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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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    1. Richard Huggins & Wen‐Han Hwang, 2011. "A Review of the Use of Conditional Likelihood in Capture‐Recapture Experiments," International Statistical Review, International Statistical Institute, vol. 79(3), pages 385-400, December.
    2. 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.
    3. Kenneth Pollock, 2002. "The use of auxiliary variables in capture-recapture modelling: An overview," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(1-4), pages 85-102.
    4. C. Y. Wang & Hua Yun Chen, 2001. "Augmented Inverse Probability Weighted Estimator for Cox Missing Covariate Regression," Biometrics, The International Biometric Society, vol. 57(2), pages 414-419, June.
    5. E. A. Catchpole & B. J. T. Morgan & G. Tavecchia, 2008. "A new method for analysing discrete life history data with missing covariate values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 445-460, April.
    6. Jun Li & Yao Yu, 2015. "A Nonparametric Test of Missing Completely at Random for Incomplete Multivariate Data," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 707-726, September.
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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. 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.
    4. 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.
    5. 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.
    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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