. In particular, we present a conditional score and a nonparametric corrected score approach that are both consistent for population size estimation. Importantly, the proposed approaches do not require the distribution assumption on the true covariates; furthermore, the latter does not require normality assumptions on the measurement errors. This is highly relevant in biological applications, as the distribution of covariates is often non-normal or unknown. We investigate finite sample performance of the new estimators via extensive simulated studies. The methods are applied to real data from a capture–recapture study. Supplementary materials accompanying this paper appear on-line.

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Acknowledgements

The authors are grateful to an associate editor and two referees for reviewing the manuscript and providing valuable comments. This work was supported by the Ministry of Science and Technology of Taiwan (Hwang), US National Institutes of Health Grants CA235122, CA239168, CA86368, and ORIP S10OD028685 (Wang).

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Authors and Affiliations

  1. Institute of Statistics, National Chung Hsing University, Taichung, Taiwan

    Wen-Han Hwang

  2. School of Mathematics and Statistics and Evolution and Ecology Research Centre, The University of New South Wales, Sydney, Australia

    Jakub Stoklosa

  3. Division of Public Health Sciences, Fred Hutchinson Cancer Research Center, P.O. Box 19024, Seattle, WA, 98109-1024, USA

    Ching-Yun Wang

Authors
  1. Wen-Han Hwang
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  2. Jakub Stoklosa
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  3. Ching-Yun Wang
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Correspondence to Ching-Yun Wang.

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Hwang, WH., Stoklosa, J. & Wang, CY. Population Size Estimation Using Zero-Truncated Poisson Regression with Measurement Error. JABES 27, 303–320 (2022). https://doi.org/10.1007/s13253-021-00481-z

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  • DOI: https://doi.org/10.1007/s13253-021-00481-z

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