@article{e31a9fc3067e4b338a351570dd3baff9,

title = "Estimating the size of an average personal network and of an event subpopulation: Some empirical results",

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.",

author = "{Russell Bernard}, H. and Johnsen, {Eugene C.} and Killworth, {Peter D.} and Scott Robinson",

note = "Funding Information: 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 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 de1 Carmen Costa, Alejandro Casteneira, Yolanda Hernandez France, Patricia Meade, and Miguel Angel Riva-Palacio for their conscientious efforts in the collection of the data analyzed in this paper. Address all correspondence and reprint requests to Eugene C. Johnsen at the Department of Mathematics, University of California, Santa Barbara, CA 93106.",

year = "1991",

month = jun,

doi = "10.1016/0049-089X(91)90012-R",

language = "English (US)",

volume = "20",

pages = "109--121",

journal = "Social Science Research",

issn = "0049-089X",

publisher = "Academic Press Inc.",

number = "2",

}