Comparing the Robustness of Simple Network Scale-Up Method Estimators

The network scale-up method (NSUM) is a cost-effective approach to estimating the size or prevalence of a group of people that is hard to reach through a standard survey. The basic NSUM involves two steps: estimating respondents’ degrees and estimating the prevalence of the hard-to-reach population of interest using respondents’ estimated degrees and the number of people they report knowing in the hard-to-reach group. Each of these two steps involves taking either an average of ratios or a ratio of averages. Using the ratio of averages for each step has so far been the most common approach. However, the authors present theoretical arguments that using the average of ratios at the second, prevalence-estimation step often has lower mean squared error when the random mixing assumption is violated, which seems likely in practice; this estimator was proposed early in NSUM development but has largely been unexplored and unused. Simulation results using an example network data set also support these findings. On the basis of this theoretical and empirical evidence, the authors suggest that future surveys that use a simple estimator may want to use this mixed estimator, and estimation methods based on this estimator may produce new improvements.