Estimating the size of an average personal network and of an event subpopulation: Some empirical results

doi:10.1016/0049-089X(91)90012-R

Social Science Research

Volume 20, Issue 2, June 1991, Pages 109-121

https://doi.org/10.1016/0049-089X(91)90012-R Get rights and content

Abstract

A compelling problem in a population is to estimate the number of people the average person knows. A consequential related problem is to estimate the size of important subpopulations. A random sample of a population is asked whether they know anyone in a given subpopulation of size e, thus yielding an estimate of the probability that this occurs in the population. Using an equal likelihood probability model, this leads to a lower bound estimate for c, the average number of people a person in the population knows. When the number of people a person knows has a binomial distribution over the population this value is an estimate for c itself. Here we test this method on data from Mexico City, where a large random sample of people was asked whether they knew anyone in each of several different subpopulations in Mexico City of known and unknown sizes. We develop procedures for obtaining various bounds and estimates for c and determine some of the respondents' attributes on which variation in probability of knowing someone in a subpopulation and variation in personal network size seem to depend. We apply these to the estimation of e for rape victims in Mexico City and the estimation of c from data on AIDS victims in the United States.

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Estimating the size of an average personal network and of an event subpopulation

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Citation Excerpt :
The first part of the questionnaire included demographic characteristics (age, education, marital status and occupation). In the NSU, data is collected from members of the general population and, participants respond on behalf of their network rather than themselves (Russell Bernard, Johnsen, Killworth, & Robinson, 1991). The NSU assumes that the prevalence of a behavior in the network of a randomly selected sample (m/ C) can be generalized to the whole population (e/ t).
The network scale up (NSU) method is an indirect size estimation method that has received remarkable attention in estimating the sensitive behaviors. Using methadone maintenance therapy (MMT), which is a treatment for opioid use disorder, is a sensitive topic in many societies. The aim of this manuscript was to estimate the number of MMT users and its failure ratio using the NSU method in the city of Kerman, Iran, in 2016.
In this cross-sectional study, 1275 men and 1275 women which were aged >18 years and who had lived in the city of Kerman for at least 5 years were recruited via multistage sampling. Data was collected via face-to-face interviews using a questionnaire that was included questions for estimating the network size of the residents of Kerman as well as the number of MMT users and the existing failure among them.
In total, the average network size of the citizens of Kerman was 235; among them, 97 were men and 138 were women. Overall, the numbers of MMT users and failures were estimated at about 5289 and 2731, respectively, leading to a failure ratio about 52%. The treatment failure ratio in the women and men was equal to 55% and 51%, respectively. Among the men, the failure ratio in all age groups was equal to ˜50%. Among the women, the failure ratio in those who were aged <18 years was equal to 76%.
The considerable failure ratio indicates the need for conducting studies on MMT services in order to understand the reasons which exist regarding this failure. This is of particular importance in specific groups, such as in young women. Further, the comparable results with other direct methods indicate that the NSU method could be used in the size estimation of MMT failure ratios.
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^☆: Presented by invitation at the Annual Meeting of the American Statistical Association, San Francisco, CA, August 17–20, 1987, under the sponsorship of the Section on Survey Research Methods. Supported in part by NSF Grant BNS-8318132 and by a Faculty Research Grant from the Graduate School, University of Florida. We particularly thank Dr. Donald Price, Vice President for Research, University of Florida, for generous support of this research, and student researchers Maria del Carmen Costa, Alejandro Casteneira, Yolanda Hernandez Franco, Patricio Meade, and Miguel Angel Riva-Palacio for their conscientious efforts in the collection of the data analyzed in this paper.

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Estimating the size of an average personal network and of an event subpopulation: Some empirical results☆

Abstract

Social Networks

Estimating the size of an average personal network and of an event subpopulation