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. / text

Recent research suggests that, besides traditional socio-demographic and built environment attributes, the attitudes and perceptions of parents toward walking and bicycling play a crucial role in deciding their children’s mode choice to school. However, very little is known about the factors that shape these parental attitudes toward their children actively commuting to school. The current study aims to investigate this unexplored avenue of research and identify the influences on parental attitudes toward their children walking and bicycling to school, as part of a larger nationwide effort to make children more physically active and combat rising trends of childhood obesity in the US. Through the use of a multivariate ordered response model (a model structure that allows different attitudes to be correlated), the current study analyses five different parental attitudes toward their children walking and bicycling to school, based on data drawn from the California add-on sample of the 2009 National Household Travel Survey. In particular, the subsample from the Los Angeles – Riverside – Orange County area is used in this study to take advantage of a rich set of micro-accessibility measures that is available for this region. It is found that school accessibility, work patterns, current mode use in the household, and socio-demographic characteristics shape parental attitudes toward children walking and bicycling to school. The study findings provide insights on policies, strategies, and campaigns that may help shift parental attitudes to be more favourable toward their children walking and bicycling to school. / text