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

• Published in: Journal of agricultural, biological, and environmental statistics Vol. 27; no. 2; pp. 303 - 320
• Main Authors: Hwang, Wen-Han, Stoklosa, Jakub, Wang, Ching-Yun
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2022; Springer; Springer Nature B.V
• Subjects: Agriculture; Biostatistics; Body weight; Capture-recapture studies; Health Sciences; mark-recapture studies; Mathematics and Statistics; Medicine; Monitoring/Environmental Analysis; Population; Population number; population size; Statistics; Statistics for Life Sciences; Capture–recapture data; Corrected score; Weighted partial likelihood; Errors-in-variables
• ISSN: 1085-7117; 1537-2693
• DOI: 10.1007/s13253-021-00481-z

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.