Model-assisted design-based estimation of parameters of a hidden population from a snowball sample

Thomas M. Menino Convention & Exhibition Center 

We present design-based Horvitz-Thompson and Multiplicity estimators of the size, total and mean of a response variable associated with the elements of a hidden population, such as drug users, to be used with the link-tracing sampling variant proposed by Félix-Medina and Thompson (Jour. Official Stat., 2004). In this sampling variant a frame of venues where the elements of the population tend to gather is constructed. The frame does not need to cover the whole population. An initial sample of venues is selected and people in those sites are asked to name other members of the population. Since the computation of the design-based estimators require to know the number of venues in the frame that are linked to each sampled person and this information is not observable, we consider a Bayesian model for the distribution of those numbers which allows us to estimate them by means of a Metropolis-Hastings within Gibbs sampling procedure and consequently to compute the design-based estimators. Inference about the parameters of interest is carried out under the design-based approach. The results of a numerical study indicate that the performance of the proposed estimators is acceptable.

Bayesian inference

Design-based inference

Hard-to-detect population

Hidden-population

Markov-Chain Monte Carlo

Snowball sampling 

Survey Research Methods Section