ABSTRACT
Many transportation data analyses deal with discrete data that are ordered. Examples include situations where respondents are asked for quantitative ratings (e.g., on a scale from 1 to 10, rate the following), ordered opinions (e.g., do you disagree, are neutral, or agree), or categorical frequency data (e.g., property damage only crash, injury crash, and fatal crash). While these response data are discrete, the application of standard discrete outcome modeling approaches does not account for the ordinal nature of the discrete data and thus the ordering information is lost. It has been shown that using standard discrete outcome modeling approaches to model ordered data results in a loss of model parameter estimation efficiency. To address the problem of ordered discrete data, ordered probability models (the ordered probit model and the ordered probit model with random effects) have been developed over the years. This chapter presents ordered probability models and discusses their various strengths and weaknesses. Examples are provided to demonstrate the application of such models in different data contexts. Overall, the chapter shows the potential applications of ordered probability models in the analysis of current and future transportation data.
