Abstract
Logistic models for capture probabilities that depend on covariates are effective if the covariates can be measured exactly. If there is measurement error so that a surrogate for the covariate is observed rather than the covariate itself, simple adjustments may be made if the parameters of joint distribution of the covariate and the surrogate are known. Here we consider the case when a surrogate is observed whenever an individual is captured and the parameters must also be estimated from the data. An estimating equation regression calibration approach is developed and it is illustrated on a real dataset where the surrogate is an individual bird’s wing-length, which varies from occasion to occasion.
This article has supplementary material online.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006), Measurement Error in Nonlinear Models: A Modern Perspective (2nd ed.), London: Chapman & Hall.
Chen, S. X. (1998), “Measurement Errors in Line Transect Surveys,” Biometrics, 54, 899–908.
Chen, S. X., and Cowling, A. (2001), “Measurement Errors in Line Transect Surveys Where Detectability Varies With Distance and Size,” Biometrics, 57, 732–742.
Gould, W. R., Stefanski, L. A., and Pollock, K. H. (1999), “Use of Simulation-Extrapolation Estimation in Catch-Effort Analysis,” Canadian Journal of Fisheries and Aquatic Sciences, 56, 1234–1240.
Huggins, R. M. (1989), “On the Statistical Analysis of Capture Experiments,” Biometrika, 76, 133–140.
Huggins, R. M., and Hwang, W.-H. (2007), “Nonparametric Estimation of Population Size From Capture-Recapture Data When the Capture Probability Depends on a Covariate,” Applied Statistics, 56, 429–443.
Hwang, W.-H., and Huang, S. Y. H. (2003), “Estimation in Capture-Recapture Models When Coavriates Are Subject to Measurement Errors,” Biometrics, 59, 1113–1122.
Hwang, W.-H., Huang, S. Y. H., and Wang, C. Y. (2007), “Effects of Measurement Error and Conditional Score Estimation in Capture-Recapture Models,” Statistics Sinica, 17, 301–316.
Johnson, N. L., Kotz, S., and Balakrishnan, N. (1995), Continuous Univariate Distributions, Vol. 2 (2nd ed.), New York: Wiley.
Marques, T. A. (2004), “Predicting and Correcting Bias Caused by Measurement Error in Line Transect Sampling Using Multiplicative Error Models,” Biometrics, 60, 757–763.
Stefanski, L. A. (1985), “The Effects of Measurement Error in Parameter Estimation,” Biometrika, 72, 583–592.
Xi, L., Watson, R., Wang, J. P., and Yip, P. S. F. (2009), “Estimation in Capture-Recapture Models When Covariates Are Subject to Measurement Errors and Missing Data,” The Canadian Journal of Statistics, to appear.
Author information
Authors and Affiliations
Corresponding author
Electronic Supplementary Material
Rights and permissions
About this article
Cite this article
Huggins, R., Hwang, WH. A Measurement Error Model for Heterogeneous Capture Probabilities in Mark-Recapture Experiments: An Estimating Equation Approach. JABES 15, 198–208 (2010). https://doi.org/10.1007/s13253-009-0003-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13253-009-0003-0