A note on estimating network dependence in a discrete choice model

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.