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

Journal of the Royal Statistical Society. Series A: Statistics in Society

Volumn 162, Issue 3, 1999, Pages 383-405

  Fienberg, Stephen E ^a   Johnson, Matthew S ^a   Junker, Brian W ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Log linear models; Markov chain Monte Carlo methods; Multiple recapture census; Quasi symmetry; Rasch model

Indexed keywords

EID: 0033472991     PISSN: 09641998     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-985X.00143     Document Type: Article

References (53)

1. Agresti, A. (1994) Simple capture-recapture models permitting unequal catchability and variable sampling effort. Biometrics, 50, 494-500.
2. Basu, S. (1998) Bayesian estimation of the number of undetected errors when both reviewers and errors are heterogeneous. In Frontiers in Reliability Analysis (eds A. P. Basu, S. K. Basu and S. Mukhopadhyay), pp. 19-36. Singapore: World Scientific.
3. Biggeri, A., Stanghellini, E., Merletti, M. and Marchi, M. (1999) Latent class models for varying catchability and correlation among sources in capture-recapture estimation of the size of a human population. Statist. Appl., to be published.
4. Bishop, Y. M. M., Fienberg, S. E. and Holland, P. (1975) Discrete Multivariate Analysis: Theory and Practice. Cambridge: Massachusetts Institute of Technology Press.
5. Bruno, G., Laporte, R., Merletti, E., Biggeri, A., McCarty, D. and Pagano, C. (1994) National diabetes programs: application of capture-recapture to "count" diabetes. Diab. Care, 17, 548-556.
6. Burnham, K. P. and Overton, W. S. (1978) Estimation of the size of a closed population when capture probabilities vary among animals. Biometrika, 65, 625-633.
7. Carriquiry, A. and Fienberg, S. E. (1998) Encyclopedia of Biostatistics, vol. 5, pp. 3724-3730. New York: Wiley.
8. Castledine, B. J. (1981) A bayesian analysis of multiple-recapture sampling for a closed population. Biometrika, 67, 197-210.
9. Chao, A. (1987) Estimating the population size for capture-recapture data with unequal catchability. Biometrics, 43, 783-791.
10. -(1989) Estimating population size for sparse data in capture-recapture experiments. Biometrics, 45, 427-438.
11. Chao, A., Lee, S.-M. and Jeng, S.-L. (1992) Estimating population size for capture-recapture data when capture probabilities vary by time and individual animal. Biometrics, 48, 201-216.
12. Cormack, R. M. (1966) A test for equal catchability. Biometrics, 22, 330-342.
13. -(1989) Log-linear models for capture-recapture. Biometrics, 45, 395-413.
14. -(1992) Interval estimates for mark-recapture studies of closed populations. Biometrics, 48, 567-576.
15. -(1994) Statistics in Ecology and Environmental Monitoring, pp. 19-32. Dunedin: University of Otago Press.
16. Coull, B. A. and Agresti, A. (1999) The use of mixed logit models to reflect heterogeneity in capture-recapture studies. Biometrics, 55, 294-301.
17. Cressie, N. and Holland, P. W. (1983) Characterizing the manifest probabilities of latent trait models. Psychometrika, 48, 129-141.
18. Darroch, J. N., Fienberg, S. E., Glonek, G. F. V. and Junker, B. W. (1993) A three-sample multiple-recapture approach to census population estimation with heterogeneous catchability. J. Am. Statist. Ass., 88, 1137-1148.
19. Darroch, J. N. and McCloud, P. I. (1990) Separating two sources of dependence in repeated influenza outbreaks. Biometrika, 77, 237-243.
20. Fienberg, S. E. (1972) Multiple-recapture census for closed populations and incomplete contingency tables. Biometrika, 59, 591-603.
21. -(1992) Bibliography on capture-recapture modelling with application to census undercount adjustment. Surv. Methodol., 18, 143-154.
22. Fienberg, S. E. and Meyer, M. M. (1983) Loglinear models and categorical data analysis with psychometric and econometric applications. J. Econometr., 22, 191-214.
23. Freeman, P. R. (1972) Sequential estimation of the size of a population. Biometrika, 59, 9-18.
24. -(1973) A numerical comparison between sequential tagging and sequential recapture. Biometrika, 60, 499-508.
25. Garthwaite, P. H., Yu, K. and Hope, P. B. (1995) Bayesian analysis of a multiple-recapture model. Communs Statist. Theory Meth., 24, 2229-2247.
26. Geiger, H. and Werner, A. (1924) Die Zahl der Ion Radium Ausgesandsena-teilchen. Z. Phys., 21, 187-201.
27. George, E. I. and Robert, C. P. (1992) Capture-recapture estimation via gibbs sampling. Biometrika, 79, 677-683.
28. Gilks, W. R. and Wild, P. (1992) Adaptive rejection sampling for Gibbs sampling. Appl. Statist., 41, 337-348.
29. Green, P. J. (1995) Reversible jump markov chain monte carlo computation and bayesian model determination. Biometrika, 82, 711-732.
30. Hay, G. (1997) The selection from multiple data sources in epidemiological capture-recapture studies. Statistician, 46, 515-520.
31. Holland, P. W. (1990) On the sampling theory foundations of item response theory models. Psychometrika, 55, 577-601.
32. International Working Group for Disease Monitoring and Forecasting (1995a) Mark-recapture and multiple-record systems: I, History and theoretical development. Am. J. Epidem., 142, 1047-1058.
33. -(1995b) Mark-recapture and multiple-record systems: II, Applications in human diseases. Am. J. Epidem., 142, 1059-1068.
34. Jannarone, R. J. (1986) Conjunctive item response theory kernels. Psychometrika, 51, 357-373.
35. Jannarone, R. J., Yu, K. F. and Laughlin, J. E. (1990) Easy bayes estimation for rasch-type models. Psychometrika, 55, 449-460.
36. Johnson, M. S., Cohen, W. M. and Junker, B. W. (1998) Measuring appropriability in research and development with item response models. Technical Report 690. Department of Statistics, Carnegie Mellon University, Pittsburgh. (Available from http: //www.stat.cmu.edu/www/cmu-stats/tr/.)
37. Kass, R. E. and Wasserman, L. (1995) A reference bayesian test for nested hypotheses and its relationship to the schwarz criterion. J. Am. Statist. Ass., 98, 928-934.
38. Kelderman, H. (1984) Loglinear rasch model tests. Psychometrika, 49, 223-245.
39. Lawrence, S. and Giles, C. L. (1998) Searching the world wide web. Science, 280, 98-100.
40. Madigan, D. and York, J. (1995) Bayesian graphical models for discrete data. Int. Statist. Rev., 63, 215-232.
41. -(1997) Bayesian methods for estimating the size of a closed population. Biometrika, 84, 19-31.
42. Mathsoft (1996) S-plus Version 3.4 Release 1 for HP 9000 Series. Seattle: Mathsoft.
43. Patz, R. J. and Junker, B. W. (1999) A straightforward approach to markov chain monte carlo methods for item response models. J. Educ. Behav. Statist., 24, 146-177.
44. Petersen, C. J. G. (1896) The yearly immigration of young plaice into the limfjord from the german sea. Rep. Dan. Biol. Stn Min. Fish., 6, 1-48.
45. Pollock, K. H. (1991) Modeling capture, recapture, and removal statistics for estimation of demographic parameters for fish and wildlife populations: past, present, and future. J. Am. Statist. Ass., 86, 225-238.
46. Rasch, G. (1960) Probabilistic Models for Some Intelligence and Attainment Tests. Chicago: University of Chicago Press.
47. Roberts, H. V. (1967) Informative stopping rules and inferences about population size. J. Am. Statist. Ass., 62, 763-775.
48. Sanathanan, L. (1972) Models and methods in visual scanning experiments. Technometrics, 14, 813-830.
49. -(1973) A comparison of some models in visual scanning experiments. Technometrics, 15, 67-78.
50. Schnabel, Z. (1938) The estimation of the total fish population of a lake. Am. Math. Mnthly, 45, 348-352.
51. Smith, P. J. (1988) Bayesian methods for multiple capture-recapture surveys. Biometrics, 44, 1177-1189.
52. -(1991) Bayesian analyses for a multiple capture-recapture model. Biometrika, 78, 399-407.
53. Wu, M. L., Adams, R. J. and Wilson, M. R. (1997) Conquest: Generalized Item Response Modeling Software. Camberwell: Australian Council on Educational Research.