Estimating Spatial Autocorrelation with Sampled Network Data

26 Pages Posted: 26 Feb 2016

See all articles by Jing Zhou

Jing Zhou

Renmin University of China

Yundong Tu

Peking University

Yuxin Chen

New York University (NYU) - New York University (NYU), Shanghai

Hansheng Wang

Peking University - Guanghua School of Management

Date Written: June 8, 2015

Abstract

Spatial autocorrelation is a parameter of importance for network data analysis. To estimate spatial autocorrelation, maximum likelihood has been popularly used. However, its rigorous implementation requires the whole network to be observed. This is practically infeasible if network size is huge (e.g., Facebook, Twitter, Weibo, WeChat, etc). In that case, one has to rely on sampled network data to infer about spatial autocorrelation. By doing so, network relationships (i.e., edges) involving unsampled nodes are overlooked. This leads to distorted network structure and underestimated spatial autocorrelation. To solve the problem, we propose here a novel solution. By temporarily assuming that the spatial autocorrelation is small, we are able to approximate the likelihood function by its first order Taylor's expansion. This leads to the method of approximate maximum likelihood estimator (AMLE), which further inspires the development of paired maximum likelihood estimator (PMLE). Compared with AMLE, PMLE is computationally superior and thus is particularly useful for large scale network data analysis. Under appropriate regularity conditions (without assuming a small spatial autocorrelation), we show theoretically that PMLE is consistent and asymptotically normal. Numerical studies based on both simulated and real datasets are presented for illustration purpose.

Keywords: Approximate Maximum Likelihood Estimator; Network Data Analysis; Paired Maximum Likelihood Estimator; Spatial Autocorrelation

JEL Classification: C3

Suggested Citation

Zhou, Jing and Tu, Yundong and Chen, Yuxin and Wang, Hansheng, Estimating Spatial Autocorrelation with Sampled Network Data (June 8, 2015). Available at SSRN: https://ssrn.com/abstract=2737691 or http://dx.doi.org/10.2139/ssrn.2737691

Jing Zhou

Renmin University of China ( email )

No. 59 Zhongguancun Road
Haidian District
Beijing, Beijing 100871
China

Yundong Tu

Peking University ( email )

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

Yuxin Chen

New York University (NYU) - New York University (NYU), Shanghai ( email )

1555 Century Ave
Shanghai, Shanghai 200122
China

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

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