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Estimation in closed capture–recapture models when covariates are missing at random

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  • Shen‐Ming Lee
  • Wen‐Han Hwang
  • Jean de Dieu Tapsoba

Abstract

Individual covariates are commonly used in capture–recapture models as they can provide important information for population size estimation. However, in practice, one or more covariates may be missing at random for some individuals, which can lead to unreliable inference if records with missing data are treated as missing completely at random. We show that, in general, such a naive complete‐case analysis in closed capture–recapture models with some covariates missing at random underestimates the population size. We develop methods for estimating regression parameters and population size using regression calibration, inverse probability weighting, and multiple imputation without any distributional assumptions about the covariates. We show that the inverse probability weighting and multiple imputation approaches are asymptotically equivalent. We present a simulation study to investigate the effects of missing covariates and to evaluate the performance of the proposed methods. We also illustrate an analysis using data on the bird species yellow‐bellied prinia collected in Hong Kong.

Suggested Citation

  • Shen‐Ming Lee & Wen‐Han Hwang & Jean de Dieu Tapsoba, 2016. "Estimation in closed capture–recapture models when covariates are missing at random," Biometrics, The International Biometric Society, vol. 72(4), pages 1294-1304, December.
    • Handle: RePEc:bla:biomet:v:72:y:2016:i:4:p:1294-1304
    DOI: 10.1111/biom.12498
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    References listed on IDEAS

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    5. Simon J. Bonner & Byron J. T. Morgan & Ruth King, 2010. "Continuous Covariates in Mark-Recapture-Recovery Analysis: A Comparison of Methods," Biometrics, The International Biometric Society, vol. 66(4), pages 1256-1265, December.
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    Cited by:

    1. Liu, Yang & Zhang, Xiuzhen & Li, Mengke & Liu, Guanfu & Zhu, Lin, 2019. "Abundance estimation based on optimal estimating function with missing covariates in capture–recapture studies," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 15-20.
    2. Shen-Ming Lee & T. Martin Lukusa & Chin-Shang Li, 2020. "Estimation of a zero-inflated Poisson regression model with missing covariates via nonparametric multiple imputation methods," Computational Statistics, Springer, vol. 35(2), pages 725-754, June.
    3. Kim-Hung Pho & Tuan-Kiet Tran & Thi Diem-Chinh Ho & Wing-Keung Wong, 2019. "Optimal Solution Techniques in Decision Sciences A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(1), pages 114-161, March.
    4. Yang Liu & Yukun Liu & Pengfei Li & Lin Zhu, 2021. "Maximum likelihood abundance estimation from capture‐recapture data when covariates are missing at random," Biometrics, The International Biometric Society, vol. 77(3), pages 1050-1060, September.
    5. Buu-Chau Truong & Nguyen Van Thuan & Nguyen Huu Hau & Michael McAleer, 2019. "Applications of the Newton-Raphson Method in Decision Sciences and Education," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(4), pages 52-80, December.
    6. Shen-Ming Lee & Truong-Nhat Le & Phuoc-Loc Tran & Chin-Shang Li, 2023. "Estimation of logistic regression with covariates missing separately or simultaneously via multiple imputation methods," Computational Statistics, Springer, vol. 38(2), pages 899-934, June.

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