On the estimation and application of flexible unordered spatial discrete choice models
Unordered choice models are commonly used in the field of transportation and several other fields to analyze discrete choice behavior. In the past decade, there have been substantial advances in specifying and estimating such models to allow unobserved taste variations and flexible error covariance structures. However, the current estimation methods are still computationally intensive and often break down when spatial dependence structures are introduced (due to the resulting high dimensionality of integration in the likelihood function). But a recently proposed method, the Maximum Approximate Composite Marginal Likelihood (MACML) method, offers an effective approach to estimate such models. The MACML approach combines a composite marginal likelihood (CML) estimation approach with an approximation method to evaluate the multivariate standard normal cumulative distribution (MVNCD) function. The composite likelihood approach replaces the likelihood function with a surrogate likelihood function of substantially lower dimensionality, which is then subsequently evaluated using an analytic approximation method rather than simulation techniques. This combination of the CML with the specific analytic approximation for the MVNCD function is effective because it involves only univariate and bivariate cumulative normal distribution function evaluations, regardless of the dimensionality of the problem. For my dissertation, I have four objectives. The first is to evaluate the performance of the MACML method to estimate unordered response models by undertaking a Monte Carlo simulation exercise. The second is to formulate and estimate a spatial and temporal unordered discrete choice model and apply this model to a land use change context and to the mode choice decision of school children. The third objective is to formulate a random coefficient model with non-normal mixing distributions on model parameters which can be estimated using the MACML approach. Finally, the fourth objective us to propose an improvement to the MACML method by incorporating a second order MVNCD function that is more accurate and evaluate its performance in estimating parameters for a variety of model structures.