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Many consumer choice situations are characterized by the simultaneous demand for multiple alternatives that are imperfect substitutes for one another. A simple and parsimonious multiple discrete-continuous extreme value (MDCEV) econometric approach to handle such multiple discreteness was formulated by Bhat (2005) within the broader Kuhn–Tucker (KT) multiple discrete-continuous economic consumer demand model of Wales and Woodland (1983). In this chapter, the focus is on presenting the basic MDCEV model structure, discussing its estimation and use in prediction, formulating extensions of the basic MDCEV structure, and presenting applications of the model. The paper examines several issues associated with the MDCEV model and other extant KT multiple discrete-continuous models. Specifically, the paper discusses the utility function form that enables clarity in the role of each parameter in the utility specification, presents identification considerations associated with both the utility functional form as well as the stochastic nature of the utility specification, extends the MDCEV model to the case of price variation across goods and to general error covariance structures, discusses the relationship between earlier KT-based multiple discrete-continuous models, and illustrates the many technical nuances and identification considerations of the multiple discrete-continuous model structure. Finally, we discuss the many applications of MDCEV model and its extensions in various fields.

To address the safety concerns generated by truck crashes occurred in big cities, this paper analyzes the zip code tabulation area (ZCTA)-based truck crash frequency across four temporal intervals – morning (6:00–10:00), mid-day (10:00–15:00), afternoon (15:00–19:00), and night (19:00–6:00) in New York City in 2010. A multivariate conditional autoregressive count model is used to recognize both spatial and temporal dependences. The results prove the presence of spatial and temporal dependencies for truck crashes that occurred in neighboring areas. Built environment attributes such as various types of business establishment density and traffic volume for different types of vehicles, which are important factors to consider for crashes occurred in an urban setting, are also examined in the study.

Mixed logit models can represent heterogeneity across individuals, in both observed and unobserved preferences, but require computationally expensive calculations to compute probabilities. A few methods for including error covariance heterogeneity in a closed form models have been proposed, and this paper adds to that collection, introducing a new form of a Network GEV model that sub-parameterizes the allocation values for the assignment of alternatives (and sub-nests) to nests. This change allows the incorporation of systematic (nonrandom) error covariance heterogeneity across individuals, while maintaining a closed form for the calculation of choice probabilities. Also explored is a latent class model of nested models, which can similarly express heterogeneity. The heterogeneous models are compared to a similar model with homogeneous covariance in a realistic scenario, and are shown to significantly outperform the homogeneous model, and the level of improvement is especially large in certain market segments. The results also suggest that the two heterogeneous models introduced herein may be functionally equivalent.

Purpose – Information collected from police crash reports has long been the primary source of data for the analysis of factors that determine the likelihood of a crash (crash frequency) and its resulting severity (measured in terms of the extent of injuries to vehicle occupants). Proper cross-sectional analyses techniques, covered in this chapter, are important for guiding safety policy and countermeasures.

Methodology – This chapter provides an overview of some of the more commonly used cross-sectional statistical and econometric methods, and discusses the nuances and their limitations with regard to how they are applied to typical crash-report data.

Findings – The wide variety of analytic methods available to safety researchers makes the selection of appropriate methods critical. This chapter provides important guidance for safety researchers in their choice of methodological approach.

Implications – Understanding the importance of proper model specification, unobserved heterogeneity, endogeneity and other factors covered in this chapter is extremely important in analysing safety data and must be given full consideration before any results are finalised.

The search for flexible models has led the simple multinomial logit model to evolve into the powerful but computationally very demanding mixed multinomial logit (MMNL) model. That flexibility search lead to discrete choice hybrid choice models (HCMs) formulations that explicitly incorporate psychological factors affecting decision making in order to enhance the behavioral representation of the choice process. It expands on standard choice models by including attitudes, opinions, and perceptions as psychometric latent variables.

In this paper we describe the classical estimation technique for a simulated maximum likelihood (SML) solution of the HCM. To show its feasibility, we apply it to data of stated personal vehicle choices made by Canadian consumers when faced with technological innovations.

We then go beyond classical methods, and estimate the HCM using a hierarchical Bayesian approach that exploits HCM Gibbs sampling considering both a probit and a MMNL discrete choice kernel. We then carry out a Monte Carlo experiment to test how the HCM Gibbs sampler works in practice. To our knowledge, this is the first practical application of HCM Bayesian estimation.

We show that although HCM joint estimation requires the evaluation of complex multi-dimensional integrals, SML can be successfully implemented. The HCM framework not only proves to be capable of introducing latent variables, but also makes it possible to tackle the problem of measurement errors in variables in a very natural way. We also show that working with Bayesian methods has the potential to break down the complexity of classical estimation.

Purpose – This chapter provides an overview of issues related to analysing crash data characterised by excess zero responses and/or long tails and how to overcome these problems. Factors affecting excess zeros and/or long tails are discussed, as well as how they can bias the results when traditional distributions or models are used. Recently introduced multi-parameter distributions and models developed specifically for such datasets are described. The chapter is intended to guide readers on how to properly analyse crash datasets with excess zeros and long or heavy tails.

Methodology – Key references from the literature are summarised and discussed, and two examples detailing how multi-parameter distributions and models compare with the negative binomial distribution and model are presented.

Findings – In the event that the characteristics of the crash dataset cannot be changed or modified, recently introduced multi-parameter distributions and models can be used efficiently to analyse datasets characterised by excess zero responses and/or long tails. They offer a simpler way to interpret the relationship between crashes and explanatory variables, while providing better statistical performance in terms of goodness-of-fit and predictive capabilities.

Research implications – Multi-parameter models are expected to become the next series of traditional distributions and models. The research on these models is still ongoing.

Practical implications – With the advancement of computing power and Bayesian simulation methods, multi-parameter models can now be easily coded and applied to analyse crash datasets characterised by excess zero responses and/or long tails.