Discrete choice modeling with interdependencies : a spatial binary probit model with endogenous weight matrix

Abstract

Many transportation phenomena involve making discrete choices with interdependencies. For example, a traveler may choose to make a trip or not (binary), travel frequency (ranked integers), and different travel modes (multi-categorical). The interdependencies refer to the situation where decision makers' behaviors influence each other. The interdependency may be caused by geographic proximity, economic interactions, or social connections between decision makers. A spatial econometric model can be established to address such interdependencies by using a weight matrix, where the element in the matrix is defined based on geographic distance or socioeconomic distance between pairs of decision makers. Traditionally, the weight matrix is treated as exogenous. This assumption is inappropriate in contexts where the interdependency structure is correlated with the final response variable. In reality, however, such correlation often occurs. For example, residents' decisions on residential locations may influence their social network in return. Carriers' travel behavior decisions may reshape their economic interactions with their peers. In such cases, the exogenous weight matrix assumption will lead to biased and inconsistent parameter estimates. Dealing with endogenous weight matrix in spatial models is an important problem in spatial econometrics. However, there has been limited work on spatial models with endogenous weight matrices, and no work has been done for discrete responses with endogenous weight matrix. The goal of this dissertation is to fill this gap.

Inspired by previous studies, a spatial binary probit model with endogenous weight matrix is developed. The model consists of two parts: A spatial autoregressive (SAR) model that addresses the discrete response and an entry equation which provides entry into the weight matrix. The endogeneity is considered when these two equations are allowed to be correlated. The Bayesian Markov Chain Monte Carlo (MCMC) method is then used to estimate the parameters. Model validation is first performed using simulated data. The estimation results show that all parameters can be reliably recovered. The model is then applied to analyze carriers' toll road use behavior. The discrete response investigated is the carriers' binary response to whether or not they will pass costs to their customers when they are subject to toll increase. The weight matrix is defined by carriers' similarity in toll road usage. The entry equation is thus the mileage of toll road each carrier uses for a typical delivery. Another application is to investigate firm location choice. The results captured the interdependencies in the decision making process and identified potential influential factors. These applications demonstrate the potential of the model in investigating transportation problems, and provide valuable reference for policy makers.