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# Handbook of Choice Modelling

## Edited by Stephane Hess and Andrew Daly

Choice modelling is an increasingly important technique for forecasting and valuation, with applications in fields such as transportation, health and environmental economics. For this reason it has attracted attention from leading academics and practitioners and methods have advanced substantially in recent years. This Handbook, composed of contributions from senior figures in the field, summarises the essential analytical techniques and discusses the key current research issues. It will be of interest to academics, students and practitioners in a wide range of areas.

# Chapter 19: Multiple discrete-continuous choice models: a reflective analysis and a prospective view

## Chandra Bhat and Abdul Pinjari

Subjects: economics and finance, environmental economics, transport, environment, environmental economics, transport, urban and regional studies, transport

## Extract

Several consumer choices are characterized by a discrete dimension as well as a continuous dimension. Examples of such choice situations include vehicle-type holdings and usage, appliance choice and energy consumption, housing tenure (rent or purchase) and square footage, brand choice and quantity, and activity-type choice and duration of time investment of participation. Two broad model structures may be identified in the literature to handle such discrete-continuous choice situations. The first structure (sometimes referred to as the ‘reduced-form’ structure) has a separate equation for the discrete choice and another separate equation for the continuous choice, with jointness introduced through the statistical correlation in the random stochastic components of each equation. That is, a discrete choice model and a continuous regression model are specified separately, and then simply statistically stitched together through the stochastic terms. This first structure has seen extensive use and has proved useful to handle many empirical situations, but it is not based off an underlying (and unifying) theoretical economic model (this structure does not include the class of indirect utility function-based models that are consistent with utility maximization, as discussed in the next section). The second structure to discrete-continuous choice modeling, and the one of interest in this chapter, originates from the classical microeconomic theory of utility maximization.