Estimation of Non-Linear Parameters with Data Collected Using Respondent-Driven Sampling
Abstract
:1. Introduction
2. Background
3. Estimation of Some Non-Linear Parameters
3.1. Estimation of the Variance and the Covariance
3.2. Estimation of the Correlation Coefficient
4. Estimation of the Variances
5. Simulation Experiments
6. Application to a Real Survey
7. Discussion
Author Contributions
Funding
Conflicts of Interest
Abbreviations
RDS | Respondent-Driven Sampling |
MCMC | Markov Chain Monte Carlo |
References
- Heckathorn, D. Respondent-driven sampling: A new approach to the study of hidden populations. Soc. Probl. 1997, 44, 174–199. [Google Scholar] [CrossRef]
- Salganik, M.; Heckathorn, D. Sampling and estimation in hidden populations using respondent-driven sampling. Sociol. Methodol. 2004, 34, 193–240. [Google Scholar] [CrossRef]
- Volz, E.; Heckathorn, D. Probability based estimation theory for respondent driven sampling. J. Off. Stat. 2008, 14, 79–97. [Google Scholar]
- Spiller, M.W.; Gile, K.J.; Handcock, M.S.; Mar, C.M.; Wejnert, C. Evaluating Variance Estimators for Respondent-Driven Sampling. J. Surv. Stat. Methodol. 2018, 6, 23–45. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Beaudry, I.S.; Gile, K.J. Correcting for differential recruitment in respondent-driven sampling data using ego-network information. Electron. J. Stat. 2020, 14, 2678–2713. [Google Scholar] [CrossRef]
- Rocha, L.E.; Thorson, A.E.; Lambiotte, R.; Liljeros, F. Respondent-driven sampling bias induced by community structure and response rates in social networks. J. R. Stat. Soc. Ser. A Stat. Soc. 2017, 180, 99–118. [Google Scholar] [CrossRef] [Green Version]
- Kan, M.; Garfinkel, D.; Samoylova, O.; Gray, R.; Little, K. Social network methods for HIV case-finding among people who inject drugs in Tajikistan. J. Int. AIDS Soc. 2018, 21, 57–64. [Google Scholar] [CrossRef] [Green Version]
- Sypsa, V.; Psichogiou, M.; Paraskevis, D. Rapid decline in HIV incidence among persons who inject drugs during a fast-track combination prevention program after an HIV outbreak in Athens. J. Infect. Dis. 2017, 215, 1496–1505. [Google Scholar]
- Card, K.G.; Lachowsky, N.J.; Cui, Z. Exploring the role of sex-seeking apps and websites in the social and sexual lives of gay, bisexual and other men who have sex with men: A cross-sectional study. Sex Health 2017, 14, 229–237. [Google Scholar] [CrossRef]
- Bernard, J.; Daňková, H.; Vašát, P. Ties, sites and irregularities: Pitfalls and benefits in using respondent-driven sampling for surveying a homeless population. Int. J. Soc. Res. Methodol. 2018, 21, 603–618. [Google Scholar] [CrossRef]
- Hipp, L.; Kohler, U.; Leumann, S. How to Implement Respondent-Driven Sampling in Practice: Insights from Surveying 24-Hour Migrant Home Care Workers. Surv. Methods Insights Field 2019. [Google Scholar] [CrossRef]
- Wong, W.; Wang, S.; Liu, H. Bootstrap standard error estimations of non-linear transport models based on linearly projected data. Transp. A 2018, 15, 1–35. [Google Scholar]
- Imani, M.; Ghoreishi, S.F.; Braga-Neto, U. Bayesian Control of Large MDPs with Unknown Dynamics in Data-Poor Environments. Adv. Neural Dyn. 2018, 8146–8156. [Google Scholar]
- Imani, M.; Dougherty, E.R.; Braga-Neto, U. Boolean Kalman Filter and Smoother under Model Uncertainty. Automatica 2020. [Google Scholar] [CrossRef]
- Avery, L.; Rotondi, N.; McKnight, C.; Firestone, M.; Smylie, J.; Rotondie, M. Unweighted regression models perform better than weighted regression techniques for respondent-driven sampling data: Results from a simulation study. BMC Med. Res. Methodol. 2019, 19, 202. [Google Scholar] [CrossRef] [Green Version]
- Beckett, M.; Firestone, M.A.; McKnight, C.D. A cross-sectional analysis of the relationship between diabetes and health access barriers in an urban First Nations population in Canada. BMJ Open 2017, 8, e018272. [Google Scholar] [CrossRef]
- da Silva Lima, F.S.; Merchán-Hamann, E.; Urdaneta, M. Fatores associados à violência contra mulheres profissionais do sexo de dez cidades brasileiras. CAD Saude Publica 2017, 33, 1–15. [Google Scholar]
- Selvaraj, B.; Boopathi, K.; Paranjape, R.; Mehendale, S. A single weighting approach to analyze respondent-driven sampling data. Indian J. Med. Res. 2016, 144, 447–459. [Google Scholar]
- Hubbart, A.E.; Ahern, J.; Fleischer, N.L.; Van der Laan, M.; Lippman, S.A.; Jewell, T.B.; Satariano, W.A. To GEE or not to GEE. Epidemiology 2010, 21, 467–474. [Google Scholar] [CrossRef]
- Rao, S.; LaRoque, R.; Jentes, E. Comparison of methods for clustered data analysis in a non-ideal situation: Results from an evaluation of predictors of yellow fever vaccine refusal in the global TravEpiNet (GTEN) consortium. Int. J. Stat. Med. Res. 2014, 3, 215–223. [Google Scholar] [CrossRef]
- Lyons, C.E.; Grosso, A.; Drame, F.M. Physical and sexual violence affecting female sex workers in Abidjan, Côte d’Ivoire: Prevalence, and the relationship with the work environment, HIV, and access to health services. J. Acquir. Immune Defic. Syndr. 2017, 75, 9–17. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Schwartz, S.; Papworth, E.; Thiam-Niangoin, M. An urgent need for integration of family planning services into HIV care. J. Acquir. Immune Defic. Syndr. 2015, 68, 91–98. [Google Scholar] [CrossRef] [PubMed]
- de Matos, M.A.; da Silva França, D.D.; dos Santos Carneiro, M.A. Viral hepatitis in female sex workers using the respondent-driven sampling. Rev. Saude Publica 2017, 51, 1–11. [Google Scholar] [CrossRef] [Green Version]
- Scheim, A.; Bauer, G.; Coleman, T. Sociodemographic differences by survey mode in a respondent-driven sampling study of transgender people in Ontario, Canada. LGBT Health 2016, 3, 391–395. [Google Scholar] [CrossRef] [PubMed]
- Pan, X.; Wu, M.; Ma, Q. High prevalence of HIV among men who have sex with men in Zhejiang, China: A respondent-driven sampling survey. BMJ Open 2015, 5, 1–7. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Maragh-Bass, A.C.; Powell, C.; Park, J. Sociodemographic and access related correlates of health-care utilization among African American injection drug users: The BESURE study. J. Ethn. Subst. Abuse 2017, 16, 344–362. [Google Scholar] [CrossRef]
- Gile, K.; Handcock, M. Respondent-driven sampling: An assessment of current methodology. Sociol. Methodol. 2010, 40, 285–327. [Google Scholar] [CrossRef] [Green Version]
- Särndal, C.E.; Swensson, B.; Wretman, J. Model Assisted Survey Sampling; Springer: Berlin/Heidelberg, Germany, 1992. [Google Scholar]
- Hansen, M.H.; Hurvitz, W.N. On the theory of sampling from finite populations. Ann. Math. Stat. 1943, 14, 333–362. [Google Scholar] [CrossRef]
- Deville, J.C.; Särndal, C.E. Calibration estimators in survey sampling. J. Am. Stat. Assoc. 1992, 87, 376–382. [Google Scholar] [CrossRef]
- Wolter, K. Introduction to Variance Estimation, 2nd ed.; Springer: Berlin/Heidelberg, Germany, 2007. [Google Scholar]
- Larrea, C.; Torres, F.; López, N.; Rueda, M. Pueblos indíGenas, Desarrollo Humano y Discriminación en el Ecuador; Abya Yala: Quito, Ecuador, 2007. [Google Scholar]
- Chisaguano, S. La Población Indígena del Ecuador (Análisis de Estadísticas Socio-Demográficas). INEC. Available online: https://www.acnur.org/fileadmin/Documentos/Publicaciones/2009/7015.pdf (accessed on 5 May 2020).
- Araki, H. Movimientos éTnicos y Multiculturalismo en el Ecuador: Pueblos indíGenas, Afrodescendientes y Montubios. Master’s Thesis, University of Kanagawa, Kanagawa, Japan, 2012. Available online: http://klibredb.lib.kanagawa-u.ac.jp/dspace/handle/10487/12164 (accessed on 5 May 2020).
- Uquillas, J.; Carrasco, T.; Rees, M. Exclusión Social y Estrategias de vida de los indíGenas Urbanos en Perú; Banco Mundial: Quito, Ecuador, 2003. [Google Scholar]
- Mullo, H.S.; Sánchez-Borrego, I.; Pasadas, S. Respondent-driven sampling for surveying ethnic minority in Ecuador. Manuscript in preparation.
Estimators | ||||
---|---|---|---|---|
Scenario 1 | 1.4953 | 0.8158 | 1.5055 | 0.8065 |
Scenario 2 | 1.7857 | 1.0906 | 1.7897 | 1.0782 |
Scenario 3 | 1.2745 | 0.6516 | 1.2924 | 0.6447 |
Estimators | ||||
---|---|---|---|---|
Scenario 1 | 0.4738 | 0.1262 | 0.4786 | 0.1245 |
Scenario 2 | 0.8656 | 0.3347 | 0.8628 | 0.3304 |
Scenario 3 | 0.1889 | 0.0244 | 0.2003 | 0.0242 |
−5.671021 | 0.8551362 | −7.147357 | 0.5216048 |
6.1371 | 0.4460 | 4.9065 | 0.2407 |
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Sánchez-Borrego, I.; Rueda, M.d.M.; Mullo, H. Estimation of Non-Linear Parameters with Data Collected Using Respondent-Driven Sampling. Mathematics 2020, 8, 1315. https://doi.org/10.3390/math8081315
Sánchez-Borrego I, Rueda MdM, Mullo H. Estimation of Non-Linear Parameters with Data Collected Using Respondent-Driven Sampling. Mathematics. 2020; 8(8):1315. https://doi.org/10.3390/math8081315
Chicago/Turabian StyleSánchez-Borrego, Ismael, María del Mar Rueda, and Héctor Mullo. 2020. "Estimation of Non-Linear Parameters with Data Collected Using Respondent-Driven Sampling" Mathematics 8, no. 8: 1315. https://doi.org/10.3390/math8081315