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Open AccessArticle

Inferring the Population Mean with Second-Order Information in Online Social Networks

by Saran Chen 1, Xin Lu 1,2,3,4,*, Zhong Liu 1 and Zhongwei Jia 5
1
College of Systems Engineering, National University of Defense Technology, Changsha 410073, China
2
School of Business, Central South University, Changsha 410083, China
3
School of Mathematics and Big Data, Foshan University, Foshan 528000, China
4
Department of Public Health Sciences, Karolinska Institutet, 17177 Stockholm, Sweden
5
National Institute of Drug Dependence, Health Science Center, Peking University, Beijing 100191, China
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(6), 480; https://doi.org/10.3390/e20060480
Received: 12 May 2018 / Revised: 16 June 2018 / Accepted: 17 June 2018 / Published: 20 June 2018
(This article belongs to the Special Issue Research Frontier in Chaos Theory and Complex Networks)
With the increasing use of online social networking platforms, online surveys are widely used in many fields, e.g., public health, business and sociology, to collect samples and to infer the population characteristics through self-reported data of respondents. Although the online surveys can protect the privacy of respondents, self-reporting is challenged by a low response rate and unreliable answers when the survey contains sensitive questions, such as drug use, sexual behaviors, abortion or criminal activity. To overcome this limitation, this paper develops an approach that collects the second-order information of the respondents, i.e., asking them about the characteristics of their friends, instead of asking the respondents’ own characteristics directly. Then, we generate the inference about the population variable with the Hansen-Hurwitz estimator for the two classic sampling strategies (simple random sampling or random walk-based sampling). The method is evaluated by simulations on both artificial and real-world networks. Results show that the method is able to generate population estimates with high accuracy without knowing the respondents’ own characteristics, and the biases of estimates under various settings are relatively small and are within acceptable limits. The new method offers an alternative way for implementing surveys online and is expected to be able to collect more reliable data with improved population inference on sensitive variables. View Full-Text
Keywords: population mean inference; second-order information; online surveys; sensitive variable population mean inference; second-order information; online surveys; sensitive variable
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Chen, S.; Lu, X.; Liu, Z.; Jia, Z. Inferring the Population Mean with Second-Order Information in Online Social Networks. Entropy 2018, 20, 480.

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