A Latent Variable Model for Individual Degree Measures in Respondent-Driven Sampling

Respondent-driven sampling (RDS) is widely used to collect data from hidden populations in social and biomedical science. Although RDS may provide comprehensive coverage of the target hidden population through social network recruitment, its non-random sampling process poses challenges for generalizing findings beyond the sample. Current analytical methods rely on the network size (degree) reported by respondents to adjust for unequal sampling probabilities. However, the accuracy of the reported degree is questionable due to reporting errors, evidenced through an unusual frequency of multiples of five and improbably large values. To address this measurement error, we leverage a byproduct of the RDS process (e.g., respondents' recruitment patterns) and develop a novel degree estimator based on a latent variable model of the true degree that accounts for response errors via a reporting mechanism and incorporates recruitment information and external demographic profiles. The effectiveness of the proposed method is demonstrated through a case study and a simulation study, which shows accurate and reliable degree estimates leading to significant improvements in population parameter estimation.