Small Domain Estimation of Census Coverage – A Case Study in Bayesian Analysis of Complex Survey Data

Atkinson, J., C. Salmond, and P. Crampton. 2019. NZ Dep 2013 index of deprivation interim research report. Technical report, Department of Public Health, University of Otago,Wellington. Available at: https://www.otago.ac.nz/wellington/otago730394.pdf. (accessed February 2022). Search in Google Scholar

Brown, J.J., C. Sexton, O. Abbott, and P.A. Smith. 2019. “The framework for estimating coverage in the 2011 census of England and Wales: Combining dual-system estimation with ratio estimation.” Statistical Journal of the International Association of Official Statistics 35: 481–499. DOI: https://doi.org/10.3233/SJI-180426. Search in Google Scholar

Bryant, J., K. Dunstan, P. Graham, N. Matheson-Dunning, E. Shrosbree, and R. Speirs. 2016. Measuring uncertainty in the 2013-base estimated resident population (Statistics New Zealand Working paper: 16–04). Wellington, New Zealand: Statistics New Zealand. Available at: https://www.stats.govt.nz/ (accessed February 2022). Search in Google Scholar

Chandrasekar, C. and W.E. Deming. 1949. “On a method of estimating birth and death rates and the extent of registration.” Journal of the American Statistical Association 44: 101–115. DOI: https://doi.org/10.1080/01621459.1949.10483294. Search in Google Scholar

Chen, C., J. Wakefield, and T. Lumley. 2014. “The use of sampling weights in Bayesian hierarchical models for small area estimation.” Spatial and Spatio-Temporal Epidemiology 11: 33–43. DOI: https://doi.org/10.1016/j.sste.2014.07.002.435736325457595 Search in Google Scholar

Chen, S.X., C.Y. Tang, and V.T. Mule Jr. 2010. “Local post-stratification in dual system accuracy and coverage evaluation for the US census.” Journal of the American Statistical Association 105: 105–119. DOI: https://doi.org/10.1198/jasa.2009.ap08404. Search in Google Scholar

Chipperfield, J., J. Brown, and P. Bell. 2017. “Estimating the count error in the Australian census.” Journal of Official Statistics 33: 43–59. DOI: https://doi.org/10.1515/jos-2017-0003. Search in Google Scholar

Elliott, M.R. and R.J. Little. 2000. “A Bayesian approach to combining information from a census, a coverage measurement survey, and demographic analysis.” Journal of the American Statistical Association 95 (450): 351–362. DOI: https://doi.org/10.1080/01621459.2000.10474205. Search in Google Scholar

Gelman, A., J. Carlin, H. Stern, D. Dunson, D. Vehtari, and A. Rubin. 2014. Bayesian Data Analysis. Boca Raton, FL.: CRC Press.10.1201/b16018 Search in Google Scholar

Gelman, A., and J. Hill. 2006. Data Analysis Using Regression and Multilevel/Hierarchical models. Cambridge: Cambridge university press.10.1017/CBO9780511790942 Search in Google Scholar

Gelman, A., A. Jakulin, M.G. Pittau, and Y.-S. Su. 2008. “A weakly informative default prior distribution for logistic and other regression models.” Annals of Applied Statistics 2: 1360–1383. DOI: https://doi.org/10.1214/08-A0AS191. Search in Google Scholar

Gelman, A. and T.C. Little. 1997. “Poststratification into many categories using hierarchical logistic regression.” Survey Methodology 23: 127–135. Available at: https://www150.statcan.gc.ca/n1/en/pub/12-001-x/1997002/article/3616-eng.pdf?st=76F1g34m (accessed July 2022). Search in Google Scholar

Gelman, A., X.-L. Meng, and H. Stern. 1996. “Posterior predictive assessment of model fitness via realized discrepancies.” Statistica Sinica 6: 733–760. Search in Google Scholar

Ghitza, Y., and A. Gelman. 2013. “Deep interactions with MRP: Election turnout and voting patterns among small electoral subgroups.” American Journal of Political Science 57: 762–776. DOI: https://doi.org/10.1111/ajps.12004. Search in Google Scholar

Ghosh, M., K. Natarajan, T. Stroud, and B.P. Carlin. 1998. “Generalized linear models for small-area estimation.” Journal of the American Statistical Association 93: 273–282. DOI: https://doi.org/10.1080/01621459.1998.10474108. Search in Google Scholar

Hogan, H.P. 1993. “The 1990 post-enumeration survey: Operations and results.” Journal of the American Statistical Association 88: 1047–1060. DOI: https://doi.org/10.1080/01621459.1993.10476374. Search in Google Scholar

Lax, J.R., and J.H. Phillips. 2009. “How should we estimate public opinion in the States?” American Journal of Political Science 53: 107–121. DOI: https://doi.org/10.1111/j.1540-5907.2008.00360.x. Search in Google Scholar

Little, R.J. 2003. “The Bayesian approach to sample survey inference.” In Analysis of Complex Surveys, edited by R. Chambers and C. Skinner: 49–57. John Wiley and Sons.10.1002/0470867205.ch4 Search in Google Scholar

Lumley, T., and A. Scott. 2017. “Fitting regression models to survey data.” Statistical Science 32: 265–278. DOI: https://doi.org/10.1214/16-STS605. Search in Google Scholar

Molina, I., B. Nandram, and J. Rao. 2014. “Small area estimation of general parameters with application to poverty indicators: a hierarchical Bayes approach.” Annals of Applied Statistics 8: 852–885. DOI: https://doi.org/10.1214/13-A0AS702. Search in Google Scholar

Mule, T., T. Schellhamer, D. Malec, and J. Maples. 2008. “Using continuous variables as modeling covariates for net coverage estimation.” In JSM Proceedings: Section on Survey Research Methods: 1941–1948. Denver. Available at: http://www.asasrms.org/Proceedings/y2008/Files/301279.pdf (accessed February 2022). Search in Google Scholar

Nandram, B., L. Chen, and B. Manandhar. 2018. “Bayesian analysis of multinomial counts from small areas and sub-areas.” In JSM proceedings: Section on Survey Research Methods: 1140–1162. Vancouver. Available at: http://www.asasrms.org/Proceedings/y2018/files/867100.pdf (accessed February 2022). Search in Google Scholar

Paige, J., G.-A. Fuglstad, A. Riebler, and J. Wakefield. 2020. “Design-and model-based approaches to small-area estimation in a low and middle income country context: comparisons and recommendations.” Journal of Survey Statistics and Methodology. DOI: https://doi.org/10.1093/jssam/smaa011. Search in Google Scholar

Pavlou, M., G. Ambler, S. Seaman, and R.Z. Omar. 2015. “A note on obtaining correct marginal predictions from a random intercepts model for binary outcomes.” BMC Medical Research Methodology 15: 1–6. DOI: http://doi.org/10.1186/s12874-015-0046-6.10.1186/s12874-015-0046-6452575126242875 Search in Google Scholar

Pfeffermann, D. 2013. “New important developments in small area estimation.” Statistical Science 28: 40–68. DOI: https://doi.org/10.1214/12-STS395. Search in Google Scholar

Pfeffermann, D., F.A.D.S. Moura, and P.L.D.N. Silva. 2006. “Multilevel modelling under informative sampling.” Biometrika 93: 943–959. DOI: https://doi.org/10.1093/biomet/93.4.943. Search in Google Scholar

R Core Team. 2019. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Available at: https://www.R-project.org/ (accessed February 2022). Search in Google Scholar

Rabe-Hesketh, S., and A. Skrondal. 2006. “Multilevel modelling of complex survey data.” Journal of the Royal Statistical Society: 169: 805–827. DOI: https://doi.org/10.1111/j.1467-985X.2006.00426.x. Search in Google Scholar

Rao, J. and I. Molina. 2014. Small-area estimation. Hoboken, NJ: John Wiley & Sons, Inc.10.1002/9781118735855 Search in Google Scholar

Rao, J., F. Verret, and M.A. Hidiroglou. 2013. “A weighted composite likelihood approach to inference for two-level models from survey data.” Survey Methodology 39(2): 263–282. Available at: https://www150.statcan.gc.ca/n1/en/pub/12-001-x/12-001-x2013002-eng.pdf?st=LsDJmvSV (accessed July 2022). Search in Google Scholar

Rubin, D.B. 1987. Multiple imputation for nonresponse in surveys. Hoboken, NJ: John Wiley & Sons.10.1002/9780470316696 Search in Google Scholar

Shirley, K.E., and A. Gelman. 2015. “Hierarchical models for estimating state and demographic trends in US death penalty public opinion.” Journal of the Royal Statistical Society 178: 1–28. DOI: https://doi.org/10.1111/rssa.12052. Search in Google Scholar

Si, Y., R. Trangucci, J.S. Gabry, and A. Gelman. 2020. “Bayesian hierarchical weighting adjustment and survey inference.” Survey Methodology 46: 181–214. Available at: https://www150.statcan.gc.ca/n1/pub/12-001-x/2020002/article/00003-eng.htm. (accessed July 2022). Search in Google Scholar

Skrondal, A., and S. Rabe-Hesketh. 2009. “Prediction in multilevel generalized linear models.” Journal of the Royal Statistical Society: 172: 659–687. DOI: https://doi.org/10.1111/j.1467-985X.2009.00587.x. Search in Google Scholar

Stan Development Team. 2020a. R Stan: the R interface to Stan. R package version 2.21.2. Available at: http://mc-stan.org/ (accessed February 2022). Stan Development Team. 2020b. Search in Google Scholar

Stan Modeling Language Users Guide and Reference Manual, version 2.25. Available at: http://mc-stan.org/ (accessed February 2022). Search in Google Scholar

Stats NZ. 2014. Coverage in the 2013 Census based on the New Zealand 2013 Post-enumeration Survey. Wellington: Statistics New Zealand. Available at: https://www.stats.govt.nz/. (accessed February 2022). Search in Google Scholar

Stats NZ. 2019. Overview of statistical methods for adding admin records to the 2018 Census dataset. Wellington, NZ: Statistics New Zealand. Available at: https://www.stats.govt.nz/ (accessed February 2022). Search in Google Scholar

Stats NZ 2020a. Estimated resident population 2018: Data sources and methods. Wellington, NZ: Statistics New Zealand. Available at: https://www.stats.govt.nz/ (accessed February 2022). Search in Google Scholar

Stats NZ. 2020b. Post-enumeration survey 2018: Methods and Results. Wellington, NZ: Statistics New Zealand. Available at: https://www.stats.govt.nz/ (accessed February 2022). Search in Google Scholar

Vehtari, A., A. Gelman, and J. Gabry. 2017. “Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC”. Statistics and Computing 27: 1413–1432. DOI: https://doi.org/10.1007/s11222-016-9696-4. Search in Google Scholar

Yi, G.Y., J. Rao, and H. Li. 2016. “A weighted composite likelihood approach for analysis of survey data under two-level models.” Statistica Sinica 26: 569–587. DOI: https://doi.org/10.5705/ss.2013.383. Search in Google Scholar

You, Y., and B. Chapman. 2006. “Small area estimation using area level models and estimated sampling variances.” Survey Methodology 32: 97–104. Available at: https://www150.statcan.gc.ca/n1/en/pub/12-001-x/2006001/article/9263-eng.pdf?st=a4rH5VTf (accessed July 2022). Search in Google Scholar

You, Y. and P. Dick. 2004. “Hierarchical Bayes small area inference to the 2001 census undercoverage estimation.” In JSM Proceedings: Section on Government Statistics: 1836–1840. Available at: http://www.asasrms.org/Proceedings/y2004/files/Jsm2004-000377.pdf (accessed February 2022). Search in Google Scholar