Statistics and Its Interface

Volume 11 (2018)

Number 3

A note on estimating network dependence in a discrete choice model

Pages: 433 – 439



Jing Zhou (School of Statistics, Renmin University of China, Beijing, China)

Da Huang (School of Management, Fudan University, Shanghai, China)

Hansheng Wang (Guanghua School of Management, Peking University, Beijing, China)


Discrete choice model is probably one of the most popularly used statistical methods in practice. The common feature of this model is that it considers the behavioral factors of a person and the assumption of independent individuals. However, this widely accepted assumption seems problematic because human beings do not live in isolation. They interact with each other and form complex networks. Then the application of discrete choice model to network data will allow for network dependence in a general framework. In this paper, we focus on a discrete choice model with probit error which is specified as a latent spatial autoregressive model (SAR). This model could be viewed as a natural extension of the classical SAR model. The key difference is that the network dependence is latent and unobservable. Instead, it could be measured by a binary response variable. Parameter estimation then becomes a challenging task due to the complicated objective function. Following the idea of composite likelihood, an approximated paired maximum likelihood estimator (APMLE) is developed. Numerical studies are carried out to assess the finite sample performance of the proposed estimator. Finally a real dataset of Sina Weibo is analyzed for illustration purpose.


approximated paired maximum likelihood estimation, discrete choice model, social network, spatial auto-correlation

2010 Mathematics Subject Classification


Jing Zhou is supported in part by the National Natural Science Foundation of China (Grant No. 71702185), the fund for building world-class universities (disciplines) of Renmin University of China.

Da Huang is supported in part by China Statistical Research (CSR, 2015LY77), the Youth Innovation Team Project for Arts and Social Science of Fudan University, and the National Natural Science Foundation of China (NSFC, 71531006, 11571080, 11571081, 71672042).

Hansheng Wang is supported in part by the National Natural Science Foundation of China (Grant No. 71532001, 11525101), China’s National Key Research Special Program (Grant No. 2016YFC0207700), and the Center for Statistical Science at Peking University.

Received 21 December 2016

Published 17 September 2018