Electronic Journal of Statistics

Unequal edge inclusion probabilities in link-tracing network sampling with implications for Respondent-Driven Sampling

Miles Q. Ott and Krista J. Gile

Full-text: Open access

Enhanced PDF (1114 KB)

Abstract

Respondent-Driven Sampling (RDS) is a widely adopted link-tracing sampling design used to draw valid statistical inference from samples of populations for which there is no available sampling frame. RDS estimators rely upon the assumption that each edge (representing a relationship between two individuals) in the underlying network has an equal probability of being sampled. We show that this assumption is violated in even the simplest cases, and that RDS estimators are sensitive to the violation of this assumption.

Article information

Source
Electron. J. Statist. Volume 10, Number 1 (2016), 1109-1132.

Dates
Received: June 2015
First available in Project Euclid: 29 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1461947420

Digital Object Identifier
doi:10.1214/16-EJS1138

Mathematical Reviews number (MathSciNet)
MR3492037

Zentralblatt MATH identifier
1335.62029

Keywords
Respondent-driven sampling link tracing network sampling edge inclusion random walk

Citation

Ott, Miles Q.; Gile, Krista J. Unequal edge inclusion probabilities in link-tracing network sampling with implications for Respondent-Driven Sampling. Electron. J. Statist. 10 (2016), no. 1, 1109--1132. doi:10.1214/16-EJS1138. https://projecteuclid.org/euclid.ejs/1461947420


Export citation

References

  • [1] Dhar, D. (1978). Self-avoiding random walks: Some exactly soluble cases., Journal of Mathematical Physics, 19:5–11.
  • [2] Domb, C. (2009). Self avoiding walks on lattices., Stochastic Processes in Chemical Physics, 15:229–259.
  • [3] Gile, K. J. (2011). Improved inference for respondent-driven sampling data with application to hiv prevalence estimation., Journal of the American Statistical Association, 106:135–146.
    Mathematical Reviews (MathSciNet): MR2816708
    Digital Object Identifier: doi:10.1198/jasa.2011.ap09475
  • [4] Gile, K. J. and Handcock, M. S. (2010). Respondent-driven sampling: An assessment of current methodology., Sociological Methodology, 40:285–327.
    Mathematical Reviews (MathSciNet): MR2758082
    Digital Object Identifier: doi:10.1214/08-AOAS221
    Project Euclid: euclid.aoas/1273584445
  • [5] Gile, K. J. and Handcock, M. S. (2011). Network model-assisted inference from respondent-driven sampling data., ArXiv e-prints.
    Mathematical Reviews (MathSciNet): MR3348351
    Digital Object Identifier: doi:10.1111/rssa.12091
  • [6] Gobel, F. and Jagers, A. (1974). Random walks on graphs., Stochastic Processes and Their Applications, 2:311–336.
    Mathematical Reviews (MathSciNet): MR397887
    Digital Object Identifier: doi:10.1016/0304-4149(74)90001-5
  • [7] Goodman, L. A. (1961). Snowball sampling., Annals of Mathematical Statistics, 32:148–170.
    Mathematical Reviews (MathSciNet): MR124140
    Digital Object Identifier: doi:10.1214/aoms/1177705148
    Project Euclid: euclid.aoms/1177705148
  • [8] Handcock, M. S. and Gile, K. (2011). Comment: On the concept of snowball sampling., Social Methodology, 41:367–371.
  • [9] Heckathorn, D. D. (1997). Respondent-driven sampling: A new approach to the study of hidden populations., Social Problems, 44(2):pp. 174–199.
  • [10] Heckathorn, D. D. (2002). Respondent-driven sampling ii: Deriving valid population estimates from chain referral samples of hidden populations., Social Problems, 49:11–34.
  • [11] Horvitz, D. G. and Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe., Journal of the American Statistical Association, 47(260):663–685.
    Mathematical Reviews (MathSciNet): MR53460
    Digital Object Identifier: doi:10.1080/01621459.1952.10483446
  • [12] Johnston, L. G., Malekinejad, M., Kendall, C., Iuppa, I. M., and Rutherford, G. W. (2008). Implementation challenges to using respondent-driven sampling methodology for hiv biological and behavioral surveillance: Field experiences in international settings., AIDS Behav, 12(4 Suppl):S131–S141.
  • [13] Lovász, L. (1993). Random walks on graphs: A survey., Combinatorics, 2:1–46.
  • [14] Lu, X., Bengtsson, L., Britton, T., Camitz, M., Kim, B., Thorson, A., and Liljeros, F. (2012). The sensistivity of respondent-driven sampling., JRSS:A, 175:191–216.
    Mathematical Reviews (MathSciNet): MR2873802
    Digital Object Identifier: doi:10.1111/j.1467-985X.2011.00711.x
  • [15] Magnani, R., Sabin, K., Saidel, T., and Heckathorn, D. (2005). Review of sampling hard-to-reach and hidden populations for hiv surveillance., AIDS, 19 Suppl 2:S67–S72.
  • [16] Malekinejad, M., Johnston, L. G., Kendall, C., Kerr, L. R. F. S., Rifkin, M. R., and Rutherford, G. W. (2008). Using respondent-driven sampling methodology for hiv biological and behavioral surveillance in international settings: A systematic review., AIDS Behav, 12(4 Suppl):S105–S130.
  • [17] Potterat, J. (2004)., Network Epidemiology: A Handbook for Survey Design and Data Collection, chapter Network Dynamism: History and Lessons of the Colorado Springs Study, pages 87–114. Oxford University Press.
  • [18] Salganik, M. J. and Heckathorn, D. D. (2004). Sampling and estimation in hidden populations using respondent-driven sampling., Sociological Methodology, 34:pp. 193–239.
  • [19] Thompson, S. K. (2002)., Sampling. Wiley.
    Mathematical Reviews (MathSciNet): MR1891249
  • [20] Thompson, S. K. (2006). Targeted random walk designs., Survey Methodology, 32:11–24.
  • [21] Tomas, A. and Gile, K. J. (2011). The effect of differential recruitment, non-response and non-recruitment on estimators for respondent-driven sampling., Electonic Journal of Statistics, 5:899–934.
    Mathematical Reviews (MathSciNet): MR2831520
    Digital Object Identifier: doi:10.1214/11-EJS630
    Project Euclid: euclid.ejs/1314018119
  • [22] Volz, E. and Heckathorn, D. D. (2008). Probability based estimation theory for respondent driven sampling., Journal of Official Statistics, 24:79–97.
  • [23] Volz, E., Wejnert, C., Cameron, C., Spiller, M., Barash, V., Degani, I., and Heckathorn, D. (2012). Respondent-driven sampling analysis tool (rdsat). Version, 7.1.
  • [24] Zachary, W. (1977). An information flow model for conflict and fission in small groups., Journal of Anthropological Research, 33:452–473.

The Institute of Mathematical Statistics and the Bernoulli Society

Electronic Journal of Statistics

New content alerts

Email RSS ToC RSS Article
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more