Survey-Based Estimation of Probe Group Sizes in the Network Scale-up Method: A Case Study from Jordan

Abstract

Estimating the size of marginalized populations is a persistent challenge in survey statistics and public health, especially where stigma and legal restrictions exclude such groups from census and administrative data. Migrant domestic workers in Jordan represent one such population. We employ the Network Scale-up Method using the direct probe group method, estimating probe group sizes from survey respondents' own membership rather than relying on external counts. Using data from a nationally representative household survey in Jordan, we combine the direct probe group method with Bayesian logistic mixed-effects models to stabilize small-area estimates at the Governorate level. We validate the method against census data, demonstrating that direct probe group estimates yield reliable inference and provide a practical alternative where known probe group sizes are unavailable. Our results highlight regional variation in social network size and connectivity to migrant domestic workers. We argue that the direct probe group method is more likely to satisfy the conditions required for unbiased estimation than relying on official record sizes. This work provides the first systematic validation of the direct probe group method in a small-area setting and offers guidance for adapting the Network Scale-up Method to surveys with limited sample sizes.