  Respondent-driven sampling (RDS) is a link-tracing procedure for surveying
hidden or hard-to-reach populations in which subjects recruit other subjects
via their social network. There is significant research interest in detecting
clustering or dependence of epidemiological traits in networks, but researchers
disagree about whether data from RDS studies can reveal it. Two distinct
mechanisms account for dependence in traits of recruiters and recruitees in an
RDS study: homophily, the tendency for individuals to share social ties with
others exhibiting similar characteristics, and preferential recruitment, in
which recruiters do not recruit uniformly at random from their available
alters. The different effects of network homophily and preferential recruitment
in RDS studies have been a source of confusion in methodological research on
RDS, and in empirical studies of the social context of health risk in hidden
populations. In this paper, we give rigorous definitions of homophily and
preferential recruitment and show that neither can be measured precisely in
general RDS studies. We derive nonparametric identification regions for
homophily and preferential recruitment and show that these parameters are not
point identified unless the network takes a degenerate form. The results
indicate that claims of homophily or recruitment bias measured from empirical
RDS studies may not be credible. We apply our identification results to a study
involving both a network census and RDS on a population of injection drug users
in Hartford, CT.
