Estimating unknown populations from informant reports using scale-up reference groups and capture-recapture inference

The network scale-up method has long been used to estimate the size of hard-to-reach populations by leveraging the fact that individuals often know members of these groups. By sampling from a frame population and asking respondents how many people they know in both the target group and a reference group of known size, researchers can infer the size of the hidden population. This approach relies on the assumption that, on average, members of both groups are equally likely to be reported by respondents. However, estimating the average visibility of a hard-to-count group can be particularly challenging. An alternative approach adapts the capture-recapture method, originally developed for wildlife populations, to informant reports. Yet, such estimates depend on strong and often questionable assumptions about the probabilities of capture and recapture. In this paper, we introduce a method that calibrates scale-up estimates using the frequencies of “recapture.” This method can also be seen as calibrating capture-recapture estimates using reference groups from the scale-up approach. Our method assumes that the distributions of the number of reports per group member are similarly shaped for both the target and reference groups—specifically, that the ratio of the variance to the square of the mean is approximately equal across groups—even when the target group’s mean and full distribution remain unknown. We propose that this approach is particularly well-suited when the target group resembles a reference group but differs in its overall “visibility” to informants, whether due to stigma, social concealment, or varying degrees of prominence. We demonstrate the utility of this method using Facebook friends of upperclassmen to estimate the size of the freshman population at 100 universities. We examine the conditions under which our approach is most effective and identify key issues that warrant further theoretical and empirical investigation. • Scale-up estimates of population size rely on questionable exogenous information. • Multiple reports about the same people calibrate estimates without extra information. • An estimation method using joint-referrals is presented and demonstrated.