Random Walks on directed networks: Inference and respondent-driven sampling

Jens Malmros*, Naoki Masuda, Tom Britton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Respondent-driven sampling (RDS) is often used to estimate population properties (e.g., sexual risk behavior) in hard-to-reach populations. In RDS, already sampled individuals recruit population members to the sample from their social contacts in an efficient snowballlike sampling procedure. By assuming a Markov model for the recruitment of individuals, asymptotically unbiased estimates of population characteristics can be obtained. Current RDS estimation methodology assumes that the social network is undirected, that is, all edges are reciprocal. However, empirical social networks in general also include a substantial number of nonreciprocal edges. In this article, we develop an estimation method for RDS in populations connected by social networks that include reciprocal and nonreciprocal edges. We derive estimators of the selection probabilities of individuals as a function of the number of outgoing edges of sampled individuals. The proposed estimators are evaluated on artificial and empirical networks and are shown to generally perform better than existing estimators. This is the case in particular when the fraction of directed edges in the network is large.

Original languageEnglish
Pages (from-to)433-459
Number of pages27
JournalJournal of Official Statistics
Issue number2
Publication statusPublished - 2016 Jun
Externally publishedYes


  • Hidden population
  • Markov model
  • Nonreciprocal relationship
  • Social network

ASJC Scopus subject areas

  • Statistics and Probability


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