Targeted random walk designs - ARCHIVED

Hidden human populations, the Internet, and other networked structures conceptualized mathematically as graphs are inherently hard to sample by conventional means, and the most effective study designs usually involve procedures that select the sample by adaptively following links from one node to another. Sample data obtained in such studies are generally not representative at face value of the larger population of interest. However, a number of design and model based methods are now available for effective inference from such samples. The design based methods have the advantage that they do not depend on an assumed population model, but do depend for their validity on the design being implemented in a controlled and known way, which can be difficult or impossible in practice. The model based methods allow greater flexibly in the design, but depend on modeling of the population using stochastic graph models and also depend on the design being ignorable or of known form so that it can be included in the likelihood or Bayes equations. For both the design and the model based methods, the weak point often is the lack of control in how the initial sample is obtained, from which link-tracing commences. The designs described in this paper offer a third way, in which the sample selection probabilities become step by step less dependent on the initial sample selection. A Markov chain "random walk" model idealizes the natural design tendencies of a link-tracing selection sequence through a graph. This paper introduces uniform and targeted walk designs in which the random walk is nudged at each step to produce a design with the desired stationary probabilities. A sample is thus obtained that in important respects is representative at face value of the larger population of interest, or that requires only simple weighting factors to make it so.