IDEAS home Printed from https://ideas.repec.org/a/bla/jorssa/v162y1999i3p383-405.html
   My bibliography  Save this article

Classical multilevel and Bayesian approaches to population size estimation using multiple lists

Author

Listed:
  • S. E. Fienberg
  • M. S. Johnson
  • B. W. Junker

Abstract

One of the major objections to the standard multiple‐recapture approach to population estimation is the assumption of homogeneity of individual ‘capture’ probabilities. Modelling individual capture heterogeneity is complicated by the fact that it shows up as a restricted form of interaction among lists in the contingency table cross‐classifying list memberships for all individuals. Traditional log‐linear modelling approaches to capture–recapture problems are well suited to modelling interactions among lists but ignore the special dependence structure that individual heterogeneity induces. A random‐effects approach, based on the Rasch model from educational testing and introduced in this context by Darroch and co‐workers and Agresti, provides one way to introduce the dependence resulting from heterogeneity into the log‐linear model; however, previous efforts to combine the Rasch‐like heterogeneity terms additively with the usual log‐linear interaction terms suggest that a more flexible approach is required. In this paper we consider both classical multilevel approaches and fully Bayesian hierarchical approaches to modelling individual heterogeneity and list interactions. Our framework encompasses both the traditional log‐linear approach and various elements from the full Rasch model. We compare these approaches on two examples, the first arising from an epidemiological study of a population of diabetics in Italy, and the second a study intended to assess the ‘size’ of the World Wide Web. We also explore extensions allowing for interactions between the Rasch and log‐linear portions of the models in both the classical and the Bayesian contexts.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssa:v:162:y:1999:i:3:p:383-405
    DOI: 10.1111/1467-985X.00143
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-985X.00143
    Download Restriction: no

    File URL: https://libkey.io/10.1111/1467-985X.00143?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Chang Xuan Mao & Ruochen Huang & Sijia Zhang, 2017. "Petersen estimator, Chapman adjustment, list effects, and heterogeneity," Biometrics, The International Biometric Society, vol. 73(1), pages 167-173, March.
    3. Fienberg Stephen E., 2015. "Discussion," Journal of Official Statistics, Sciendo, vol. 31(3), pages 527-535, September.
    4. 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.
    5. Mark S. Handcock & Krista J. Gile & Corinne M. Mar, 2015. "Estimating the size of populations at high risk for HIV using respondent-driven sampling data," Biometrics, The International Biometric Society, vol. 71(1), pages 258-266, March.
    6. repec:jss:jstsof:25:i08 is not listed on IDEAS
    7. 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.
    8. Daniel Manrique‐Vallier, 2016. "Bayesian population size estimation using Dirichlet process mixtures," Biometrics, The International Biometric Society, vol. 72(4), pages 1246-1254, December.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. William A. Link & Richard J. Barker, 2005. "Modeling Association among Demographic Parameters in Analysis of Open Population Capture–Recapture Data," Biometrics, The International Biometric Society, vol. 61(1), pages 46-54, March.
    14. 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.
    15. Sheng, Yanyan, 2008. "Markov Chain Monte Carlo Estimation of Normal Ogive IRT Models in MATLAB," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 25(i08).
    16. Johnson, Matthew S., 2007. "Modeling dichotomous item responses with free-knot splines," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4178-4192, May.
    17. 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.
    18. J. Andrew Royle, 2006. "Site Occupancy Models with Heterogeneous Detection Probabilities," Biometrics, The International Biometric Society, vol. 62(1), pages 97-102, March.
    19. Heijden Peter G.M. van der & Smith Paul A. & Cruyff Maarten & Bakker Bart, 2018. "An Overview of Population Size Estimation where Linking Registers Results in Incomplete Covariates, with an Application to Mode of Transport of Serious Road Casualties," Journal of Official Statistics, Sciendo, vol. 34(1), pages 239-263, March.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jorssa:v:162:y:1999:i:3:p:383-405. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.