# Survey Methodology Combining link-tracing sampling and cluster sampling to estimate the size of a hidden population in presence of heterogeneous link-probabilitiesSurvey Methodology Combining link-tracing sampling and cluster sampling to estimate the size of a hidden population in presence of heterogeneous link-probabilities

by Martín H. Félix-Medina, Pedro E. Monjardin and Aida N. Aceves-CastroNote 1

• Release date: December 17, 2015

## Abstract

Félix-Medina and Thompson (2004) proposed a variant of link-tracing sampling to sample hidden and/or hard-to-detect human populations such as drug users and sex workers. In their variant, an initial sample of venues is selected and the people found in the sampled venues are asked to name other members of the population to be included in the sample. Those authors derived maximum likelihood estimators of the population size under the assumption that the probability that a person is named by another in a sampled venue (link-probability) does not depend on the named person (homogeneity assumption). In this work we extend their research to the case of heterogeneous link-probabilities and derive unconditional and conditional maximum likelihood estimators of the population size. We also propose profile likelihood and bootstrap confidence intervals for the size of the population. The results of simulations studies carried out by us show that in presence of heterogeneous link-probabilities the proposed estimators perform reasonably well provided that relatively large sampling fractions, say larger than 0.5, be used, whereas the estimators derived under the homogeneity assumption perform badly. The outcomes also show that the proposed confidence intervals are not very robust to deviations from the assumed models.

Key Words: Bootstrap; Capture-recapture; Chain referral sampling; Maximum likelihood estimator; Profile likelihood confidence interval; Snowball sampling.

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