IDEAS home Printed from https://ideas.repec.org/a/vrs/offsta/v37y2021i4p865-905n10.html
   My bibliography  Save this article

Combining Cluster Sampling and Link-Tracing Sampling to Estimate Totals and Means of Hidden Populations in Presence of Heterogeneous Probabilities of Links

Author

Listed:
  • Félix-Medina Martín Humberto

    (Facultad de Ciencias Fisico-Matemáticas, Universidad Autónoma de Sinaloa, Ciudad Universitaria, Av. de Las Américas y Universitarios, Culiacán, Sinaloa 80013, México.)

Abstract

We propose Horvitz-Thompson-like and Hájek-like estimators of the total and mean of a response variable associated with the elements of a hard-to-reach population, such as drug users and sex workers. A portion of the population is assumed to be covered by a frame of venues where the members of the population tend to gather. An initial cluster sample of elements is selected from the frame, where the clusters are the venues, and the elements in the sample are asked to name their contacts who belong to the population. The sample size is increased by including in the sample the named elements who are not in the initial sample. The proposed estimators do not use design-based inclusion probabilities, but model-based inclusion probabilities which are derived from a Rasch model and are estimated by maximum likelihood estimators. The inclusion probabilities are assumed to be heterogeneous, that is, they depend on the sampled people. Variance estimates are obtained by bootstrap and are used to construct confidence intervals. The performance of the proposed estimators and confidence intervals is evaluated by two numerical studies, one of them based on real data, and the results show that their performance is acceptable.

Suggested Citation

  • Félix-Medina Martín Humberto, 2021. "Combining Cluster Sampling and Link-Tracing Sampling to Estimate Totals and Means of Hidden Populations in Presence of Heterogeneous Probabilities of Links," Journal of Official Statistics, Sciendo, vol. 37(4), pages 865-905, December.
    • Handle: RePEc:vrs:offsta:v:37:y:2021:i:4:p:865-905:n:10
    DOI: 10.2478/jos-2021-0038
    as

    Download full text from publisher

    File URL: https://doi.org/10.2478/jos-2021-0038
    Download Restriction: no
    File URL: https://libkey.io/10.2478/jos-2021-0038?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. S. E. Fienberg & M. S. Johnson & B. W. Junker, 1999. "Classical multilevel and Bayesian approaches to population size estimation using multiple lists," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(3), pages 383-405.
    2. Shirley Pledger, 2000. "Unified Maximum Likelihood Estimates for Closed Capture–Recapture Models Using Mixtures," Biometrics, The International Biometric Society, vol. 56(2), pages 434-442, June.
    3. Brent A. Coull & Alan Agresti, 1999. "The Use of Mixed Logit Models to Reflect Heterogeneity in Capture-Recapture Studies," Biometrics, The International Biometric Society, vol. 55(1), pages 294-301, March.
    4. Katherine St. Clair & Daniel O'Connell, 2012. "A Bayesian Model for Estimating Population Means Using a Link-Tracing Sampling Design," Biometrics, The International Biometric Society, vol. 68(1), pages 165-173, March.
    5. Forrest W. Crawford & Jiacheng Wu & Robert Heimer, 2018. "Hidden Population Size Estimation From Respondent-Driven Sampling: A Network Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 755-766, April.
    6. McCormick, Tyler H. & Salganik, Matthew J. & Zheng, Tian, 2010. "How Many People Do You Know?: Efficiently Estimating Personal Network Size," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 59-70.
    7. Wen-Han Hwang & Richard Huggins, 2005. "An examination of the effect of heterogeneity on the estimation of population size using capture-recapture data," Biometrika, Biometrika Trust, vol. 92(1), pages 229-233, March.
    8. Bilal Khan & Hsuan-Wei Lee & Ian Fellows & Kirk Dombrowski, 2018. "One-step estimation of networked population size: Respondent-driven capture-recapture with anonymity," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-39, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. J. Andrew Royle, 2006. "Site Occupancy Models with Heterogeneous Detection Probabilities," Biometrics, The International Biometric Society, vol. 62(1), pages 97-102, March.
    2. B. J. T. Morgan & M. S. Ridout, 2008. "A new mixture model for capture heterogeneity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 433-446, September.
    3. Fodé Tounkara & Louis‐Paul Rivest, 2015. "Mixture regression models for closed population capture–recapture data," Biometrics, The International Biometric Society, vol. 71(3), pages 721-730, September.
    4. Richard Arnold & Yu Hayakawa & Paul Yip, 2010. "Capture–Recapture Estimation Using Finite Mixtures of Arbitrary Dimension," Biometrics, The International Biometric Society, vol. 66(2), pages 644-655, June.
    5. Robert M. Dorazio & J. Andrew Royle, 2005. "Rejoinder to "The Performance of Mixture Models in Heterogeneous Closed Population Capture-Recapture"," Biometrics, The International Biometric Society, vol. 61(3), pages 874-876, September.
    6. Robert M. Dorazio & J. Andrew Royle, 2003. "Mixture Models for Estimating the Size of a Closed Population When Capture Rates Vary among Individuals," Biometrics, The International Biometric Society, vol. 59(2), pages 351-364, June.
    7. R. King & S. P. Brooks, 2008. "On the Bayesian Estimation of a Closed Population Size in the Presence of Heterogeneity and Model Uncertainty," Biometrics, The International Biometric Society, vol. 64(3), pages 816-824, September.
    8. Hannah Worthington & Rachel S. McCrea & Ruth King & Richard A. Griffiths, 2019. "Estimation of Population Size When Capture Probability Depends on Individual States," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(1), pages 154-172, March.
    9. Ben C. Stevenson & Rachel M. Fewster & Koustubh Sharma, 2022. "Spatial correlation structures for detections of individuals in spatial capture–recapture models," Biometrics, The International Biometric Society, vol. 78(3), pages 963-973, September.
    10. Francesco Bartolucci & Antonio Forcina, 2001. "Analysis of Capture-Recapture Data with a Rasch-Type Model Allowing for Conditional Dependence and Multidimensionality," Biometrics, The International Biometric Society, vol. 57(3), pages 714-719, September.
    11. Jennifer B Smith & Bryan S Stevens & Dwayne R Etter & David M Williams, 2020. "Performance of spatial capture-recapture models with repurposed data: Assessing estimator robustness for retrospective applications," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-16, August.
    12. Louis-Paul Rivest & Sophie Baillargeon, 2007. "Applications and Extensions of Chao's Moment Estimator for the Size of a Closed Population," Biometrics, The International Biometric Society, vol. 63(4), pages 999-1006, December.
    13. Richard Huggins & Wen‐Han Hwang, 2007. "Non‐parametric estimation of population size from capture–recapture data when the capture probability depends on a covariate," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(4), pages 429-443, August.
    14. Francesco Bartolucci & Fulvia Pennoni, 2007. "A Class of Latent Markov Models for Capture–Recapture Data Allowing for Time, Heterogeneity, and Behavior Effects," Biometrics, The International Biometric Society, vol. 63(2), pages 568-578, June.
    15. Francesco Bartolucci & Monia Lupparelli, 2008. "Focused Information Criterion for Capture–Recapture Models for Closed Populations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 629-649, December.
    16. Elena Stanghellini & Peter G. M. van der Heijden, 2004. "A Multiple-Record Systems Estimation Method that Takes Observed and Unobserved Heterogeneity into Account," Biometrics, The International Biometric Society, vol. 60(2), pages 510-516, June.
    17. William A. Link, 2003. "Nonidentifiability of Population Size from Capture-Recapture Data with Heterogeneous Detection Probabilities," Biometrics, The International Biometric Society, vol. 59(4), pages 1123-1130, December.
    18. Riki Herliansyah & Ruth King & Stuart King, 2022. "Laplace Approximations for Capture–Recapture Models in the Presence of Individual Heterogeneity," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(3), pages 401-418, September.
    19. Jakub Stoklosa & Wen-Han Hwang & Sheng-Hai Wu & Richard Huggins, 2011. "Heterogeneous Capture–Recapture Models with Covariates: A Partial Likelihood Approach for Closed Populations," Biometrics, The International Biometric Society, vol. 67(4), pages 1659-1665, December.
    20. Baffour Bernard & Brown James J. & Smith Peter W.F., 2021. "Latent Class Analysis for Estimating an Unknown Population Size – with Application to Censuses," Journal of Official Statistics, Sciendo, vol. 37(3), pages 673-697, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vrs:offsta:v:37:y:2021:i:4:p:865-905:n:10. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.sciendo.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.