Validity of methods for model selection, weighting for model uncertainty, and small sample adjustment in capture-recapture estimation
Abstract
In log-linear capture-recapture approaches to population size, the method of model selection may have a major effect upon the estimate. In addition, the estimate may also be very sensitive if certain cells are null or very sparse, even with the use of multiple sources. The authors evaluated 1) various approaches to the issue of model uncertainty and 2) a small sample correction for three or more sources recently proposed by Hook and Regal. The authors compared the estimates derived using 1) three different information criteria that included Akaike's Information Criterion (AIC) and two alternative formulations of the Bayesian Information Criterion (BIC), one proposed by Draper ("two pi") and one by Schwarz ("not two pi"); 2) two related methods of weighting estimates associated with models; 3) the independent model; and 4) the saturated model, with the known totals in 20 different populations studied by five separate groups of investigators. For each method, we also compared the estimate derived with or without the proposed small sample correction. At least in these data sets, the use of AIC appeared on balance to be preferable. The BIC formulation suggested by Draper appeared slightly preferable to that suggested by Schwarz. Adjustment for model uncertainty appears to improve results slightly. The proposed small sample correction appeared to diminish relative log bias but only when sparse cells were present. Otherwise, its use tended to increase relative log bias. Use of the…
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Recall and reporting errors may have occurred, especially when remembering details of medical events such as treatments, procedures, and days lost from work.
“Recall and reporting errors may have also occurred, especially when trying to remember the details of medical events (when did they occur, what were the costs), such as treatments, procedures, and days lost from work (41-43).”
From Patients’ report on how endometriosis affects health, work, and daily life (2010) · cites this paper as [43]
Cites
Estimating the Dimension of a Model
Schwarz, G. (1978) · The Annals of Statistics · doi:10.1214/aos/1176344136 · Cited by 47,033 · see citing works
Hapeman, D. E., & Agresti, A. (1991) · Technometrics · doi:10.1080/00401706.1991.10484817 · Cited by 9,406 · see citing works
Discrete Multivariate Analysis: Theory and Practice.
Beniger, J. R., Bishop, Y. M. M., Feinberg, S. E., Holland, P. W., Light, R. J., & Mosteller, F. C. (1975) · Contemporary Sociology A Journal of Reviews · doi:10.2307/2063625 · Cited by 5,119 · see citing works
Assessment and Propagation of Model Uncertainty
Draper, D. (1995) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1995.tb02015.x · Cited by 1,599 · see citing works
Akaike Information Criterion Statistics.
Grove, D., Sakamoto, Y., Ishiguro, M., & Kitagawa, G. (1988) · Journal of the Royal Statistical Society Series D (The Statistician) · doi:10.2307/2348776 · Cited by 1,184 · see citing works
Akaike Information Criterion Statistics
Brooks, D. G., Sakamoto, Y., Ishiguro, M., & Kitagawa, G. (1989) · Technometrics · doi:10.2307/1268842 · Cited by 769 · see citing works
Capture-Recapture Methods in Epidemiology: Methods and Limitations
Hook, E. B., & Regal, R. R. (1995) · Epidemiologic Reviews · doi:10.1093/oxfordjournals.epirev.a036192 · Cited by 736 · see citing works
Self-citationBreiman, L. (1992) · Journal of the American Statistical Association · doi:10.1080/01621459.1992.10475276 · Cited by 277 · see citing works
The multiple recapture census for closed populations and incomplete 2 k contingency tables
Fienberg, S. E. (1972) · Biometrika · doi:10.1093/biomet/59.3.591 · Cited by 250 · see citing works
Wittes, J. T., Colton, T., & Sidel, V. W. (1974) · Journal of Chronic Diseases · doi:10.1016/0021-9681(74)90005-8 · Cited by 188 · see citing works
A generalization of the simple capture-recapture model with applications to epidemiological research
Wittes, J., & Sidel, V. W. (1968) · Journal of Chronic Diseases · doi:10.1016/0021-9681(68)90038-6 · Cited by 152 · see citing works
Goodness‐of‐fit based confidence intervals for estimates of the size of a closed population
Regal, R. R., & Hook, E. B. (1984) · Statistics in Medicine · doi:10.1002/sim.4780030310 · Cited by 100 · see citing works
Self-citationFrischer, M., Leyland, A. H., Cormack, R. M., et al. (1993) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a116843 · Cited by 94 · see citing works
Use of Capture-Recapture to Estimate the Prevalence of Opiate Addiction in Barcelona, Spain, 1989
Domingo‐Salvany, A., Hartnoll, R., Maguire, A., Suelves, J. M., & Antó, J. M. (1995) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a117472 · Cited by 65 · see citing works
Applications of a Multinomial Capture-Recapture Model to Epidemiological Data
Wittes, J. T. (1974) · Journal of the American Statistical Association · doi:10.1080/01621459.1974.10480133 · Cited by 64 · see citing works
Wittes, J. T. (1972) · Biometrics · doi:10.2307/2556173 · Cited by 61 · see citing works
Hook, E. B. (1993) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a116638 · Cited by 57 · see citing works
Self-citationLaPorte, R. E., Dearwater, S. R., Chang, Y., et al. (1995) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a117560 · Cited by 52 · see citing works
Bruno, G., Bargero, G., Vuolo, A., Pisu, E., & Pagano, G. (1992) · Diabetologia · doi:10.1007/bf00399931 · Cited by 46 · see citing works
Internal Validity Analysis: A Method for Adjusting Capture-Recapture Estimates of Prevalence
Hook, E. B., & Regal, R. R. (1995) · American Journal of Epidemiology · doi:10.1093/aje/142.supplement_9.s48 · Cited by 32 · see citing works
Self-citationThe Exploratory Analysis of Survey Data Using Log-Linear Models
UPTON, G. J. G. (1991) · Journal of the Royal Statistical Society Series D (The Statistician) · doi:10.2307/2348489 · Cited by 16 · see citing works
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Patients’ report on how endometriosis affects health, work, and daily life
Fourquet, J., Gao, X., Zavala, D., Orengo, J. C., Abac, S., Ruiz, A., Laboy, J., & Flores, I. (2010) · Fertility and Sterility · doi:10.1016/j.fertnstert.2009.09.017 · Cited by 252 · see citing works
“especially when trying to remember the details of medical events (when did they occur, what were the costs), such as treatments, procedures, and days lost from work (41-43).”
Hope, V. D., Hickman, M., & Tilling, K. (2005) · Addiction · doi:10.1111/j.1360-0443.2005.01244.x · Cited by 66 · see citing works
- Authors
- Hook, E. B., & Regal, R. R.
- Affiliations
- University of California, San Francisco (US)
- University of Minnesota (US)
- Corresponding author
- Hook, E. B.
- Venue
- American Journal of Epidemiology
- Publisher
- Oxford University Press (OUP)
- Published
- 1997-06-15
- Volume
- 145
- Issue
- 12
- Pages
- 1138-1144
- ISSN
- 0002-9262 (ISSN-L)
- 1476-6256
- OpenAlex
- W2165962753
- Cited by
- 94
- References
- 21
- Citations by year
- 2026: 1 · 2024: 2 · 2023: 3 · 2022: 1 · 2021: 2 · 2020: 3 · 2018: 2 · 2017: 1 · 2016: 5 · 2015: 5 · 2014: 4 · 2013: 7 · 2012: 9
- FWCI
- 7.92
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- American Journal of Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- HighWire Press Open Archive (submittedVersion)
- Funders
- U.S. Public Health Service (U83/CCU908694-02)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Census and Population Estimation
- Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Keywords
- mark-recapture, population size estimation, model selection, model uncertainty, model weighting, small sample correction, Akaike information criterion, Bayesian information criterion, log-linear models, multiple sources, saturated models, independent model
- MeSH terms
- Bayes Theorem, Data Interpretation, Statistical, Epidemiologic Methods, Humans, Reproducibility of Results, Likelihood Functions, Linear Models, Sample Size
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