The Better Simple Network Scale-Up Model (NSUM) Estimator Is the Average of Ratios, Not the Ratio of Averages

• Activity Number: 427 - Intelligent Systems and Decision Support
• Type: Contributed
• Date/Time: Wednesday, August 10, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): Jessica P Kunke* and Tyler McCormick and Ian Laga and Xiaoyue Niu
• Companies: University of Washington and University of Washington and Penn State University and The Pennsylvania State University
• Keywords: Network scale-up models (NSUM); Size estimation; Hidden populations; Aggregated relational data (ARD)

Abstract

Network scale-up model (NSUM) estimators were developed as a cost-effective method for estimating the size of a “hidden” subpopulation that is hard to reach through a standard survey. The two most basic NSUM estimators are the ratio of average response to average degree (the MLE) and the average of individual response-degree ratios (the PIMLE). The binomial model from which both estimators are derived relies on a strong assumption, the constant proportion assumption, which is known to be nonnegligibly violated in practice. Various models have been proposed to relax this assumption but they are more complex, require additional data, and are not always feasible; hence many surveys continue to use the simple estimators. The conventional wisdom holds that the MLE is the better estimator of the two; under the binomial model, both the MLE and PIMLE are unbiased and the MLE has lower variance than the PIMLE. However, we provide theoretical and empirical results demonstrating that even under fairly mild violations of the constant proportion assumption, the bias and MSE are lower for the PIMLE.